techniques used for problem solving and decision making

What is Problem Solving? (Steps, Techniques, Examples)

By Status.net Editorial Team on May 7, 2023 — 5 minutes to read

What Is Problem Solving?

Definition and importance.

Problem solving is the process of finding solutions to obstacles or challenges you encounter in your life or work. It is a crucial skill that allows you to tackle complex situations, adapt to changes, and overcome difficulties with ease. Mastering this ability will contribute to both your personal and professional growth, leading to more successful outcomes and better decision-making.

Problem-Solving Steps

The problem-solving process typically includes the following steps:

Identify the issue : Recognize the problem that needs to be solved.
Analyze the situation : Examine the issue in depth, gather all relevant information, and consider any limitations or constraints that may be present.
Generate potential solutions : Brainstorm a list of possible solutions to the issue, without immediately judging or evaluating them.
Evaluate options : Weigh the pros and cons of each potential solution, considering factors such as feasibility, effectiveness, and potential risks.
Select the best solution : Choose the option that best addresses the problem and aligns with your objectives.
Implement the solution : Put the selected solution into action and monitor the results to ensure it resolves the issue.
Review and learn : Reflect on the problem-solving process, identify any improvements or adjustments that can be made, and apply these learnings to future situations.

Defining the Problem

To start tackling a problem, first, identify and understand it. Analyzing the issue thoroughly helps to clarify its scope and nature. Ask questions to gather information and consider the problem from various angles. Some strategies to define the problem include:

Brainstorming with others
Asking the 5 Ws and 1 H (Who, What, When, Where, Why, and How)
Analyzing cause and effect
Creating a problem statement

Generating Solutions

Once the problem is clearly understood, brainstorm possible solutions. Think creatively and keep an open mind, as well as considering lessons from past experiences. Consider:

Creating a list of potential ideas to solve the problem
Grouping and categorizing similar solutions
Prioritizing potential solutions based on feasibility, cost, and resources required
Involving others to share diverse opinions and inputs

Evaluating and Selecting Solutions

Evaluate each potential solution, weighing its pros and cons. To facilitate decision-making, use techniques such as:

SWOT analysis (Strengths, Weaknesses, Opportunities, Threats)
Decision-making matrices
Pros and cons lists
Risk assessments

After evaluating, choose the most suitable solution based on effectiveness, cost, and time constraints.

Implementing and Monitoring the Solution

Implement the chosen solution and monitor its progress. Key actions include:

Communicating the solution to relevant parties
Setting timelines and milestones
Assigning tasks and responsibilities
Monitoring the solution and making adjustments as necessary
Evaluating the effectiveness of the solution after implementation

Utilize feedback from stakeholders and consider potential improvements. Remember that problem-solving is an ongoing process that can always be refined and enhanced.

Problem-Solving Techniques

During each step, you may find it helpful to utilize various problem-solving techniques, such as:

Brainstorming : A free-flowing, open-minded session where ideas are generated and listed without judgment, to encourage creativity and innovative thinking.
Root cause analysis : A method that explores the underlying causes of a problem to find the most effective solution rather than addressing superficial symptoms.
SWOT analysis : A tool used to evaluate the strengths, weaknesses, opportunities, and threats related to a problem or decision, providing a comprehensive view of the situation.
Mind mapping : A visual technique that uses diagrams to organize and connect ideas, helping to identify patterns, relationships, and possible solutions.

Brainstorming

When facing a problem, start by conducting a brainstorming session. Gather your team and encourage an open discussion where everyone contributes ideas, no matter how outlandish they may seem. This helps you:

Generate a diverse range of solutions
Encourage all team members to participate
Foster creative thinking

When brainstorming, remember to:

Reserve judgment until the session is over
Encourage wild ideas
Combine and improve upon ideas

Root Cause Analysis

For effective problem-solving, identifying the root cause of the issue at hand is crucial. Try these methods:

5 Whys : Ask “why” five times to get to the underlying cause.
Fishbone Diagram : Create a diagram representing the problem and break it down into categories of potential causes.
Pareto Analysis : Determine the few most significant causes underlying the majority of problems.

SWOT Analysis

SWOT analysis helps you examine the Strengths, Weaknesses, Opportunities, and Threats related to your problem. To perform a SWOT analysis:

List your problem’s strengths, such as relevant resources or strong partnerships.
Identify its weaknesses, such as knowledge gaps or limited resources.
Explore opportunities, like trends or new technologies, that could help solve the problem.
Recognize potential threats, like competition or regulatory barriers.

SWOT analysis aids in understanding the internal and external factors affecting the problem, which can help guide your solution.

Mind Mapping

A mind map is a visual representation of your problem and potential solutions. It enables you to organize information in a structured and intuitive manner. To create a mind map:

Write the problem in the center of a blank page.
Draw branches from the central problem to related sub-problems or contributing factors.
Add more branches to represent potential solutions or further ideas.

Mind mapping allows you to visually see connections between ideas and promotes creativity in problem-solving.

Examples of Problem Solving in Various Contexts

In the business world, you might encounter problems related to finances, operations, or communication. Applying problem-solving skills in these situations could look like:

Identifying areas of improvement in your company’s financial performance and implementing cost-saving measures
Resolving internal conflicts among team members by listening and understanding different perspectives, then proposing and negotiating solutions
Streamlining a process for better productivity by removing redundancies, automating tasks, or re-allocating resources

In educational contexts, problem-solving can be seen in various aspects, such as:

Addressing a gap in students’ understanding by employing diverse teaching methods to cater to different learning styles
Developing a strategy for successful time management to balance academic responsibilities and extracurricular activities
Seeking resources and support to provide equal opportunities for learners with special needs or disabilities

Everyday life is full of challenges that require problem-solving skills. Some examples include:

Overcoming a personal obstacle, such as improving your fitness level, by establishing achievable goals, measuring progress, and adjusting your approach accordingly
Navigating a new environment or city by researching your surroundings, asking for directions, or using technology like GPS to guide you
Dealing with a sudden change, like a change in your work schedule, by assessing the situation, identifying potential impacts, and adapting your plans to accommodate the change.
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Effective Decision Making Techniques for Every Situation

In this guide, we will explore effective decision-making techniques to help you make better decisions in various aspects of your life. Whether you’re facing personal dilemmas, professional challenges, or ethical quandaries, these techniques will provide you with the tools you need to navigate through any situation with confidence and clarity.

What is a Decision Making Technique?

A decision-making technique is a method or approach used to help people make better decisions. These techniques provide step-by-step processes or tools to consider options, weigh their pros and cons, and choose the best course of action. Examples include listing the advantages and disadvantages of each option, visualizing potential outcomes, or prioritizing based on key factors. These techniques help people make clearer, more informed decisions in different situations, like personal choices or business strategies.

6 Decision Making Techniques for Better Decisions

Here are 6 decision-making techniques that can be applied in various contexts, including personal decision-making, professional decision-making, strategic planning, problem-solving, and more. These techniques help individuals and organizations make better choices by providing structured approaches to analyze options, mitigate risks, and achieve desired outcomes.

1. Pugh Matrix

What it is : The Pugh Matrix, also known as the Decision Matrix, is a structured technique for comparing multiple alternatives against a set of criteria. It helps objectively evaluate options by assigning scores based on predefined criteria.

How to use it in decision-making :

Identify the decision to be made and the alternatives available.
Determine the criteria for evaluation, such as cost, time, quality, etc.
Assign weights to each criterion based on its importance.
Compare each alternative against the criteria and assign scores.
Calculate the total scores for each alternative to determine the best option.
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Brainstorming

What it is : Brainstorming is a creative technique used to generate a large number of ideas or solutions to a problem in a short amount of time. It encourages free thinking and idea generation without criticism.

How to use it in decision making :

Gather a group of participants with diverse backgrounds and perspectives.
Clearly define the problem or decision to be addressed.
Set a time limit and encourage participants to generate as many ideas as possible.
Record all ideas without judgment or evaluation.
After brainstorming, evaluate and refine the ideas generated to identify potential solutions.

The Heuristic Method

What it is : The heuristic method involves using practical rules or shortcuts to make decisions quickly, often in situations with limited information or time.

Identify the decision to be made and any constraints or limitations.
Use heuristics, or mental shortcuts, to simplify the decision-making process .
Examples of heuristics include the “satisficing” approach (choosing the first option that meets the minimum criteria), the “availability heuristic” (relying on readily available information), or the “anchoring and adjustment heuristic” (starting with an initial estimate and adjusting based on new information).

Tiered Voting

What it is : Tiered voting is a decision-making technique where participants vote on options in multiple rounds, with the lowest-ranking options eliminated in each round until a consensus is reached.

Present the options to be voted on to the participants.
In the first round of voting, each participant ranks the options from best to worst.
Eliminate the options with the lowest rankings and proceed to the next round of voting.
Repeat the process until only one option remains, or until a predetermined threshold for consensus is reached.

SWOT Analysis

What it is : SWOT Analysis is a strategic planning tool used to identify the Strengths, Weaknesses, Opportunities, and Threats of a decision, project, or organization.

Identify the decision or project to be analyzed.
List the internal Strengths and Weaknesses, such as resources, capabilities, or limitations.
Identify external Opportunities and Threats, such as market trends, competition, or regulatory changes.
Analyze the SWOT factors to inform decision-making and develop strategies to capitalize on strengths, address weaknesses, exploit opportunities, and mitigate threats.

Game Theory

What it is : Game Theory is a mathematical framework used to analyze decision-making in situations where the outcomes depend on the choices of multiple parties, or “players.”

Identify the decision or interaction involving multiple parties with conflicting interests.
Define the players, their available strategies, and the possible outcomes.
Use mathematical models to analyze the potential strategies and outcomes, considering factors such as payoff, risk, and utility.
Determine the optimal strategy for each player, considering the potential responses of others, to achieve the best possible outcome or equilibrium.

Scenario Planning

What it is : Scenario planning is a technique used to make decisions in the face of uncertainty about the future. It involves creating multiple plausible future scenarios and analyzing their potential impact on the decision at hand.

Identify the decision to be made and any uncertainties or future factors that could influence the outcome.
Develop multiple scenarios, each depicting a different plausible future based on various combinations of key uncertainties.
Evaluate each scenario’s potential impact on the decision, considering factors such as risks, opportunities, and challenges.
Assess the robustness of the decision under each scenario and identify strategies to mitigate risks or capitalize on opportunities.
Make the decision based on an understanding of how it would perform across different possible futures.

Priority Matrix

What it is : A Priority Matrix, also known as an Eisenhower Matrix or Urgent-Important Matrix, is a tool used to prioritize tasks or decisions based on their urgency and importance. It helps individuals or teams focus their efforts on the most critical tasks or decisions, thereby improving productivity and effectiveness.

Identify the decisions or tasks that need to be prioritized.
Create a prioritization grid with four quadrants: Urgent and Important, Important but Not Urgent, Urgent but Not Important, and Neither Urgent nor Important.
Place each decision or task into one of the quadrants based on its level of urgency and importance.
Focus on addressing tasks in the Urgent and Important quadrant first, as they require immediate attention.
Delegate or schedule tasks in the Important but Not Urgent quadrant for later action, to prevent them from becoming urgent.
Consider whether tasks in the Urgent but Not Important quadrant can be delegated or deferred, as they may distract from more critical priorities.
Minimize or eliminate tasks in the Neither Urgent nor Important quadrant, as they contribute little value to achieving goals.

Effective decision making is a skill that can be honed through practice and awareness. By understanding the decision-making process, utilizing proven decision making techniques, and adapting to different contexts, you can navigate through life’s challenges with confidence and clarity. Remember, every decision you make shapes your future, so choose wisely.

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29 Decision-making techniques for making effective decisions

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In our groups and organizations, we want to move forward and have an impact. We want to get things done, take action and change things in the world. To do that, we need to align on what we will do together, and how. In other words, we need to decide . But what decision making techniques are the most effective at making good decisions quickly and effectively?

Deciding in a group setting is not always easy! In fact, arguments over whether a decision has been taken (and it’s time to implement it) or not yet (so we are still discussing) are one of the most common sources of conflicts in a team.

In this post, we have put together a collection of 27 decision-making techniques you can facilitate to help your team make a decision together!

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What is decision-making?

Any group process follows a flow, like a story unfolding. We start with a question, a challenge, or a problem to solve. Next, we ideate and brainstorm (aka “diverge”), gathering different ideas on what to do and how to move forward. After a divergent phase comes convergence when we refine and select among different possibilities and choose a direction or solution. At some point, we need to agree that the process is over: we have a decision!* Deciding collectively is not always necessary (see this blog piece for more on decision-making rules and possibilities), but it can be a key to obtaining high levels of buy-in and enthusiasm from all. For high-stake decisions that require many people to participate in implementation, it’s important to know how to involve everyone in the process of deciding together. To be honest, the facilitation community has so far dedicated more attention to the diverging and ideation phase of this process than to the last steps, converging and deciding. That said, there are still a lot of decision making tools you can pick from to support making decisions in a group.

* A decision is not really the end point of the story, of course. Instead of “happily ever after”, we now get the job of implementing and monitoring the decision, coming back to it in a few days, months or years to see how it’s going, revise, confirm or change it.

What are the benefits of using decision-making techniques?

Trying to imagine how to reach a decision in a group without the support of facilitated activities or processes is hard indeed! By using agreed-upon tools and methods we can streamline the process, make it efficient, and distribute power in a way that makes sense for the type of decision and organisation we are in. By introducing activities and methods to support a group in weighing up the pros and cons before taking a final decision we can reap a lot of benefits.

Make sure all voices are heard

Many of these activities aim to enable the group to listen to itself, in all its components. At the 2022 Facilitation Impact Awards , co-host Shalaka Gundi reminded the assembly to “encourage the expression of all perspectives, including unconventional ones”. Complex challenges require a diversity of viewpoints and approaches; if we have ways for all voices to be heard, we have a higher chance of finding novel solutions to the challenges we face.

Pave the way for easy implementation

When people are given an opportunity to express their opinions and take part in shaping a decision, they will be more likely to support its implementation. This is a matter of “buy-in”. Offering activities for participatory decision making will reduce the effort needed later to ensure tasks get done and work goes ahead.

a wall covered in post-its with dot votes

Reduce uncertaint y

By spending time in a decision making process together, it’s easier for a team to identify potential risks in fair advance. Going through structured steps to articulate the possible consequences of a decision improves clarity. Many conflicts are avoided by clearing away potential misunderstandings at the start of the process rather than carrying them with us like dead weights.

When people claim that deciding together is a waste of time, they are probably thinking of unstructured conversations, in which participants take tangents, lose track of the topic, and ultimately agree out of sheer exhaustion. Using facilitated activities, on the other hand, can help reach convergence relatively quickly, even in a large assembly. Furthermore, in a classic paradox familiar to any facilitator, taking more time to work through a process together saves time in the long run. This might not be initially evident, and in fact is the source of much resistance to facilitated processes: they take time. Over and over again though, we see how involving stakeholders and potential users can save a lot of trouble, time and resources in the long run. An exhaustive cost-benefit analysis, for example, can help ensure more intelligent business decisions are made.

Increase trust

Through deciding together, a team grows! We learn to understand one another’s needs and concerns better, both in a personal sense and in terms of the needs of the different roles and departments. In the long run, working together towards a shared course of action increases trust and awareness in a group.

Better decisions!

What makes a decision “good”? Once the results are out, we hope to see that our decisions have been efficient, get us closer to our goals, and in a cost- or resource-effective way. Deciding on our own might be the fastest solution (and is sometimes a perfectly adequate one, see this blog article for more on why), but deciding together leads to more sustainable decisions in time.

techniques used for problem solving and decision making

The most effective decision-making techniques

Facilitation often focuses on the divergent part of a group process, brainstorming and creativity, but decision-making can be fun and effective as well!

Here are 27 decision making methods and activities that can help you learn how to decide better as a group, and make more effective decisions together in a well-managed flow.

Decision-making techniques for ranking and prioritization

Many facilitated decision-making processes go something like this: first we brainstorm options, then we vote on them, then we choose one or more to continue working on and refining. This sequence can apply, for example, to a consultation process, in which a team lead might ask the group for recommendations on actions to take in the next few months. There does not necessarily need to be “one single answer”, but an indication of interest. In another scenario, the group might be looking for a direction for a proposal. The actual proposal will be worked on by a committee or a delegate and decided upon at a later time. Today, we are looking for ideas on what to base that proposal on. These are two possible situations in which what we are looking for is not yet a decision, but a prioritization. Here are 6 decision-making tools that can help a group indicate preferences and rank alternatives.

This section is all about prioritization, and for prioritization, nothing beats dot-voting! Whether you prefer sheets of sticky dots or just giving people markers, whether you are working in the physical world or with votes online, facilitators love dot-voting! Dot-voting allows a group to clearly and quickly visualize preferences and priorities at a glance. It’s a flexible, basic tool, easy to adapt to online environments as well. There is even a mathematical formula for how many dots to assign. The formula is: N=[(T/2)xT]/P, where T=number of issues or topics, P=number of participants and N=number of dots needed for each person. Intrigued by that? Head over to this piece by John Amrhein, over at Michigan State University for a thorough explanation. Also note that it can be perfectly ok to give extra dots to the project lead or team manager, or tweak the system any other way that makes sense for your situation!

Dotmocracy #action #decision making #group prioritization #hyperisland #remote-friendly Dotmocracy is a simple method for group prioritization or decision-making. It is not an activity on its own, but a method to use in processes where prioritization or decision-making is the aim. The method supports a group to quickly see which options are most popular or relevant. The options or ideas are written on post-its and stuck up on a wall for the whole group to see. Each person votes for the options they think are the strongest, and that information is used to inform a decision.

Impact and Effort Matrix

When inviting people to prioritize, it’s very important to pay attention to the words you use in formulating a question.

Rather than using generic terms such as “vote for your favorite” or “put three dots on the idea you think is best”, take some time to consider what kind of direction you are really looking for. An inspiring version of this comes from John Croft, who suggests asking “Which of these actions, if taken first, will lead to all the others happening?”. That gives a clear sense of looking for priority in time, and speaks to unblocking resources and enabling future actions. Another useful tip is to use matrixes such as this one from the Gamestorming innovation toolkit. In this decision-making exercise, possible actions are mapped based on two factors: effort required to implement and potential impact. While this is similar to a cost benefit analysis, one bonus is that this matrix visualizes your various options as a basis for comparison and discussion.

Impact and Effort Matrix #gamestorming #decision making #action #remote-friendly In this decision-making exercise, possible actions are mapped based on two factors: effort required to implement and potential impact. Categorizing ideas along these lines is a useful technique in decision making, as it obliges contributors to balance and evaluate suggested actions before committing to them.

How-Now-Wow Matrix

The How-Now-Wow matrix follows a similar principle, but while the Impact and Effort matrix is focused on return on investment, this one is designed to select the most innovative and original plans. The X-axis denotes the originality of the idea and the Y-axis shows the ease of implementation, and the group is looking for steps forward toward the most innovative and plausible courses of action. When people want to develop new ideas, they most often think out of the box in the brainstorming or divergent phase. However, when it comes to convergence, people often end up picking ideas that are most familiar to them. This is called a ‘creative paradox’ or a ‘creadox’. T he How-Now-Wow matrix is an idea selection tool that breaks the creadox and helps the group sift through plans to select the “Wow” ones they wish to continue to work on.

How-Now-Wow Matrix #gamestorming #idea generation #remote-friendly When people want to develop new ideas, they most often think out of the box in the brainstorming or divergent phase. However, when it comes to convergence, people often end up picking ideas that are most familiar to them. This is called a ‘creative paradox’ or a ‘creadox’. The How-Now-Wow matrix is an idea selection tool that breaks the creadox by forcing people to weigh each idea on 2 parameters.

Cost Benefit #decision making #planning #strategy #gamestorming #action This game is most probably the most simple collaborative cost benefit analysis ever.It is applicable onto subjects where a group has expert knowledge about costs and/or benefits.

20/20 Vision

This team activity is useful to increase focus and alignment in a team, particularly when there are a lot of possible options, activities or campaigns on the table. In the 20/20 Vision sequence, participants are called to spell out the perceived benefits of different courses of action, then rank them by general importance. After this part, which is arguably the real value of the method, the facilitator asks the team to compare initiatives to one another in pairs. Which of these two is more important for the organisation? The question gets repeated, and discussions continue until all proposals are ranked.

20/20 Vision #gamestorming #action #decision making The 20/20 Vision game is about getting group clarity around which projects or initiatives should be more of a priority than others. Because employees’ attention is so often divided among multiple projects, it can be refreshing to refocus and realign more intently with the projects that have the biggest bang for the buck. And defining the “bang” together helps ensure that the process of prioritization is quality.

Cost Benefit Analysis

Simple, tried and tested techniques might not be flashy, but they’re still effective ways to help you make a good decision. A Cost/Benefit analysis is among the most universally known way to help a company make a financial decision on how to move forward.

Start by clustering your ideas and then measure each by the cost associated with them as a team. Be sure to involve stakeholders to get an accurate costing, then move onto perceived benefits. Rank your items along these two axes to see which potential decision makes the most sense.

The 100$ Test

Working with restrictions, conditions and limiting factors is very useful to converge on a realistic decision. The 100$ test activity leverages this to speed up decision making and keep discussions grounded in the realities of resource allocation. Participants are asked to rank a list of items, initiatives or ideas based on how they would allocate an imaginary budget spending to each. By using the concept of cash, this decision making technique captures more attention and keeps participants more engaged than an arbitrary point or ranking system. If this activity had a slogan it would surely be: put your money where your mouth is!

100$ Test #gamestorming #action #decision making In this method of prioritization, participants assign relative value to a list of items by spending an imaginary $100 together. By using the concept of cash, the exercise captures more attention and keeps participants more engaged than an arbitrary point or ranking system.

The convergent phase of a decision making process flows best when constraints are clearly identified. The NUF Test helps with this by encouraging team members to test a potential decision against three limiting factors: is it New? Is it Useful? Is it Feasible? This test, which is derived from processes used in patents, consists in a simple matrix written up on a whiteboard. Include a line for each idea, and rank solutions in terms of novelty, feasibility, and usefulness. This kind of simple analysis can really help make comparing pros and cons easier.

NUF Test #gamestorming #decision making #action As a group is developing ideas in a brainstorming session, it may be useful to do a quick “reality check” on proposed ideas. In the NUF Test, participants rate an idea on three criteria: to what degree is it New, Useful, and Feasible?

Decision-making techniques that mitigate the risk of groupthink

One of the most talked-about (and feared!) group dynamics is Groupthink. This refers to the risk that people will prefer harmony over innovation and, in any decision-making process, will go with whatever is the most popular option—or the option preferred by whoever is in charge! This is truly a dangerous dynamic that can take groups down the rabbit hole of complacency. How to prevent it from happening? In general, groupthink is less likely to happen the more trust there is in the team. In an environment of psychological safety, everyone is encouraged to express their actual thoughts, not what they think others want them to think. Much of the facilitator’s work is directed at creating just such an environment. In the specific context of decision-making, here are 4 decision-making techniques that support psychological safety and will help you avoid groupthink!

1-2-4-all is the essential go-to method to combine in a single, effective flow, individual reflection, paired discussion and shared opinions. Any activity that includes individual reflection before making statements that are heard by others will help prevent groupthink. Ask participants to brainstorm their ideas in their own notes, or to decide what they will dot-vote and write it on a sheet of paper. Give some time for individual work and only then invite actions that make that work visible to all (such as marking a vote on a shared whiteboard). It’s that simple!

1-2-4-All #idea generation #liberating structures #issue analysis With this facilitation technique you can immediately include everyone regardless of how large the group is. You can generate better ideas and more of them faster than ever before. You can tap the know-how and imagination that is distributed widely in places not known in advance. Open, generative conversation unfolds. Ideas and solutions are sifted in rapid fashion. Most importantly, participants own the ideas, so follow-up and implementation is simplified. No buy-in strategies needed! Simple and elegant!

The six thinking hats

In De Bono’s classic thinking hats method , the different hats represent different points of view on a topic with the facilitator (blue hat) inviting everyone to “wear” the different hats in turn. The white hat is for collecting data, and the green hat is for innovative ideas. Avoid groupthink by making sure everyone gets to wear the black hat before making decisions. If a team is afraid to express contrasting views or, perhaps, unwilling to straight-out criticize a plan coming from the manager, a facilitator can make it safer to navigate that territory by explicitly inviting criticism in. In De Bono’s method, this is called the black hat. When we wear the black hat we are looking for risks, weak points and blind spots . Let’s all wear the black hat for a moment and see if we can come up with thoughts on why this is not a good idea!

The Six Thinking Hats #creative thinking #meeting facilitation #problem solving #issue resolution #idea generation #conflict resolution The Six Thinking Hats are used by individuals and groups to separate out conflicting styles of thinking. They enable and encourage a group of people to think constructively together in exploring and implementing change, rather than using argument to fight over who is right and who is wrong.

Remove the obstacles to critical thinking with TRIZ! In this seriously fun method, participants dwell on the question: What could we do to make sure we achieve the absolute worst result possible? Next, in a second round: what are we already doing that looks like that (and we therefore should stop doing)? Laughter often erupts, issues that are otherwise taboo get a chance to be aired and confronted. With creative destruction come opportunities for renewal as local action and innovation rush in to fill the vacuum. According to this intriguing article from the Harvard Business Review, avoiding groupthink is all about creating enough trust to be able to constructively challenge the way things have been done so far, and TRIZ is the perfect tool for that!

Making Space with TRIZ #issue analysis #liberating structures #issue resolution You can clear space for innovation by helping a group let go of what it knows (but rarely admits) limits its success and by inviting creative destruction. TRIZ makes it possible to challenge sacred cows safely and encourages heretical thinking. The question “What must we stop doing to make progress on our deepest purpose?” induces seriously fun yet very courageous conversations. Since laughter often erupts, issues that are otherwise taboo get a chance to be aired and confronted. With creative destruction come opportunities for renewal as local action and innovation rush in to fill the vacuum. Whoosh!

Affinity Map

Conducting an analysis of various solutions and ideas without relying on intuition is a great method to bring to your process. Use an affinity map when you want to see pattens and make recommendations based the data generated from a brainstorm or other idea generation activity.

Start by putting all your ideas and possible solutions on post-its and then cluster them based on relationships and ideas clusters. Once you’ve clustered your ideas, you can then combine, remove and refine in order to move close to a final decision.

Affinity Map #idea generation #gamestorming Most of us are familiar with brainstorming—a method by which a group generates as many ideas around a topic as possible in a limited amount of time. Brainstorming works to get a high quantity of information on the table. But it begs the follow-up question of how to gather meaning from all the data. Using a simple Affinity Diagram technique can help us discover embedded patterns (and sometimes break old patterns) of thinking by sorting and clustering language-based information into relationships. It can also give us a sense of where most people’s thinking is focused

Decision-making techniques to converge upon a solution

In collective decision making it is key to find ways to enable everyone to express their agreement or disagreement with a certain course of action. It’s important to make space to hear different perspectives and evaluate before making decisions. Here are four practical decision making tools you can use to test the waters and enable all participants to make their voices heard.

Agreement-Certainty Matrix

As a precondition to collective decision making, we should know what type of problem we are facing. Different levels of uncertainty require different decision-making rules. If a problem is simple, for example, it’s not worth spending collective energy and time working on. An individual decision will suffice. On the other hand, group decision making is best suited to complicated or complex scenarios which require expertise and diversity. But how do we know what kind of problem we are facing? The Agreement-Certainty practice from Liberating Structures invites participants to sit in small groups with the question “What type of problem are we facing?” Participants are invited to place their current challenges in a matrix based on these two questions:

What is the degree of agreement among the participants regarding the challenge and the best way to address it?
What is the degree of certainty and predictabilit y about what results will be generated from the solutions proposed for addressing the challenge?

An awareness of the distinctions between simple, complicated, complex and chaotic scenarios is an important part of a team’s journey toward decision making mastery. The Cynefin framework is a more in-depth look into this topic, designed to support leaders to make decisions in context .

Agreement-Certainty Matrix #issue analysis #liberating structures #problem solving You can help individuals or groups avoid the frequent mistake of trying to solve a problem with methods that are not adapted to the nature of their challenge. The combination of two questions makes it possible to easily sort challenges into four categories: simple, complicated, complex , and chaotic . A problem is simple when it can be solved reliably with practices that are easy to duplicate. It is complicated when experts are required to devise a sophisticated solution that will yield the desired results predictably. A problem is complex when there are several valid ways to proceed but outcomes are not predictable in detail. Chaotic is when the context is too turbulent to identify a path forward. A loose analogy may be used to describe these differences: simple is like following a recipe, complicated like sending a rocket to the moon, complex like raising a child, and chaotic is like the game “Pin the Tail on the Donkey.” The Liberating Structures Matching Matrix in Chapter 5 can be used as the first step to clarify the nature of a challenge and avoid the mismatches between problems and solutions that are frequently at the root of chronic, recurring problems.

Let’s Check Resistance

A big obstacle to taking decisions together is a tendency to want to push one’s favorite course of action rather than accept a decision that will work well, but is not everyone’s first preference. A concept that vastly helps to overcome this obstacle is the idea of a range of tolerance . This activity from Airbus Leadership University invites participants to clarify and share what options are a “Personal preference”, which would encounter their firm “Objection” and what falls in their “Range of tolerance”. Visualising a wider area of tolerance, rather than limiting choices to a narrow Yes/No binary, makes it easier to find solutions that are acceptable to all parties. Very useful before a final decision is made.

Collective Decision making: Let's check resistance ! #decision making #u-certified #remote-friendly Objective is to support a group which needs to prioritize and/or decide among various available solutions

Feedback Frames

Feedback Frames are a colorful and fun solution designed by Jason Diceman in 2014 to facilitate the expression and visualization of preferences after a brainstorming or ideation session. Participants rate statements by dropping tokens in a range of slots that are hidden by a cover, with results later revealed as a visual graph of opinions. This simple in-person analog tool (which can be ordered internationally at the Feedback Frames website ) uses secret score voting to recognize nuanced gradients of agreement towards consensus and avoid traditional voting problems such as groupthink and vote-splitting.

Feedback Frames for Prioritizing a Brainstorm #decision making #action A fun and reliable technique for scoring many ideas, with instant visual results. Participants rate statements by dropping tokens in Feedback Frames in a range of slots that are hidden by a cover, with results later revealed as a visual graph of opinions. This simple in-person analog tool uses secret score voting to recognize n uanced gradients of agreement towards consensus and avoid traditional voting problems such as groupthink and vote-splitting, which are common in sticker dot voting.

Gradients of Agreement

Once the group has prioritized a few possible courses of action, a decision-making technique like Gradients of Agreement helps clarify how everyone feels with respect to each option. This tool supports inclusion by ensuring team members have an opportunity to specify the level of their agreement or disagreement with a decision under discussion. By marking their choice of a statement ranging from whole-hearted endorsement to vetoing, participants can express views in a more nuanced way than a mere “yes/no” vote. This version of what is also known as “quality voting” comes from the work of Sam Kaner and associates in the classic Facilitator’s Guide to Participatory Decision-Making.

Gradients of Agreement #decision making #consensus building #convergence A scale upon which to measure participants’ levels of agreement with a given statement or course of action.

Fist to Five

Fist to Five is a simple series of hand signals solving the problem of how to test for agreement, and move towards convergence, in a way that is easy to communicate, quick to do, and can work for large gatherings. Like other solutions such as Gradients of Agreement and Feedback Frames , it is based on the idea of giving participants more options than just Yes or No, in this case inviting them to show interest in a certain proposal on a scale from 0 to 5, with a show of hands (or, better, of fingers). This 1-minute activity can on its own be enough to quickly clarify which course of action the group should take. In other cases, it might not be decisive on its own, but can still help decision makers and facilitators decide the next steps. Checking for agreement in this quick way might, for example, lead to discarding one option but keeping another two to continue working with using other tools.

Fist to five #decision making #vote #empowerment #practice Fist to Five is quality voting. It has the elements of consensus built in and can prepare groups to transition into consensus if they wish. Most people are accustomed to the simplicity of “yes” and “no” voting rather than the complex and more community-oriented consensus method of decision making. Fist to Five introduces the element of the quality of the “yes.” A fist is a “no” and any number of fingers is a “yes,” with an indication of how good a “yes” it is. This moves a group away from quantity voting to quality voting, which is considerably more informative. Fist to Five can also be used during consensus decision making as a way to check the “sense of the group,” or to check the quality of the consensus.

Closing activities to turn a decision into action

In closing, it’s useful to support individuals in understanding what individual action they will need to take personally to implement the decision. Once the direction has been set collectively, what are the practical next steps? The next 5 decision-making tools are great to close a workshop session on a pragmatic note, ensuring that everyone leaves with a clear sense of their personal next steps.

Start, Stop, Continue

Start, Stop, Continue is a very flexible exercise developed by Gamestorming methods . It simply asks participants to share their responses to 3 questions: What do we need to start doing? Stop doing? Continue doing? Use this activity after a decision has been agreed upon to define the practical next steps for its implementation. Sharing what we need to start, stop and continue will of course lead to a discussion. If there is no time left for that, you can still use a variation of the same activity, simply asking each participant for one action they will start, stop and/or continue in order to make sure the decision is implemented effectively.

Start, Stop, Continue #gamestorming #action #feedback #decision making The object of Start, Stop, Continue is to examine aspects of a situation or develop next steps. Additionally, it can be a great framework for feedback

Backcasting

Backcasting is a very effective planning tool to support defining next steps. It makes sense to use it after a decision making process if the decision is long-term and implementation steps are not yet clear. In a bit of time-travel, the facilitator invites participants to describe what success will be like in, say, 5 or 10 years if the decision is implemented. Then, the group moves to ideating what needs to be done in 5, 2, 1 year, in order to put the conditions for success in place. And what about in 6 months? And tomorrow? Backcasting is a wonderful tool for transforming a common goal into a practical plan.

Backcasting #define intentions #create #design #action Backcasting is a method for planning the actions necessary to reach desired future goals. This method is often applied in a workshop format with stakeholders participating. To be used when a future goal (even if it is vague) has been identified.

3 Action Steps

In a similar vein to backcasting, this activity from Hyper Island encourages participants to use their imagination to visualise what will happen in the future once the decision is implemented, then works backwards to define practical actions. In small groups, participants share the overall vision, supporting and hindering factors, and land on defining three next steps to take. This is a small-scale strategic planning session that helps groups and individuals to take action toward a desired change. It is often used at the end of a workshop or programme.

3 Action Steps #hyperisland #action #remote-friendly This is a small-scale strategic planning session that helps groups and individuals to take action toward a desired change. It is often used at the end of a workshop or programme. The group discusses and agrees on a vision, then creates some action steps that will lead them towards that vision. The scope of the challenge is also defined, through discussion of the helpful and harmful factors influencing the group.

15% Solutions

Economist Gareth Morgan popularized the idea of 15% solutions in his 1998 article , where he stated that small actions that can be taken easily have the potential to trigger substantial change. “ What is your 15 percent? Where do you have discretion and freedom to act? What can you do without more resources or authority? ” Use this quick, practical decision making technique to encourage participants to take immediate action to implement a decision they have just taken. Make sure to stress that this is about small, easy actions (a phone call, an email, setting a meeting): taking action immediately is a boost to motivation, empowerment and self-organisation.

15% Solutions #action #liberating structures #remote-friendly You can reveal the actions, however small, that everyone can do immediately. At a minimum, these will create momentum, and that may make a BIG difference. 15% Solutions show that there is no reason to wait around, feel powerless, or fearful. They help people pick it up a level. They get individuals and the group to focus on what is within their discretion instead of what they cannot change. With a very simple question, you can flip the conversation to what can be done and find solutions to big problems that are often distributed widely in places not known in advance. Shifting a few grains of sand may trigger a landslide and change the whole landscape.

Training activities to learn about decision-making

Looking for some activities for a training workshop on decision-making? Here are 5 ideas to start with! These are games and simulations designed to help a group think through a decision together. Run them with your team, then settle down to debrief and discuss what works well for you in deciding together!

Delegation levels

It’s important for a team to build a shared understanding of the different possible ways a decision can be taken. Delegation levels is a decision making technique designed to get your group talking about when it is appropriate for a leader to decide on their own, when consultation is necessary, when to decide together. The group over at Management 3.0 has designed handouts and a set of “poker cards” to help you clarify management styles and possible different approaches to decision-making. Having more options in mind allows for more flexibility and adaptability in the team!

Delegation Levels #leadership #decision making #agility #empowerment #wondercards The delegation levels are a model help leaders to find the appropriate level of delegation depending on the assessed situation

Escape hopeland

Escape hopeland is a game created for an Erasmus+ youth exchange which can definitely inspire you to create something similar based on the specific needs of the team you are working with. Create a map, which can refer to a real-world situation, a board game, or an online whiteboard with a series of “stations”. Each station represents a decision, a choice, or an ethical dilemma. Participants navigate the map differently based on their choices, then regroup at the end to discuss.

As with all such role-playing games, the debrief part of the activity is crucial. Facilitate a conversation around powerful questions such as: how did you influence one another in deciding?

Escape Hopeland #decision making Plan several stations in your area. Each station will present a ethical dilemma. Participants are traveling in groups and falling to smaller groups as they are choosing different answers. In the end, they all arrive to the final. The reflection is focused on their decision-making process.

Decisions, decisions

Becoming skilled decision-makers also implies being aware of personal biases, styles and approaches in deciding. By learning more about them, we grow in personal awareness, and increase trust and effectiveness in a team. This activity from Thiagi group is designed to open a discussion around risk-taking. Why are some people more or less risk averse, and how will that influence our decisions as a whole? Personally, I remember when my co-facilitator casually mentioned in passing that I was more risk-averse than him. It led to a cascade of realizations; talking about this difference in our preferences and styles brought us to a wiser place, where I take decisions for the team if a situation is risky, and he does the same in safer spaces, leading to a better balance and a forward momentum in our team!

Decisions, Decisions… #communication #decision making #thiagi #action #issue analysis When it comes to decision-making, why are some of us more prone to take risks while others are risk-averse? One explanation might be the way the decision and options were presented. This exercise, based on Kahneman and Tversky’s classic study , illustrates how the framing effect influences our judgement and our ability to make decisions . The participants are divided into two groups. Both groups are presented with the same problem and two alternative programs for solving them. The two programs both have the same consequences but are presented differently. The debriefing discussion examines how the framing of the program impacted the participant’s decision.

The trolley dilemma

In this simulation meant to stretch our moral and ethics muscles, the group discusses options they would take in a difficult scenario. The debrief focusses on understanding that we make decisions based on different personal sets of values. The implication here is that in order to efficiently make decisions as a group, we need to first clarify our group values, as well as share a general understanding of each other’s value sets, so that they may all be acknowledged and addressed. Shared group values can become north stars to guide and align decision-making.

Trolley Dilemma #decision making Very handful exercise to put the participants in the situation where they have to make hard decision under time pressure.

The cushions game

The cushions game is a playful way to start a deep conversation around competition, cooperation, win-win solutions and the importance of clear communication of goals. The facilitator assigns three groups different instructions that appear to be incompatible. There is, in fact, a win-win-win solution , but in order to reach it participants must be willing to start communicating with the perceived adversary and reveal their goal. I’ve led this game innumerable times, and have unforgettable memories of members of a small political party turning it into an unsolvable pillow fight… as well as of conflict resolution students solving it in less than 60 seconds (admirable, albeit anti-climatic). Extremes apart, it is a fun game that can lead to some powerful revelations in the debrief section.

Cushions game #decision making #training #conflict A fun, dynamic game useful for introducing topics related to decision making, conflict resolution, win-win scenarios and the importance of clear communication of goals.

Activity flows designed for taking collective decision making

Now that you are familiar with the building blocks of converging on a group decision, you might be wondering how to string these all together. Here are four examples of complete workflows going from brainstorming all the way to implementing a shared decision.

Lighting Decision Jam

A very pragmatic, lighting-quick approach to going from ideation to decision comes in this method card contributed by AJ&Smart . Here is a great example of putting it all together in a design-sprint inspired flow! Start by framing the challenge, go on to ideating solutions, dot-voting, prioritizing via an impact/effort matrix, and selecting actionable tasks for implementation. Short, focused sessions like this are great for making decisions quickly and effectively as a group.

Lightning Decision Jam (LDJ) #action #decision making #problem solving #issue analysis #innovation #design #remote-friendly The problem with anything that requires creative thinking is that it’s easy to get lost—lose focus and fall into the trap of having useless, open-ended, unstructured discussions. Here’s the most effective solution I’ve found: Replace all open, unstructured discussion with a clear process. What to use this exercise for: Anything which requires a group of people to make decisions, solve problems or discuss challenges. It’s always good to frame an LDJ session with a broad topic, here are some examples: The conversion flow of our checkout Our internal design process How we organise events Keeping up with our competition Improving sales flow

Sociocratic “Consent” Decision Making

Consent decision-making, as described by practitioners of Sociocracy, is a highly effective way to reach group decisions. Once a team is skilled in using it (which, disclaimer, can take some time and training!), decisions come quickly and efficiently. Participants know that their fears will be kept into consideration and included in the decision, as long as they see clear risks to the group and its mission. In this activity, you’ll find a summary explanation of how consent works in teams. The practice develops as a series of talking rounds, in which participants can ask clarification questions, then express their feelings and comments and finally give their consent or objection to a proposal. In effect, the proposal is co-designed by the entire team through a structured process. To find more details on sociocracy you can refer to the education organization Sociocracy for All’s website.

Collective decision making : consent ('sociocratic") decision making #u-certified #empowerment #decision making ##sociocracy # #holacracy This sequence, also called objection-based decision-making, describes the consent decision-making process as the sociocracy movement promotes it

Decision-making meeting

Consent decision-making in practice works as a series of facilitated rounds, designed to refine a proposal and ensure concerns are identified and integrated into an improved decision. Find here a detailed template you can read through and take inspiration from to ferry a group from ideation into deciding based on sociocratic principles.

How to Facilitate a Quarterly Planning Process (detailed guide)

How to effectively take decisions together while working in a fully remote team? At SessionLab we use a structured decision making process to set priorities and decide what we will work on each quarter. Check out this detailed article to see what works for us, from ideating actions to checking who will do what.

This is a highly participatory consultation process, as each team manager has the last word as to tasks to prioritize and metrics to assign. We’ve found it an effective way of making business decisions as a team. In the accompanying template you can find further details on how much time to assign to each step.

How to facilitate a Quarterly Planning Process (Detailed Guide)

What activities have you used to support decision-making? Do they reflect the ones we’ve collected here? If you have any new ones, consider adding them to SessionLab’s library of methods : as mentioned above, facilitators tend to have a richer toolkit for divergence than for convergence, so let’s work on closing that gap!

Deborah Rim Moiso is an Endorsed Facilitator with the IAF – International Association of Facilitators and former co-chair of the Italian IAF Chapter.

She is the author of a manual and deck of cards on facilitation available in Italian ( Facilitiamoci! ). Deborah has been working with groups since 2009 in the fields of innovation in education, citizen participation, and environmental conflicts.

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Problem Solving and Decision Making: Key Differences & Applications

Explore the nuances of solving complex problems and making intricate decisions in this insightful blog. Gain a deeper understanding of the key distinctions between them. In this blog, explore Problem Solving and Decision Making, their key differences and how to apply these abilities in the workplace. Let's dive in!

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Have you ever faced the trouble of deciding what is right or wrong? In our daily lives, we often come across situations that require us to confront challenges and make choices. This is why two critical cognitive processes are involved in addressing these situations: Problem Solving and Decision Making. While the terms are frequently used interchangeably, they represent distinct mental activities with specific objectives. Problem Solving involves identifying and resolving issues using critical thinking and creativity. On the other hand, Decision Making entails choosing the best course of action among alternatives and considering risks and rewards. In this blog, we will Learn the differences between Problem Solving and Decision Making, how to apply these abilities at work, and some advice on how to improve them.

Table of Contents

1) What do you understand by Decision Making?

2) Understanding Problem Solving

3) What are the differences between Problem Solving and Decision Making?

4) Tips on how to improve Problem-solving and Decision-making skills

5) How can you integrate Decision Making and Problem Solving?

6) Conclusion

What do you understand by Decision Making?

It is a hard choice when we are faced with the question to make important decisions, in organisational setting and personal life as well. Nevertheless, it is not a reason to be afraid, but rather, to master these tasks through comprehensive knowledge of their consequences. First, we should define Decision Making before going on to the difference between Decision Making and Problem Solving.

It is an intellectual process that has a direct impact on our everyday and work-life matters. It is the process of analysing different options to find the best one in line with various factors and the one that is going to meet the objectives.

Effective Decision Making combines Critical Thinking, analysis, and judgment, and it can be the determinant of outcome and consequences. Let's uncover the important steps to Decision -making and some real-life examples:

1) Evaluation of alternatives: The first step in Decision Making requires the identification of problems and conceptualisation of possible alternatives that can help to deal with the given situation or problem.

2) Rationality and objectivity: The correct Decision Making process consists of a detailed analysis of all the data that is accessible, assessing the pros and cons of each scenario, and selecting a logical and beneficial option.

3) Heuristics and biases: Sometimes, it is possible that you may have mental heuristics to be quick in the decision process. However, biases may be introduced by shortcuts and suboptimal choices could become inevitable for you.

4) Decision Making under uncertainty: Some times, you have to make important decisions based on the information that is not complete or with determined assumptions. The risk is directly connected and making risk assessment is considered to be the answer to this question. You must enhance on your flexibility to address the unpredictable.

5) Group Decision Making: In collaborative contexts, people may arrive at a decision together having discussed, brainstormed and found a common consensus with one another. Such a method taps into the different perceptions and skills.

6) Strategic Decision Making: In organisations, Strategic Decision Making requires being concerned with the possible long-term implications, aligning decisions with organisational goals, and trying to anticipate potential impacts on stakeholders.

7) Ethical considerations: This involves assessing the moral implications of choices, decisions, and actions. It revolves around making the right and just choices, guided by one's ethical values and principles.

8) Learning from outcomes: As an effective decision-maker, one should have the audacity to learn from both successful and unsuccessful outcomes because learning from these will only enhance future Decision Making processes.

Here are some real-life examples that may require you to make some justified decisions:

a) Choosing between two job offers based on salary, benefits, and career prospects.

b) Deciding which college or university to attend, considering factors like location, courses offered, and campus culture.

c) Selecting an investment option after analysing risk, return potential, and financial goals.

d) Determining the best marketing strategy for a new product launch, considering target audience, budget, and competition.

e) Making a medical treatment choice for a patient after weighing the benefits, risks, and patient preferences.

Understanding Problem Solving

You're now aware of how you can make effective Decision Making. Let us now learn how to effectively carry out Problem Solving tasks in our daily life. Problem Solving is a fundamental cognitive process that entails identifying challenges, finding solutions, and accompliching the set goals.

It is a logical process aimed at knowing the problem, looking for possible solutions, and choosing the most efficient solution. This helps you to navigate complexities and arrive at successful conclusions. Let us now look at some tips that can help you in Problem Solving effectively:

Steps to be efficient in problem Solving

1) Problem identification: As a first step towards Problem Solving, effectively carry out tasks. Also, recognise and define the issue or challenge that needs to be addressed.

2) Data gathering: Gathering relevant information and data related to the problem is essential for understanding its root causes and implications. This helps you become a good problem solver.

3) Analysis and diagnosis: Analyse the gathered information to identify the underlying causes of the problem. This helps you in devising targeted solutions.

4) Solution generation: Brainstorming and generating multiple potential solutions is crucial for you when you are exploring diverse approaches to resolve the problem.

5) Evaluation of alternatives: Carefully evaluate the pros and cons of each solution. This helps you in selecting the most feasible and effective one.

6) Implementation: After choosing a solution, you have to put the chosen solution into action. This requires planning, coordination, and effective execution.

7) Creative thinking: Sometimes adopting an open-minded view towards finding a solution to the challenging situations will encourage you to be creative.

8) Root cause analysis: Finding and tackling the cause behind the problem in itself can make a change that lasts and you will get a much better, sustainable solution to your problem.

Let us now see some real-life examples where you need to apply your Problem Solving skills:

a) Resolving a technical issue with a computer by identifying and troubleshooting the actual cause of the problem.

b) Finding an alternative transportation route when faced with unexpected road closures.

c) Addressing a communication breakdown within a team by facilitating open discussions and conflict resolution.

d) Solving a math problem by applying various Problem Solving Techniques and mathematical principles.

e) Fixing a malfunctioning appliance by diagnosing the issue and performing necessary repairs.

Learn to be more Mindful when you are applying your Problem Solving skills with our Conflict Management Training .

What are the differences between Problem Solving and Decision Making?

Let us now have a look how Problem Solving and Decision Making skills are different from each other:


	Selecting from available alternatives to achieve a specific goal or outcome.	Identifying and resolving an issue or challenge to reach a desired state.
	Making a choice among options.	Finding a solution to a problem
	Choosing the best course of action.	Understanding the problem and generating potential solutions
	Evaluating alternatives, considering risks and rewards.	Identifying the problem, gathering data, analysing, and implementing solutions.
	Often involves a logical and systematic approach.	Requires critical thinking and creativity.
	It involves available information and past experiences.	Data and insights related to the problem at hand.
	Leads to a final decision.	Results in a resolved problem or improved situation.
	Often applied to challenges or obstacles in various domains.	Troubleshooting technical issues and finding solutions to production problems.
	Decision Making may follow effective Problem Solving.	Effective Problem Solving often leads to better Decision-making.
	Applicable to a wide range of situations.	Often applied to challenges or obstacles in various domains.

1) Definition

Problem Solving is a step-by-step approach that one uses to identify, analyse, and finally come up with the solution to the issues or challenges they face. It seeks to find the origin of a problem, generate possible ideas or solutions, and choose the best alternative to be implemented. In most researches and practices, the primary aim of Problem Solving is reducing or overcoming the negative impacts of the problem.

On the other hand, the Decision Making process gives the choice, which can be taken from different alternatives. Every process of Decision Making produces a choice like taking action, a strategy, or making a resolution. There is not necessarily a problem but it is applicable in any situation which requires making a choice.

2) Objective

Problem Solving is an effort to overcome a given obstacle or challenge. Its basic aim is to produce a solution that would change the current situation from less desirable to more desirable. On the other hand, Decision Making aims at selecting the best possible choice from among several alternatives. It could be proactive, such as deciding on an expansion strategy for the market, or it could be reactive, such as deciding on a course of action in response to the moves of a competitor.

3) Nature

In the Problem Solving process, a problem often arises as a response to a discrepancy between what was expected and what is actually experienced, necessitating a solution. This process is typically reactive. On the other hand, Decision Making can be both proactive and reactive. Proactive Decision Making involves making choices based on anticipation of future events, while reactive Decision Making involves selecting courses of action in response to an immediate situation or problem.

4) Process

The process of Problem Solving usually starts with understanding and diagnosing the problem. This is followed by brainstorming various solutions and analysing the suitability of each before finally implementing the most fitting one.

On the other hand, the Decision Making process typically begins with identifying a need, often through gathering information. This leads to the search for alternatives and compiling a list of these options. The alternatives are then weighed against criteria such as risks, benefits, and implications before making a choice.

5) Tools and techniques

In Problem Solving, commonly used tools include root cause analysis, brainstorming, SWOT analysis, and fishbone diagrams (Ishikawa). These tools help in pinpointing the origin of a problem and exploring all possible solutions.

On the other hand, Decision Making often utilises techniques such as decision trees, cost-benefit analysis, pros and cons lists, and grid analysis. These methods assist in evaluating the implications of each available choice.

6) Skills required

The major skills required in Problem Solving include critical thinking, analytical skills, creativity, and resilience. It is crucial to have the ability to persevere and not be overwhelmed by challenges.

However, Decision Making requires analytical skills, risk assessment, intuition, and foresight. The essential capability here is to be accountable for decisions, which involves predicting the outcomes of every choice

7) Duration and finality

Problem Solving is time-consuming. It requires a deep dive into understanding the problem before moving on to solutions. The process concludes once a solution is implemented, and the problem is resolved.

On the other hand, Decision Making can be swift (like everyday decisions) or prolonged (strategic decisions) depending on the complexity of the problems. Once a decision is made, the next step is to implement it, but decisions can sometimes be revisited based on outcomes or changing scenarios.

Gain a deeper understanding of yourself to take more effective Decision Making with our Decision Making Course .

Tips on how to improve Problem Solving and Decision Making skills

Decision Making and Problem Solving are two most important skills that every individual must possess to excel in their career and in their personal life. There are multiple ways which can be used to improve these skills. Let’s have a look at some of these tips to improve these skills:

Developing skills related to Decision Making and Problem Solving

You can improve your Decision-making and Problem-solving skills by developing other skills such as analytical thinking, creativity and critical thinking. These allied skills will help you boost your analytical thinking skills, will help you think creatively and outside the box. Moreover, honing these skills will help you understand the problems deeply and analyse them without getting partial with your decisions.

Effective communication

Communication is the one of the major keys to success. Effective communication helps in solving problems, miscommunications and helps you understand different perspectives to the same problem. By practicing effective communication, you can convey an information or tasks seamlessly to you team members or colleagues. It helps you understand the root cause of any problem and helps you take an informed decision.

Think about past decisions

It may seem unrelated to you in this context, however, thinking back on your decisions that you made previously can help you not repeat the mistakes, or save you the time that you previously took to make a small decision. Reflecting on past decisions helpin analysing the current problems impartially and help you learn more about your own methods to decide or solve a problem.

Research your industry

Before you make any important decision, or solve out a problem, you need to know about your industry in detail. Since not all situations are same, neither are the industries. Every industry, company or business have their own set of goals, requirements, ideologies, and policies. Whenever you are a part of that specific industry, you should keep in mind, their framework. If you are going beyond their framework or their principles, while solving a problem, there may not be any significant impact taken by your decisions.

Keep yourself updated

It is necessary that you keep yourself updated. As you know that our world is going through many technological advancements. Hence you need to know and update yourself so that you can incorporate all these inventions and discoveries in your industry.

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How can you integrate Decision Making and Problem Solving?

Even though Decision Making and Problem-solving have their differences, there are still instances where you need to integrate these two special skills so that you can carry out any challenging tasks or situations, whether it be in the workplace or in your personal life. The following tips will help you show how you can take effective decisions and simultaneously solve problems:

1) Foster a systematic approach: You can start by adopting a systematic approach to Problem Solving. It involves defining the issue, gathering relevant information, analysing data, generating potential solutions, and evaluating alternatives. Then, you can implement your structured Problem Solving process, which provides a solid foundation for your informed Decision Making.

2) Identify decision points: You can recognise the key decision points within the Problem-solving process. Then you have to determine which factors require choices and weigh the consequences of each decision on the overall Problem Solving outcome.

3) Incorporate critical thinking: You can emphasise your critical thinking throughout both Problem Solving and Decision Making. Engage in objective analysis so that you can consider multiple perspectives and challenge assumptions to arrive at well-rounded solutions and decisions.

4) Utilise data-driven decisions: Ensure that the decisions made during the Problem Solving process are backed by relevant data and evidence. Your data-driven Decision-making minimises biases and increases the chances of arriving at the most suitable solutions.

Gain a deeper understanding of yourself to take more effective Decision-mking with our Personal & Organisational Development Training .

Conclusion

If you integrate both Problem Solving and Decision Making, you can have a more potent approach toward various challenges or tasks. This will help you in making well-informed choices in those circumstances. Moreover, this synergy will empower you to have a Problem -solving mindset to navigate complexities with clarity and achieve effective outcomes.

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Frequently Asked Questions

Problem Solving is both a skill and a competency. It involves the ability to analyse situations, identify issues, generate solutions, and implement them effectively. Developing this capability enhances decision-making, creativity, and adaptability in various personal and professional contexts.

The five steps for Problem Solving and decision-making are:

1) Define the problem

2) Identify possible solutions

3) Evaluate alternatives

4) Make a decision

5) Implement and monitor the chosen solution.

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Tips and techniques for problem-solving and decision-making.

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Divya Parekh , of The DP Group, covers business growth, storytelling, high-impact performance and authority building.

Are you struggling to find effective solutions to problems you face in your professional or entrepreneurial ventures? Are you often indecisive when faced with complex decisions?

The ability to solve problems and make decisions quickly and effectively can mean the difference between success and failure. There are two main approaches to problem-solving and decision-making: vertical thinking and horizontal thinking. Both approaches have strengths and weaknesses, so understanding the differences between them can help you apply the right method at the right time.

Let's look at a few case studies to understand the very different benefits of these two approaches.

Vertical Thinking For Decision-Making

First, let's take Jane, the CFO of a financial services company. She needs to decide whether to invest in a new company software system.

Jane gathers all the relevant data about the software system and analyzes it thoroughly. She compares the cost of the system to the potential benefits, evaluates the risks involved and consults with subject matter experts. After careful consideration, she decides the benefits outweigh the costs and risks, and the company should invest in the software system.

This is vertical thinking: making a well-informed decision based on a thorough analysis of the data. Vertical thinking is especially useful in situations where there is a clear goal and a need for a precise, data-driven approach. Experts often use it in fields like finance, where decisions depend heavily on facts and figures.

Horizontal Thinking For Problem-Solving

Let's move on to Sophie, the head of marketing for a fashion company. The company has been struggling to attract new customers.

Sophie sets up a brainstorming meeting with different department heads. They come up with a variety of creative solutions based on their diverse perspectives. One idea that stands out is to partner with a popular social media influencer to promote the company's products. The team works together to develop a plan to reach out to the influencer and negotiate a partnership.

This is horizontal thinking: working with a team to generate a variety of ideas and consider different perspectives to find an innovative solution. Horizontal thinking is a great approach for problem-solving when the problem is complex and there may be multiple solutions or approaches. Creative professionals, especially in marketing, advertising and designing, highly value this approach.

How Emotions Affect These Approaches

Over several years of coaching, I've noticed that emotions can play a significant role in problem-solving and decision-making, regardless of the thinking style used.

For instance, when using vertical thinking, emotions such as frustration and impatience can arise when a person or team has been working on a problem for an extended period with no clear solution. Conversely, when a team lands on a solution, there can be a sense of relief and accomplishment.

Similarly, when using horizontal thinking, emotions such as excitement and optimism can arise during a brainstorming session when new and creative ideas are being generated. However, disappointment or frustration can also arise when an idea fails to work.

It's important to recognize and acknowledge these emotions as they can affect team dynamics and ultimately, the success of the problem-solving process. I encourage leaders to create a safe and supportive environment where team members feel comfortable expressing their emotions and concerns.

Make These Thinking Styles Work For You

In my experience, a personalized approach that balances both vertical and horizontal thinking can help manage emotions and any other issues that arise effectively. By using vertical thinking to identify specific problems and solutions, and horizontal thinking to generate creative ideas, you can create a problem-solving process that encourages collaboration, creativity and innovation while minimizing negative emotions.

Are you ready to take your problem-solving and decision-making skills to the next level?

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Problem Solving And Decision Making: 10 Hacks That Managers Love

Understanding problem solving & decision making, why are problem solving and decision making skills essential in the workplace, five techniques for effective problem solving, five techniques for effective decision making, frequently asked questions.

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Steps in problem solving and decision making

Improved efficiency and productivity: Employees with strong problem solving and decision making skills are better equipped to identify and solve issues that may arise in their work. This leads to improved efficiency and productivity as they can complete their work more timely and effectively.
Improved customer satisfaction: Problem solving and decision making skills also help employees address any concerns or issues customers may have. This leads to enhanced customer satisfaction as customers feel their needs are being addressed and their problems are resolved.
Effective teamwork: When working in teams, problem solving and decision making skills are essential for effective collaboration . Groups that can effectively identify and solve problems together are more likely to successfully achieve their goals.
Innovation: Effective problem-solving and decision-making skills are also crucial for driving innovation in the workplace. Employees who think creatively and develop new solutions to problems are more likely to develop innovative ideas to move the business forward.
Risk management: Problem solving and decision making skills are also crucial for managing risk in the workplace. By identifying potential risks and developing strategies to mitigate them, employees can help minimize the negative impact of risks on the business.

Brainstorming: Brainstorming is a technique for generating creative ideas and solutions to problems. In a brainstorming session, a group of people share their thoughts and build on each other’s suggestions. The goal is to generate a large number of ideas in a short amount of time. For example, a team of engineers could use brainstorming to develop new ideas for improving the efficiency of a manufacturing process.
Root Cause Analysis: Root cause analysis is a technique for identifying the underlying cause of a problem. It involves asking “why” questions to uncover the root cause of the problem. Once the root cause is identified, steps can be taken to address it. For example, a hospital could use root cause analysis to investigate why patient falls occur and identify the root cause, such as inadequate staffing or poor lighting.
SWOT Analysis: SWOT analysis is a technique for evaluating the strengths, weaknesses, opportunities, and threats related to a problem or situation. It involves assessing internal and external factors that could impact the problem and identifying ways to leverage strengths and opportunities while minimizing weaknesses and threats. For example, a small business could use SWOT analysis to evaluate its market position and identify opportunities to expand its product line or improve its marketing.
Pareto Analysis: Pareto analysis is a technique for identifying the most critical problems to address. It involves ranking problems by impact and frequency and first focusing on the most significant issues. For example, a software development team could use Pareto analysis to prioritize bugs and issues to fix based on their impact on the user experience.
Decision Matrix Analysis: Decision matrix analysis evaluates alternatives and selects the best course of action. It involves creating a matrix to compare options based on criteria and weighting factors and selecting the option with the highest score. For example, a manager could use decision matrix analysis to evaluate different software vendors based on criteria such as price, features, and support and select the vendor with the best overall score.

Cost-Benefit Analysis: Cost-benefit analysis is a technique for evaluating the costs and benefits of different options. It involves comparing each option’s expected costs and benefits and selecting the one with the highest net benefit. For example, a company could use cost-benefit analysis to evaluate a new product line’s potential return on investment.
Decision Trees: Decision trees are a visual representation of the decision-making process. They involve mapping out different options and their potential outcomes and probabilities. This helps to identify the best course of action based on the likelihood of different outcomes. For example, a farmer could use a decision tree to choose crops to plant based on the expected weather patterns.
SWOT Analysis: SWOT analysis can also be used for decision making. By identifying the strengths, weaknesses, opportunities, and threats of different options, a decision maker can evaluate each option’s potential risks and benefits. For example, a business owner could use SWOT analysis to assess the potential risks and benefits of expanding into a new market.
Pros and Cons Analysis: Pros and cons analysis lists the advantages and disadvantages of different options. It involves weighing the pros and cons of each option to determine the best course of action. For example, an individual could use a pros and cons analysis to decide whether to take a job offer.
Six Thinking Hats: The six thinking hats technique is a way to think about a problem from different perspectives. It involves using six different “hats” to consider various aspects of the decision. The hats include white (facts and figures), red (emotions and feelings), black (risks and drawbacks), yellow (benefits and opportunities), green (creativity and new ideas), and blue (overview and control). For example, a team could use the six thinking hats technique to evaluate different options for a marketing campaign.

Aastha Bensla

Aastha, a passionate industrial psychologist, writer, and counselor, brings her unique expertise to Risely. With specialized knowledge in industrial psychology, Aastha offers a fresh perspective on personal and professional development. Her broad experience as an industrial psychologist enables her to accurately understand and solve problems for managers and leaders with an empathetic approach.

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Nine essential problem solving tools: The ultimate guide to finding a solution

October 26, 2023 by MindManager Blog

Problem solving may unfold differently depending on the industry, or even the department you work in. However, most agree that before you can fix any issue, you need to be clear on what it is, why it’s happening, and what your ideal long-term solution will achieve.

Understanding both the nature and the cause of a problem is the only way to figure out which actions will help you resolve it.

Given that most problem-solving processes are part inspiration and part perspiration, you’ll be more successful if you can reach for a problem solving tool that facilitates collaboration, encourages creative thinking, and makes it easier to implement the fix you devise.

The problem solving tools include three unique categories: problem solving diagrams, problem solving mind maps, and problem solving software solutions.

They include:

Fishbone diagrams
Strategy maps
Mental maps
Concept maps
Layered process audit software
Charting software
MindManager

In this article, we’ve put together a roundup of versatile problem solving tools and software to help you and your team map out and repair workplace issues as efficiently as possible.

Let’s get started!

Problem solving diagrams

Mapping your way out of a problem is the simplest way to see where you are, and where you need to end up.

Not only do visual problem maps let you plot the most efficient route from Point A (dysfunctional situation) to Point B (flawless process), problem mapping diagrams make it easier to see:

The root cause of a dilemma.
The steps, resources, and personnel associated with each possible solution.
The least time-consuming, most cost-effective options.

A visual problem solving process help to solidify understanding. Furthermore, it’s a great way for you and your team to transform abstract ideas into a practical, reconstructive plan.

Here are three examples of common problem mapping diagrams you can try with your team:

1. Fishbone diagrams

Fishbone diagrams are a common problem solving tool so-named because, once complete, they resemble the skeleton of a fish.

With the possible root causes of an issue (the ribs) branching off from either side of a spine line attached to the head (the problem), dynamic fishbone diagrams let you:

Lay out a related set of possible reasons for an existing problem
Investigate each possibility by breaking it out into sub-causes
See how contributing factors relate to one another

Fishbone diagrams are also known as cause and effect or Ishikawa diagrams.

2. Flowcharts

A flowchart is an easy-to-understand diagram with a variety of applications. But you can use it to outline and examine how the steps of a flawed process connect.

Made up of a few simple symbols linked with arrows indicating workflow direction, flowcharts clearly illustrate what happens at each stage of a process – and how each event impacts other events and decisions.

3. Strategy maps

Frequently used as a strategic planning tool, strategy maps also work well as problem mapping diagrams. Based on a hierarchal system, thoughts and ideas can be arranged on a single page to flesh out a potential resolution.

Once you’ve got a few tactics you feel are worth exploring as possible ways to overcome a challenge, a strategy map will help you establish the best route to your problem-solving goal.

Problem solving mind maps

Problem solving mind maps are especially valuable in visualization. Because they facilitate the brainstorming process that plays a key role in both root cause analysis and the identification of potential solutions, they help make problems more solvable.

Mind maps are diagrams that represent your thinking. Since many people struggle taking or working with hand-written or typed notes, mind maps were designed to let you lay out and structure your thoughts visually so you can play with ideas, concepts, and solutions the same way your brain does.

By starting with a single notion that branches out into greater detail, problem solving mind maps make it easy to:

Explain unfamiliar problems or processes in less time
Share and elaborate on novel ideas
Achieve better group comprehension that can lead to more effective solutions

Mind maps are a valuable problem solving tool because they’re geared toward bringing out the flexible thinking that creative solutions require. Here are three types of problem solving mind maps you can use to facilitate the brainstorming process.

4. Mental maps

A mental map helps you get your thoughts about what might be causing a workplace issue out of your head and onto a shared digital space.

Because mental maps mirror the way our brains take in and analyze new information, using them to describe your theories visually will help you and your team work through and test those thought models.

5. Idea maps

Idea maps let you take advantage of a wide assortment of colors and images to lay down and organize your scattered thought process. Idea maps are ideal brainstorming tools because they allow you to present and explore ideas about the best way to solve a problem collaboratively, and with a shared sense of enthusiasm for outside-the-box thinking.

6. Concept maps

Concept maps are one of the best ways to shape your thoughts around a potential solution because they let you create interlinked, visual representations of intricate concepts.

By laying out your suggested problem-solving process digitally – and using lines to form and define relationship connections – your group will be able to see how each piece of the solution puzzle connects with another.

Problem solving software solutions

Problem solving software is the best way to take advantage of multiple problem solving tools in one platform. While some software programs are geared toward specific industries or processes – like manufacturing or customer relationship management, for example – others, like MindManager , are purpose-built to work across multiple trades, departments, and teams.

Here are three problem-solving software examples.

7. Layered process audit software

Layered process audits (LPAs) help companies oversee production processes and keep an eye on the cost and quality of the goods they create. Dedicated LPA software makes problem solving easier for manufacturers because it helps them see where costly leaks are occurring and allows all levels of management to get involved in repairing those leaks.

8. Charting software

Charting software comes in all shapes and sizes to fit a variety of business sectors. Pareto charts, for example, combine bar charts with line graphs so companies can compare different problems or contributing factors to determine their frequency, cost, and significance. Charting software is often used in marketing, where a variety of bar charts and X-Y axis diagrams make it possible to display and examine competitor profiles, customer segmentation, and sales trends.

9. MindManager

No matter where you work, or what your problem-solving role looks like, MindManager is a problem solving software that will make your team more productive in figuring out why a process, plan, or project isn’t working the way it should.

Once you know why an obstruction, shortfall, or difficulty exists, you can use MindManager’s wide range of brainstorming and problem mapping diagrams to:

Find the most promising way to correct the situation
Activate your chosen solution, and
Conduct regular checks to make sure your repair work is sustainable

MindManager is the ultimate problem solving software.

Not only is it versatile enough to use as your go-to system for puzzling out all types of workplace problems, MindManager’s built-in forecasting tools, timeline charts, and warning indicators let you plan, implement, and monitor your solutions.

By allowing your group to work together more effectively to break down problems, uncover solutions, and rebuild processes and workflows, MindManager’s versatile collection of problem solving tools will help make everyone on your team a more efficient problem solver.

Download a free trial today to get started!

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Why choose MindManager?

MindManager® helps individuals, teams, and enterprises bring greater clarity and structure to plans, projects, and processes. It provides visual productivity tools and mind mapping software to help take you and your organization to where you want to be.

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Turn your team into skilled problem sol ...

Turn your team into skilled problem solvers with these problem-solving strategies

Picture this, you're handling your daily tasks at work and your boss calls you in and says, "We have a problem."

Unfortunately, we don't live in a world in which problems are instantly resolved with the snap of our fingers. Knowing how to effectively solve problems is an important professional skill to hone. If you have a problem that needs to be solved, what is the right process to use to ensure you get the most effective solution?

In this article we'll break down the problem-solving process and how you can find the most effective solutions for complex problems.

What is problem solving?

Problem solving is the process of finding a resolution for a specific issue or conflict. There are many possible solutions for solving a problem, which is why it's important to go through a problem-solving process to find the best solution. You could use a flathead screwdriver to unscrew a Phillips head screw, but there is a better tool for the situation. Utilizing common problem-solving techniques helps you find the best solution to fit the needs of the specific situation, much like using the right tools.

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4 steps to better problem solving

While it might be tempting to dive into a problem head first, take the time to move step by step. Here’s how you can effectively break down the problem-solving process with your team:

1. Identify the problem that needs to be solved

One of the easiest ways to identify a problem is to ask questions. A good place to start is to ask journalistic questions, like:

Who : Who is involved with this problem? Who caused the problem? Who is most affected by this issue?

What: What is happening? What is the extent of the issue? What does this problem prevent from moving forward?

Where: Where did this problem take place? Does this problem affect anything else in the immediate area?

When: When did this problem happen? When does this problem take effect? Is this an urgent issue that needs to be solved within a certain timeframe?

Why: Why is it happening? Why does it impact workflows?

How: How did this problem occur? How is it affecting workflows and team members from being productive?

Asking journalistic questions can help you define a strong problem statement so you can highlight the current situation objectively, and create a plan around that situation.

Here’s an example of how a design team uses journalistic questions to identify their problem:

Overarching problem: Design requests are being missed

Who: Design team, digital marketing team, web development team

What: Design requests are forgotten, lost, or being created ad hoc.

Where: Email requests, design request spreadsheet

When: Missed requests on January 20th, January 31st, February 4th, February 6th

How : Email request was lost in inbox and the intake spreadsheet was not updated correctly. The digital marketing team had to delay launching ads for a few days while design requests were bottlenecked. Designers had to work extra hours to ensure all requests were completed.

In this example, there are many different aspects of this problem that can be solved. Using journalistic questions can help you identify different issues and who you should involve in the process.

2. Brainstorm multiple solutions

If at all possible, bring in a facilitator who doesn't have a major stake in the solution. Bringing an individual who has little-to-no stake in the matter can help keep your team on track and encourage good problem-solving skills.

Here are a few brainstorming techniques to encourage creative thinking:

Brainstorm alone before hand: Before you come together as a group, provide some context to your team on what exactly the issue is that you're brainstorming. This will give time for you and your teammates to have some ideas ready by the time you meet.

Say yes to everything (at first): When you first start brainstorming, don't say no to any ideas just yet—try to get as many ideas down as possible. Having as many ideas as possible ensures that you’ll get a variety of solutions. Save the trimming for the next step of the strategy.

Talk to team members one-on-one: Some people may be less comfortable sharing their ideas in a group setting. Discuss the issue with team members individually and encourage them to share their opinions without restrictions—you might find some more detailed insights than originally anticipated.

Break out of your routine: If you're used to brainstorming in a conference room or over Zoom calls, do something a little different! Take your brainstorming meeting to a coffee shop or have your Zoom call while you're taking a walk. Getting out of your routine can force your brain out of its usual rut and increase critical thinking.

3. Define the solution

After you brainstorm with team members to get their unique perspectives on a scenario, it's time to look at the different strategies and decide which option is the best solution for the problem at hand. When defining the solution, consider these main two questions: What is the desired outcome of this solution and who stands to benefit from this solution?

Set a deadline for when this decision needs to be made and update stakeholders accordingly. Sometimes there's too many people who need to make a decision. Use your best judgement based on the limitations provided to do great things fast.

4. Implement the solution

To implement your solution, start by working with the individuals who are as closest to the problem. This can help those most affected by the problem get unblocked. Then move farther out to those who are less affected, and so on and so forth. Some solutions are simple enough that you don’t need to work through multiple teams.

After you prioritize implementation with the right teams, assign out the ongoing work that needs to be completed by the rest of the team. This can prevent people from becoming overburdened during the implementation plan . Once your solution is in place, schedule check-ins to see how the solution is working and course-correct if necessary.

Implement common problem-solving strategies

There are a few ways to go about identifying problems (and solutions). Here are some strategies you can try, as well as common ways to apply them:

Trial and error

Trial and error problem solving doesn't usually require a whole team of people to solve. To use trial and error problem solving, identify the cause of the problem, and then rapidly test possible solutions to see if anything changes.

This problem-solving method is often used in tech support teams through troubleshooting.

The 5 whys problem-solving method helps get to the root cause of an issue. You start by asking once, “Why did this issue happen?” After answering the first why, ask again, “Why did that happen?” You'll do this five times until you can attribute the problem to a root cause.

This technique can help you dig in and find the human error that caused something to go wrong. More importantly, it also helps you and your team develop an actionable plan so that you can prevent the issue from happening again.

Here’s an example:

Problem: The email marketing campaign was accidentally sent to the wrong audience.

“Why did this happen?” Because the audience name was not updated in our email platform.

“Why were the audience names not changed?” Because the audience segment was not renamed after editing.

“Why was the audience segment not renamed?” Because everybody has an individual way of creating an audience segment.

“Why does everybody have an individual way of creating an audience segment?” Because there is no standardized process for creating audience segments.

“Why is there no standardized process for creating audience segments?” Because the team hasn't decided on a way to standardize the process as the team introduced new members.

In this example, we can see a few areas that could be optimized to prevent this mistake from happening again. When working through these questions, make sure that everyone who was involved in the situation is present so that you can co-create next steps to avoid the same problem.

A SWOT analysis

A SWOT analysis can help you highlight the strengths and weaknesses of a specific solution. SWOT stands for:

Strength: Why is this specific solution a good fit for this problem?

Weaknesses: What are the weak points of this solution? Is there anything that you can do to strengthen those weaknesses?

Opportunities: What other benefits could arise from implementing this solution?

Threats: Is there anything about this decision that can detrimentally impact your team?

As you identify specific solutions, you can highlight the different strengths, weaknesses, opportunities, and threats of each solution.

This particular problem-solving strategy is good to use when you're narrowing down the answers and need to compare and contrast the differences between different solutions.

Even more successful problem solving

After you’ve worked through a tough problem, don't forget to celebrate how far you've come. Not only is this important for your team of problem solvers to see their work in action, but this can also help you become a more efficient, effective , and flexible team. The more problems you tackle together, the more you’ll achieve.

Looking for a tool to help solve problems on your team? Track project implementation with a work management tool like Asana .

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How to build your critical thinking skills in 7 steps (with examples)

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How to Strengthen Problem-Solving Skills in Everyday Life

Problem-solving is an essential skill that we rely on in both personal and professional settings. From minor inconveniences to complex challenges, we are constantly presented with situations that require us to find effective solutions. Strengthening your problem-solving abilities can improve decision-making, reduce stress, and lead to more successful outcomes.

Whether you’re facing a difficult task at work, managing personal relationships, or navigating everyday life, honing your problem-solving skills is key. By cultivating a strategic mindset, staying mentally sharp, and using the right techniques, you can become more effective at identifying solutions to problems. Some individuals also use brain supplements like nootropics to support mental clarity, focus, and cognitive performance, making problem-solving easier and more efficient.

Ask the Right Questions

The benefits of a step-by-step approach, techniques to foster creativity, stress management techniques for problem-solving, embrace a growth mindset, daily practices to sharpen problem-solving skills, define the problem clearly.

The first step to solving any problem is understanding exactly what the problem is. Many people jump into problem-solving mode without fully analyzing the situation, which can lead to incomplete solutions or overlooked details. Taking the time to clearly define the problem will help you identify the best approach and ensure that you are solving the right issue.

To clearly define a problem, start by asking questions that help you get to the root of the issue. For example, what is the real challenge here? What are the contributing factors? Who is affected by this problem, and why? By breaking the problem down and examining all of its aspects, you can gain a deeper understanding of what needs to be addressed.

In both personal and professional settings, it’s important to differentiate between symptoms and root causes. While it’s tempting to address surface-level symptoms, solving the root cause will prevent the problem from reoccurring. Taking time to ask the right questions and fully define the problem sets the stage for more effective solutions.

Break the Problem into Manageable Steps

Large, complex problems can feel overwhelming, leading to procrastination or poor decision-making. Breaking a problem into smaller, manageable steps makes it easier to approach systematically and keeps you focused on the next actionable task. This step-by-step approach not only simplifies the problem but also helps reduce stress and mental fatigue.

Breaking a problem down into smaller parts allows you to tackle each aspect one at a time. This reduces overwhelm and helps you stay organized throughout the process. For example, if you’re working on a challenging project at work, break it down into research, planning, execution, and review stages. Focus on completing one stage before moving to the next, allowing for greater clarity and concentration.

Identify Sub-Problems: Break the larger problem into smaller sub-problems that can be addressed independently. This makes the overall challenge more manageable and gives you a clear starting point.
Create Actionable Steps: Turn each sub-problem into a specific action step that you can take to move forward. Having a clear plan of action keeps you focused and reduces the chances of becoming overwhelmed.

For individuals seeking enhanced cognitive performance during problem-solving, some find that using nootropics supports mental clarity and sustained focus, making it easier to work through each step without losing momentum.

Use Creative Problem-Solving Techniques

Creative problem-solving involves looking beyond traditional solutions and thinking outside the box to find new, innovative approaches. This technique is particularly useful when facing complex challenges or when conventional methods aren’t working. Cultivating creativity in problem-solving can lead to unexpected breakthroughs and more effective solutions.

One popular creative problem-solving method is brainstorming. During a brainstorming session, you generate as many ideas as possible without immediately judging or discarding them. This helps you explore a wide range of possibilities before narrowing down your options. Another effective technique is mind mapping, which involves visually organizing ideas and solutions in a diagram, helping you see connections that might not be immediately obvious.

Brainstorming: Write down every idea, no matter how unconventional, and explore each one before deciding on the best solution. You might be surprised by the creative insights that emerge.
Mind Mapping: Draw a visual representation of the problem, with the central issue in the middle and branches representing possible solutions. This helps you see relationships and generate new ideas.

Creative problem-solving requires mental flexibility and the ability to see beyond traditional approaches. Many individuals use brain supplements like nootropics to enhance cognitive flexibility, supporting innovative thinking and creativity during the problem-solving process.

Stay Calm and Manage Stress

Problem-solving is much more difficult when you’re feeling stressed or overwhelmed. High stress levels can cloud judgment, reduce cognitive function, and make it harder to think clearly. Learning how to manage stress effectively is essential for maintaining mental sharpness and approaching problems with a clear, focused mindset.

One of the best ways to reduce stress while problem-solving is to practice mindfulness. Mindfulness helps you stay present and focused on the task at hand, rather than becoming distracted by anxiety or worry about the outcome. Taking regular breaks to breathe deeply, meditate, or step away from the problem for a few minutes can also help you reset and return to the issue with fresh energy.

Physical activity, such as going for a walk or engaging in light exercise, can reduce stress and boost mental clarity, helping you approach problems with a clearer perspective. Staying calm under pressure allows you to think more rationally, helping you find more effective solutions to the challenges you face.

For those looking for additional support in managing stress and maintaining focus, some turn to brain supplements like nootropics to enhance cognitive resilience. These supplements may help reduce mental fatigue, promote calmness, and support better decision-making during stressful situations.

Learn from Mistakes and Adapt

Not every solution will work perfectly the first time. Learning from mistakes and remaining adaptable is a key part of strengthening your problem-solving skills. When a solution doesn’t lead to the desired outcome, it’s important to analyze what went wrong and adjust your approach accordingly.

A growth mindset—the belief that skills and abilities can be developed through effort and learning—helps you view challenges as opportunities for growth. Rather than becoming discouraged by setbacks, see them as valuable learning experiences. Each mistake brings you closer to understanding the problem more deeply and finding the right solution.

Take time to reflect on what went wrong, whether it was a flaw in the solution itself or in the approach you used. This reflection helps you adapt your problem-solving techniques and develop more effective strategies for the future. By staying flexible and open to learning, you strengthen your overall problem-solving abilities.

Adaptability and a willingness to learn from mistakes are essential for long-term success. Many individuals find that using nootropics helps improve cognitive flexibility, making it easier to adjust their strategies and think critically about what changes need to be made.

Practice Problem-Solving Regularly

Like any skill, problem-solving improves with practice. The more you challenge your brain to find solutions, the sharper and more effective your problem-solving skills become. Incorporating problem-solving exercises into your daily routine helps keep your mind sharp and better prepared to tackle challenges as they arise.

One way to practice problem-solving regularly is to engage in puzzles, logic games, or brainteasers. These exercises challenge your brain to think critically and explore different approaches to finding solutions. Additionally, applying problem-solving techniques to everyday challenges, such as organizing your schedule or resolving a conflict, provides valuable real-world practice.

Another effective practice is to reflect on recent challenges you’ve faced and analyze how you approached them. Consider what worked, what didn’t, and how you could improve your approach in the future. By making problem-solving a regular part of your daily routine, you strengthen your mental agility and become more confident in handling any issues that arise.

Some individuals use brain supplements like nootropics to support cognitive performance and problem-solving skills, helping them stay sharp and focused even during complex challenges. Nootropics can provide an additional mental boost, enhancing clarity, focus, and creativity while solving problems.

Problem Solving

Problem solving is a valuable skill that can really only be learnt, and perfected, through continual practice. A wide range of problem solving models and techniques are available to assist in evaluating and solving diverse problems of varying degrees of complexity. As a manager you, are encouraged to find the model which best works for you - one that is flexible and can be adapted to suit your own specific circumstances. Over time, your model of choice should become an automatic and integral part of your working practices.

Problem Solving Definition

A problem is the distance between how things currently are and the way they should be. Problem solving forms the ‘bridge’ between these two elements. In order to close the gap, you need to understand the way things are (problem) and the way they ought to be (solution).

Difference Between Problem Solving And Decision Making

Although there is a clear distinction between problem solving and decision making, the two are often confused. Problem solving differs fundamentally from decision making. A problem occurs when something is not behaving as it should, something is deviating from the norm or something goes wrong. Decision making is a case of choosing between different alternatives. Decision making is required in response to the question: "Which computer shall I buy?" Problem solving is needed in response to the statement: "My computer won't work".

Most problem solving methods follow a common pattern, beginning with a definition of the problem, moving on to the consideration of potential solutions, and culminating with the selection, testing and implementation of a chosen course of action. Divergent thinking techniques can be helpful in generating creative ideas, while convergent thinking can assist in structuring and evaluating potential solutions.

Problems can be classified into one of two categories: the ‘fix-it’ or the ‘do-it’ scenario:

Fix-it – solving an existing problem, (e.g. a current product range is falling short of its sales targets). An immediate short-term solution could be to increase marketing activity, for example.
Do-it – moving you in the right direction for what you want to achieve, (e.g. a new product range needs to be introduced to compete with market rivals). This type of problem will require longer term planning in order to achieve its objectives.

Irrespective of the severity or complexity of the problem, the process should:

be systematic and thorough
provide evidence to show how the problem was solved
avoid a rush to a solution without first understanding the cause of the problem
enable possible causes to be assessed

Problem solving process and framework

Effective managers include below actions into their problem solving strategies.

Define and understand the problem
Assess the scale of the problem
Gather relevant information
Identify the root causes
Test the hypothesis
Involve others
Consider the proposed solution(s)
Test the proposed solution
Champion your decision
Monitor the results

To learn more about problem solving and detailed description of the action checklist, view the guide below:

Download the guide

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Critical Thinking

Decision-making and Problem-solving

Appreciate the complexities involved in decision-making & problem solving.

Develop evidence to support views

Analyze situations carefully

Discuss subjects in an organized way

Predict the consequences of actions

Weigh alternatives

Generate and organize ideas

Form and apply concepts

Design systematic plans of action

A 5-Step Problem-Solving Strategy

Specify the problem – a first step to solving a problem is to identify it as specifically as possible. It involves evaluating the present state and determining how it differs from the goal state.

Analyze the problem – analyzing the problem involves learning as much as you can about it. It may be necessary to look beyond the obvious, surface situation, to stretch your imagination and reach for more creative options.

seek other perspectives

be flexible in your analysis

consider various strands of impact

brainstorm about all possibilities and implications

research problems for which you lack complete information. Get help.

Formulate possible solutions – identify a wide range of possible solutions.

try to think of all possible solutions

be creative

consider similar problems and how you have solved them

Evaluate possible solutions – weigh the advantages and disadvantages of each solution. Think through each solution and consider how, when, and where you could accomplish each. Consider both immediate and long-term results. Mapping your solutions can be helpful at this stage.

Choose a solution – consider 3 factors:

compatibility with your priorities

amount of risk

practicality

Keys to Problem Solving

Think aloud – problem solving is a cognitive, mental process. Thinking aloud or talking yourself through the steps of problem solving is useful. Hearing yourself think can facilitate the process.

Allow time for ideas to "gel" or consolidate. If time permits, give yourself time for solutions to develop. Distance from a problem can allow you to clear your mind and get a new perspective.

Talk about the problem – describing the problem to someone else and talking about it can often make a problem become more clear and defined so that a new solution will surface.

Decision Making Strategies

Decision making is a process of identifying and evaluating choices. We make numerous decisions every day and our decisions may range from routine, every-day types of decisions to those decisions which will have far reaching impacts. The types of decisions we make are routine, impulsive, and reasoned. Deciding what to eat for breakfast is a routine decision; deciding to do or buy something at the last minute is considered an impulsive decision; and choosing your college major is, hopefully, a reasoned decision. College coursework often requires you to make the latter, or reasoned decisions.

Decision making has much in common with problem solving. In problem solving you identify and evaluate solution paths; in decision making you make a similar discovery and evaluation of alternatives. The crux of decision making, then, is the careful identification and evaluation of alternatives. As you weigh alternatives, use the following suggestions:

Consider the outcome each is likely to produce, in both the short term and the long term.

Compare alternatives based on how easily you can accomplish each.

Evaluate possible negative side effects each may produce.

Consider the risk involved in each.

Be creative, original; don't eliminate alternatives because you have not heard or used them before.

An important part of decision making is to predict both short-term and long-term outcomes for each alternative. You may find that while an alternative seems most desirable at the present, it may pose problems or complications over a longer time period.

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Recognizing Propaganda Techniques and Errors of Faulty Logic
Developing the Ability to Analyze Historical and Contemporary Information
Recognize and Value Various Viewpoints
Appreciating the Complexities Involved in Decision-Making and Problem-Solving
Being a Responsible Critical Thinker & Collaborating with Others
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3 Ways to Improve Your Decision Making

by Walter Frick

Summary .

To get better at making decisions, you have to improve your ability to make predictions (how different choices change the likelihood of different outcomes) and your judgment (how desirable each of those outcomes is). While there are countless ways to work on these two skills, there are three simple rules that can help the most. First, be less certain. We’re all more confident about each step of the decision-making process than we ought to be. What else would you think about if you were less sure that A would cause B, or that B is preferable to C? Second, always ask yourself ask “How often does that typically happen?” If you think outcome B is preferable to outcome C, you might ask: How often has that historically been the case? Third, brush up on your understanding of probability. Research has shown that even basic training in probability makes people better forecasters and helps them avoid certain cognitive biases.

To make a good decision, you need to have a sense of two things: how different choices change the likelihood of different outcomes and how desirable each of those outcomes is. In other words, as Ajay Agrawal, Joshua Gans, and Avi Goldfarb have written , decision making requires both prediction and judgment.

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How to Enhance Your Decision-Making Skills as a Leader

Leader making decision with team watching

14 Mar 2024

As a leader, you make countless decisions—from whom to hire and which projects to prioritize to where to make budget cuts.

If you’re a new leader, acclimating to being a decision-maker can be challenging. Luckily, like other vital business skills, you can learn how to make better decisions through education and practice.

Here’s a primer on why decision-making skills are crucial to leadership and six ways to enhance yours.

Access your free e-book today.

Why Are Decision-Making Skills Important?

While decision-making is built into most leaders’ job descriptions, it’s a common pain point. According to a 2023 Oracle study , 85 percent of business leaders report suffering from “decision distress”—regretting, feeling guilty about, or questioning a decision they made in the past year.

When distressed by difficult decisions, it can be easy to succumb to common pitfalls , such as:

Defaulting to consensus
Not offering alternatives to your proposed solution
Mistaking opinions for facts
Losing sight of purpose
Truncating debate

By defaulting to the “easy answer” or avoiding working through a decision, you can end up with outcomes that are stagnant at best and disastrous at worst.

Yet, decision-making is a skill you can sharpen in your leadership toolkit. Here are six ways to do so.

6 Ways to Enhance Your Leadership Decision-Making Skills

1. involve your team.

One common pitfall of leadership is thinking you must make every decision yourself. While you may have the final judgment call, enlisting others to work through challenging decisions can be helpful.

Asking for peers’ input can open your mind to new perspectives. For instance, if you ask your direct reports to brainstorm ways to improve your production process’s efficiency, chances are that they’ll have some ideas you didn’t think of.

If a decision is more private—such as whether to promote one employee over another—consider consulting fellow organizational leaders to approach it from multiple angles.

Another reason to involve your team in the decision-making process is to achieve buy-in. Your decision will likely impact each member, whether it’s about a new or reprioritized strategic initiative. By helping decide how to solve the challenge, your employees are more likely to feel a sense of ownership and empowerment during the execution phase.

Related: How to Get Employee Buy-In to Execute Your Strategic Initiatives

2. Understand Your Responsibilities to Stakeholders

When facing a decision, remember your responsibilities to stakeholders. In the online course Leadership, Ethics, and Corporate Accountability —offered as a Credential of Leadership, Impact, and Management in Business (CLIMB) program elective or individually—Harvard Business School Professor Nien-hê Hsieh outlines your three types of responsibilities as a leader: legal, economic, and ethical .

Hsieh also identifies four stakeholder groups—customers, employees, investors, and society—that you must balance your obligations to when making decisions.

For example, you have the following responsibilities to customers and employees:

Well-being: What’s ultimately good for the person
Rights: Entitlement to receive certain treatment
Duties: A moral obligation to behave in a specific way
Best practices: Aspirational standards not required by law or cultural norms

“Many of the decisions you face will not have a single right answer,” Hsieh says in the course. “Sometimes, the most viable answer may come with negative effects. In such cases, the decision is not black and white. As a result, many call them ‘gray-area decisions.’”

As a starting point for tackling gray-area decisions, identify your stakeholders and your responsibilities to each.

Related: How to Choose Your CLIMB Electives

3. Consider Value-Based Strategy

If you make decisions that impact your organization’s strategy, consider how to create value. Often, the best decision provides the most value to the most stakeholders.

The online course Business Strategy —one of seven courses comprising CLIMB's New Leaders learning path—presents the value stick as a visual representation of a value-based strategy's components.

By toggling each, you can envision how strategic decisions impact the value you provide to different shareholders.

For instance, if you choose to lower price, customer delight increases. If you lower the cost of goods, you increase value for your firm but decrease it for suppliers.

This kind of framework enables you to consider strategic decisions’ impact and pursue the most favorable outcome.

4. Familiarize Yourself with Financial Statements

Any organizational leadership decision you make is bound to have financial implications. Building your decision-making skills to become familiar and comfortable with your firm’s finances is crucial.

The three financial statements you should know are:

The balance sheet , which provides a snapshot of your company’s financial health for a given period
The income statement , which gives an overview of income and expenses during a set period and is useful for comparing metrics over time
The cash flow statement , which details cash inflows and outflows for a specific period and demonstrates your business’s ability to operate in the short and long term

In addition to gauging your organization’s financial health, learn how to create and adhere to your team or department’s budget to ensure decisions align with resource availability and help your team stay on track toward goals.

By sharpening your finance skills , you can gain confidence and back your decisions with financial information.

5. Leverage Data

Beyond financial information, consider other types of data when making decisions. That data can come in the form of progress toward goals or marketing key performance indicators (KPIs) , such as time spent on your website or number of repeat purchases. Whatever the decision, find metrics that provide insight into it.

For instance, if you need to prioritize your team’s initiatives, you can use existing data about projects’ outcomes and timelines to estimate return on investment .

By leveraging available data, you can support your decisions with facts and forecast their impact.

Related: The Advantages of Data-Driven Decision-Making

6. Learn from Other Leaders

Finally, don’t underestimate the power of learning from other leaders. You can do so by networking within your field or industry and creating a group of peers to bounce ideas off of.

One way to build that group is by taking an online course. Some programs, including CLIMB , have peer learning teams built into them. Each term, you’re sorted into a new team based on your time zone, availability, and gender. Throughout your educational experience, you collaborate with your peers to synthesize learnings and work toward a capstone project—helping you gain new perspectives on how to approach problem-solving and decision-making.

In addition to learning from peers during your program, you can network before and after it. The HBS Online Community is open to all business professionals and a resource where you can give and receive support, connect over topics you care about, and collaborate toward a greater cause.

When searching for courses, prioritize those featuring real-world examples . For instance, HBS Online’s courses feature business leaders explaining situations they’ve encountered in their careers. After learning the details of their dilemmas, you’re prompted to consider how you’d handle them. Afterward, the leaders explain what they did and the insights they gained.

By listening to, connecting with, and learning from other leaders, you can discover new ways to approach your decisions.

Elevate Your Career. Transform Your Organization | Download Brochure

Gaining Confidence as a Leader

Taking an online leadership course can help you gain confidence in your decision-making skills. In a 2022 City Square Associates survey , 84 percent of HBS Online learners said they have more confidence making business decisions, and 90 percent report feeling more self-assured at work.

If you want to improve your skills, consider a comprehensive business program like CLIMB .

It features three courses on foundational topics:

Finance and accounting

And three courses on cutting-edge leadership skills:

Dynamic Teaming
Personal Branding
Leading in the Digital World

Additionally, you select an open elective of your choice from HBS Online’s course catalog .

Through education and practice, you can build your skills and boost your confidence in making winning decisions for your organization.

Are you ready to level up your leadership skills? Explore our yearlong Credential of Leadership, Impact, and Management in Business (CLIMB) program , which comprises seven courses for leading in the modern business world. Download the CLIMB brochure to learn about its curriculum, admissions requirements, and benefits.

About the Author

Kepner-Tregoe Problem Analysis: A Comprehensive Guide for Decision-Making

Master decision-making with our in-depth Kepner-Tregoe Problem Analysis guide. Elevate your skills to solve complex issues efficiently.

In the early days of my career as a project manager, I often felt like I was juggling flaming torches while riding a unicycle—one wrong move, and everything could come crashing down. I remember a particularly challenging project where our team was tasked with launching a new product line within an impossible deadline. We were scrambling, tensions were high, and despite our best efforts, we kept hitting roadblocks. It felt like we were putting out fires rather than making any real progress.

One evening, over a much-needed cup of coffee, a mentor introduced me to the Kepner-Tregoe Problem Analysis method. Skeptical but desperate for a solution, I decided to give it a shot. Little did I know, this decision would not only save our project but also transform the way I approach problem-solving in both my professional and personal life.

Understanding the Foundations of Kepner-Tregoe

The moment of realization: more than just a tool.

At first glance, Kepner-Tregoe seemed like just another analytical framework—dry, technical, and somewhat intimidating. But as I delved deeper, I realized it was much more than that. It was a systematic way to dissect complex issues, understand their root causes, and develop effective solutions. For someone like me, who often got lost in the chaos of multifaceted problems, this method was a revelation.

I began to see patterns in the problems we faced. It wasn't just about missed deadlines or budget overruns; there were underlying issues that we hadn't identified. This method provided a structured approach to peel back the layers and see the core of the problem.

Breaking Down the Method: Four Essential Steps

The Kepner-Tregoe Problem Analysis is built on four fundamental steps:

Identifying the Problem

Analyzing the Problem

Considering Possible Solutions

Implementing the Best Solution

Each step requires meticulous attention but offers immense clarity. I found that by not skipping any stages, we could avoid the pitfalls of jumping to conclusions or implementing quick fixes that didn't last.

Diving Deep into the Problem-Solving Process

Identifying the problem: the first hurdle.

In our project, we initially thought the problem was the tight deadline imposed by upper management. It was easy to blame time constraints for our struggles. However, when we sat down and applied the first step of the Kepner-Tregoe method, we realized that the real issue was a lack of clear communication between departments.

I recall a meeting where team members from different departments admitted they weren't sure about their specific responsibilities. It was a lightbulb moment for all of us. The symptom was delays, but the underlying problem was ambiguity in role definitions.

Analyzing the Problem: Uncovering Root Causes

With the problem identified, we moved on to analyzing it. We asked ourselves critical questions: Why was there a communication breakdown? Were there existing protocols that weren't being followed? Was there a cultural barrier between teams?

We used tools like cause-and-effect diagrams to map out potential factors. It turned out that recent organizational changes had altered reporting lines, and not everyone was updated. This gap led to confusion and duplicated efforts.

I felt a mix of frustration and relief. Frustration because the issue seemed so basic, and relief because we finally knew what we were dealing with.

Considering Possible Solutions: Brainstorming Together

The next step was to consider possible solutions . We gathered representatives from all departments for a brainstorming session. No idea was off the table. Some suggested regular inter-departmental meetings, others proposed a shared online platform for updates.

One of my colleagues, known for her creative flair, suggested we create an internal newsletter highlighting each team's progress. At first, it seemed unconventional, but the more we discussed it, the more it made sense. It would not only keep everyone informed but also foster a sense of community.

Implementing the Best Solution: Taking Action

After evaluating all options, we decided on a multi-faceted approach:

Establishing a shared project management tool accessible to all relevant parties.

Scheduling weekly coordination meetings with clear agendas.

Launching the internal newsletter as a pilot project.

Implementing these solutions required commitment. There were initial hiccups—some team members were resistant to change, and there was a learning curve with the new software. But with persistence and open communication, we gradually saw improvements.

Deadlines were met, misunderstandings decreased, and there was a noticeable boost in team morale. Witnessing these positive changes reinforced my belief in the effectiveness of the Kepner-Tregoe method.

Reflecting on the Impact and Limitations

The benefits i've witnessed firsthand.

Adopting the Kepner-Tregoe Problem Analysis has been a game-changer. It provides a clear roadmap, reducing the overwhelming feeling that often accompanies complex problems. By breaking down issues into manageable steps, it becomes easier to tackle them systematically.

I've also found that this method promotes team collaboration. Everyone gets a chance to contribute, leading to more comprehensive solutions. It's not just about fixing a problem but also about enhancing overall team dynamics.

Recognizing the Method's Limitations

However, it's important to acknowledge that this approach isn't a one-size-fits-all solution. In crisis situations where immediate action is required, going through each step may not be feasible. I've been in scenarios where quick decision-making was essential, and lengthy analysis wasn't an option.

Additionally, the method relies heavily on accurate information. If the data collected is flawed, the analysis will be off-target. It's crucial to ensure that all information is verified and that team members are honest and open during discussions.

Applying Kepner-Tregoe Beyond the Workplace

Personal life applications: more than a professional tool.

Interestingly, I've started applying the Kepner-Tregoe method to personal challenges as well. When faced with a significant financial decision, like buying a new home, my partner and I used this approach to weigh our options. We identified our needs, analyzed the housing market, considered various neighborhoods, and ultimately made a choice that we're happy with.

Another instance was when I was training for a marathon. After a minor injury, I had to reassess my training plan. Using the method, I identified the problem (overtraining), analyzed why it happened, considered solutions (rest, adjust the training schedule, consult a trainer), and implemented the best course of action.

Encouraging Others to Embrace Structured Problem-Solving

I've become somewhat of an advocate for the Kepner-Tregoe method. Whenever colleagues or friends express frustration over complex issues, I share my experiences. Recently, a friend struggling with launching his startup applied this method and found clarity he hadn't achieved before.

It's rewarding to see others benefit from a tool that has had such a positive impact on my life. I believe that with the right guidance, anyone can adopt this approach to improve their decision-making skills.

Final Thoughts: Embracing a Methodical Approach

The journey with Kepner-Tregoe Problem Analysis has taught me the value of patience, thoroughness, and collaboration. In a world that often demands quick fixes, taking the time to systematically address problems can lead to more sustainable solutions.

For anyone feeling overwhelmed by complex challenges—whether in business, personal projects, or daily life—I highly recommend exploring this method. It might require an initial investment of time and effort, but the long-term benefits are well worth it.

Helpful Resources:

Kepner-Tregoe Official Website : Offers detailed information and training options.

Fishbone Diagram Guide: A useful tool for root cause analysis.

What are the key principles that underpin Kepner-Tregoe Problem Analysis

Understanding kepner-tregoe problem analysis.

Kepner-Tregoe Problem Analysis stands on structured problem solving. It offers a comprehensive stepwise method. Businesses leverage it to pinpoint and resolve issues effectively. Four key principles form its foundation.

Principle 1: Clear Problem Definition

One must state the problem clearly. Ambiguity has no place here. A well-defined problem guides towards a solution. This involves describing what we observe. We avoid assumptions and generalizations.

Principle 2: Problem Dissection

Break the problem into smaller components. Analyze each piece individually. This simplification aids in managing complexity. It facilitates a more focused investigation. Understanding of each part becomes critical.

Principle 3: Root Cause Identification

Seek the problem's origin. We gather and evaluate data methodically. It's about asking the right questions. Hypotheses form through this inquiry process. Each is tested against the facts.

Principle 4: Decision Analysis and Resolution

We must consider potential solutions. Each option requires careful evaluation. Risks and benefits receive equal attention. The decision-making process is deliberate and logical. It leads to selecting the best solution.

Application in Real-World Scenarios

In practice, teams apply these principles systematically. They start by gathering information. Detail is key. Inferring causes happens next. It involves critical thinking. Potential solutions emerge through brainstorming. Decision-making follows. It sets action plans in motion. Monitoring outcomes forms the final step.

The success of Kepner-Tregoe Problem Analysis lies in its rigor. It demands discipline from practitioners. Structured problem-solving replaces intuition. Each step builds on the previous. This results in a robust solution process.

- Clarity : Define the problem precisely.

- Dissection : Break down complex issues.

- Root Cause : Search for underlying causes.

- Decision Analysis : Weigh all possible solutions.

These principles provide a lens for viewing problems. They force a systematic approach. Intuition blends with logic. This yields better decisions. Organizations that adopt these principles often see improved outcomes.

Transforming Challenges into Opportunities

Kepner-Tregoe Problem Analysis reshapes how we approach challenges. The methodology instills a disciplined thinking process. Problems represent opportunities for improvement. The structured framework assists in capitalizing on these opportunities.

The analysis is not about quick fixes. It focuses on sustainable solutions. Teams become adept at identifying actionable intelligence. Insight replaces guesswork.

This strategy's adoption spans industries. It enhances capabilities in problem-solving. As a result, it contributes to organizational resilience. Effective problem resolution becomes a competitive advantage.

Kepner-Tregoe's principles guide us towards objective analysis. They champion a rational approach in chaotic environments. In essence, these principles encourage a mindset pivot. Problems change from stumbling blocks to stepping stones. They guide teams in navigating the complexities of business issues. The goal is to reach logical, data-driven conclusions every time.

Understanding Kepner-Tregoe Problem Analysis Kepner-Tregoe Problem Analysis stands on structured problem solving. It offers a comprehensive stepwise method. Businesses leverage it to pinpoint and resolve issues effectively. Four key principles form its foundation. Principle 1: Clear Problem Definition One must state the problem clearly. Ambiguity has no place here. A well-defined problem guides towards a solution. This involves describing what we observe. We avoid assumptions and generalizations. Principle 2: Problem Dissection Break the problem into smaller components. Analyze each piece individually. This simplification aids in managing complexity. It facilitates a more focused investigation. Understanding of each part becomes critical. Principle 3: Root Cause Identification Seek the problems origin. We gather and evaluate data methodically. Its about asking the right questions. Hypotheses form through this inquiry process. Each is tested against the facts. Principle 4: Decision Analysis and Resolution We must consider potential solutions. Each option requires careful evaluation. Risks and benefits receive equal attention. The decision-making process is deliberate and logical. It leads to selecting the best solution. Application in Real-World Scenarios In practice, teams apply these principles systematically. They start by gathering information. Detail is key. Inferring causes happens next. It involves critical thinking. Potential solutions emerge through brainstorming. Decision-making follows. It sets action plans in motion. Monitoring outcomes forms the final step. The success of Kepner-Tregoe Problem Analysis lies in its rigor. It demands discipline from practitioners. Structured problem-solving replaces intuition. Each step builds on the previous. This results in a robust solution process. - Clarity : Define the problem precisely. - Dissection : Break down complex issues. - Root Cause : Search for underlying causes. - Decision Analysis : Weigh all possible solutions. These principles provide a lens for viewing problems. They force a systematic approach. Intuition blends with logic. This yields better decisions. Organizations that adopt these principles often see improved outcomes. Transforming Challenges into Opportunities Kepner-Tregoe Problem Analysis reshapes how we approach challenges. The methodology instills a disciplined thinking process. Problems represent opportunities for improvement. The structured framework assists in capitalizing on these opportunities. The analysis is not about quick fixes. It focuses on sustainable solutions. Teams become adept at identifying actionable intelligence. Insight replaces guesswork. This strategys adoption spans industries. It enhances capabilities in problem-solving. As a result, it contributes to organizational resilience. Effective problem resolution becomes a competitive advantage. Kepner-Tregoes principles guide us towards objective analysis. They champion a rational approach in chaotic environments. In essence, these principles encourage a mindset pivot. Problems change from stumbling blocks to stepping stones. They guide teams in navigating the complexities of business issues. The goal is to reach logical, data-driven conclusions every time.

How does the Kepner-Tregoe Problem Analysis approach aid in structuring and simplifying complex decision-making processes

In business and management, decision-makers confront complex challenges daily. These require structured methods to tackle effectively. Among these methods stands the Kepner-Tregoe Problem Analysis. It aids in streamlining and organizing the problem-solving process.

Core Components of the Kepner-Tregoe Method

The Kepner-Tregoe approach comprises four key stages. These stages are Situation Appraisal , Problem Analysis , Decision Analysis , and Potential Problem Analysis .

- Situation Appraisal - Identify the issue .

- Problem Analysis - Clarify the problem .

- Decision Analysis - Evaluate alternatives .

- Potential Problem Analysis - Anticipate future issues .

This structured sequence prevents haphazard decision-making. It encourages methodical progression through problems.

Simplifying Decision-Making

Each stage in the Kepner-Tregoe model serves to simplify decisions. Here's how:

- Clarify concerns. Essential for mastering complex situations.

- Establish priorities. Critical in focusing efforts and resources.

- Evaluate information. Ensures decisions rely on factual data.

- Generate solutions. Opens avenues for innovative thinking and solutions.

- Assess risks. Prepares for potential future complications.

Incremental Learning and Decision-Making

The Kepner-Tregoe method promotes incremental learning. Decision-makers build on foundational knowledge. Each problem teaches new lessons. Each decision draws on past experiences.

Enhancing Communication

Clear communication is fundamental in complex scenarios. The Kepner-Tregoe process requires clear articulation of issues. It mandates detailed discussion of potential solutions. As a result, it enhances team understanding and synergy.

Result-Oriented Focus

The method strives for actionable outcomes. It avoids indecision and theoretical loops. It leans on pragmatic steps towards solution implementation.

Benefits of Kepner-Tregoe Problem Analysis

Logical sequencing.

The approach enforces logical order in addressing problems. It detangles complexities through systematic analysis. This logical sequence guides decision-makers and reduces the risk of oversight.

Comprehensive Examination

Each step requires thorough examination of present elements. This scrutiny reveals root causes. It avoids superficial judgments common in hurried decisions.

Prioritization

With its focus on priorities, the method ensures efficient resource allocation. It aids in distinguishing critical issues from less urgent ones. This ensures the most significant concerns receive needed attention.

Risk Management

The final stage, Potential Problem Analysis, prepares for future uncertainties. It strengthens strategies and renders them more robust.

Employing the Kepner-Tregoe Problem Analysis leads to structured, simplified decision-making. It equips decision-makers to untangle complexities. It provides a blueprint guiding them to judicious, informed choices.

Understanding Kepner-Tregoe Problem Analysis In business and management, decision-makers confront complex challenges daily. These require structured methods to tackle effectively. Among these methods stands the Kepner-Tregoe Problem Analysis. It aids in streamlining and organizing the problem-solving process. Core Components of the Kepner-Tregoe Method The Kepner-Tregoe approach comprises four key stages. These stages are Situation Appraisal , Problem Analysis , Decision Analysis , and Potential Problem Analysis . - Situation Appraisal - Identify the issue . - Problem Analysis - Clarify the problem . - Decision Analysis - Evaluate alternatives . - Potential Problem Analysis - Anticipate future issues . This structured sequence prevents haphazard decision-making. It encourages methodical progression through problems. Simplifying Decision-Making Each stage in the Kepner-Tregoe model serves to simplify decisions. Heres how: - Clarify concerns. Essential for mastering complex situations. - Establish priorities. Critical in focusing efforts and resources. - Evaluate information. Ensures decisions rely on factual data. - Generate solutions. Opens avenues for innovative thinking and solutions. - Assess risks. Prepares for potential future complications. Incremental Learning and Decision-Making The Kepner-Tregoe method promotes incremental learning. Decision-makers build on foundational knowledge. Each problem teaches new lessons. Each decision draws on past experiences. Enhancing Communication Clear communication is fundamental in complex scenarios. The Kepner-Tregoe process requires clear articulation of issues. It mandates detailed discussion of potential solutions. As a result, it enhances team understanding and synergy. Result-Oriented Focus The method strives for actionable outcomes. It avoids indecision and theoretical loops. It leans on pragmatic steps towards solution implementation. Benefits of Kepner-Tregoe Problem Analysis Logical Sequencing The approach enforces logical order in addressing problems. It detangles complexities through systematic analysis. This logical sequence guides decision-makers and reduces the risk of oversight. Comprehensive Examination Each step requires thorough examination of present elements. This scrutiny reveals root causes. It avoids superficial judgments common in hurried decisions. Prioritization With its focus on priorities, the method ensures efficient resource allocation. It aids in distinguishing critical issues from less urgent ones. This ensures the most significant concerns receive needed attention. Risk Management The final stage, Potential Problem Analysis, prepares for future uncertainties. It strengthens strategies and renders them more robust. Conclusion Employing the Kepner-Tregoe Problem Analysis leads to structured, simplified decision-making. It equips decision-makers to untangle complexities. It provides a blueprint guiding them to judicious, informed choices.

Can you discuss in detail the step-by-step process involved in the Kepner-Tregoe Problem Analysis method?

Introduction to kepner-tregoe problem analysis.

Kepner-Tregoe Problem Analysis offers a systematic method. It aids in solving complex issues. Organizations widely apply this method. It structures the problem-solving process effectively. Here, we dissect this technique into sequential steps.

The Step-by-Step Process

Step 1: describe the problem.

Begin by stating the issue clearly. Focus on what you observe. Detail what , where , when , and extent . Each factor helps in understanding the issue's scope.

- Identify what is wrong

- Specify where the issue occurs

- Note when it happens

- Quantify the issue's extent

Step 2: Establish the Problem's Priority

Determining urgency is vital. Consider the problem's effect on operations. Ask which issue to tackle first. Prioritize based on impact and urgency.

- Assess the problem's impact

- Rank based on urgency

Step 3: Identify Possible Causes

List all potential causes. Think broadly and creatively. Consider every possible source. Your goal is to not miss any potential cause.

- Brainstorm all possible causes

- Be inclusive and creative

Step 4: Evaluate the Most Likely Causes

Examine each cause critically. Collect data and evidence. Contrast each cause against your problem description. Look for patterns that match.

- Gather data on causes

- Compare against problem specifics

Step 5: Test the Most Probable Cause

Now, verify the likely cause. Create an experiment or a test. Ensure the test is controlled. Gather results diligently.

- Conduct a controlled test

- Collect and record results

Step 6: Confirm the True Cause

Assess your test findings. Check if the cause and effect align. Confirm if the cause explains all the problem aspects. Ensure no contradiction exists.

- Review test outcomes

- Ensure cause-effect consistency

Step 7: Implement the Solution

After confirming the cause, act on it. Develop a plan to address the issue. Implement your solution with care. Monitor the results closely.

- Develop an action plan

- Execute and observe

Step 8: Monitor the Solution's Effectiveness

Monitoring is a critical follow-up. Check if the problem resolves. Note any unforeseen effects. Adjust your actions as required.

- Track the problem resolution

- Adjust as needed

Kepner-Tregoe Problem Analysis is a disciplined approach. It ensures effective issue resolution. It demands clear thinking and precise action. Employing this method offers a higher probability of solving complex problems efficiently.

Introduction to Kepner-Tregoe Problem Analysis Kepner-Tregoe Problem Analysis offers a systematic method. It aids in solving complex issues. Organizations widely apply this method. It structures the problem-solving process effectively. Here, we dissect this technique into sequential steps. The Step-by-Step Process Step 1: Describe the Problem Begin by stating the issue clearly. Focus on what you observe. Detail what , where , when , and extent . Each factor helps in understanding the issues scope. - Identify what is wrong - Specify where the issue occurs - Note when it happens - Quantify the issues extent Step 2: Establish the Problems Priority Determining urgency is vital. Consider the problems effect on operations. Ask which issue to tackle first. Prioritize based on impact and urgency. - Assess the problems impact - Rank based on urgency Step 3: Identify Possible Causes List all potential causes. Think broadly and creatively. Consider every possible source. Your goal is to not miss any potential cause. - Brainstorm all possible causes - Be inclusive and creative Step 4: Evaluate the Most Likely Causes Examine each cause critically. Collect data and evidence. Contrast each cause against your problem description. Look for patterns that match. - Gather data on causes - Compare against problem specifics Step 5: Test the Most Probable Cause Now, verify the likely cause. Create an experiment or a test. Ensure the test is controlled. Gather results diligently. - Conduct a controlled test - Collect and record results Step 6: Confirm the True Cause Assess your test findings. Check if the cause and effect align. Confirm if the cause explains all the problem aspects. Ensure no contradiction exists. - Review test outcomes - Ensure cause-effect consistency Step 7: Implement the Solution After confirming the cause, act on it. Develop a plan to address the issue. Implement your solution with care. Monitor the results closely. - Develop an action plan - Execute and observe Step 8: Monitor the Solutions Effectiveness Monitoring is a critical follow-up. Check if the problem resolves. Note any unforeseen effects. Adjust your actions as required. - Track the problem resolution - Adjust as needed Conclusion Kepner-Tregoe Problem Analysis is a disciplined approach. It ensures effective issue resolution. It demands clear thinking and precise action. Employing this method offers a higher probability of solving complex problems efficiently.

He is a content producer who specializes in blog content. He has a master's degree in business administration and he lives in the Netherlands.

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Problems are a regular part of our lives. They are natural in any business. And your success will largely depend on how you solve these problems and how much effort you put into addressing them.

In the early stages of business development, you will face many challenges. Whether it's handling operational inefficiencies or managing customer expectations, problem-solving skills are essential for driving growth.

In this article, we will reveal five key problem-solving skills that every entrepreneur and leader who wants to lead a team should possess. These qualities help you tackle immediate challenges and prepare your business for sustainable long-term growth.

Analytical Thinking: Breaking Down Complex Problems

Any problem can seem overwhelmingly complicated until you break it down into many small components, each of which requires one specific action. This is known as analytical thinking — the ability to recognize the main challenge, identify the key goals to overcome it, and compile a list of tasks to achieve them. For example, if you are faced with negative customer feedback, analytical thinking will help you to highlight the key points in it, find the roots of the problem in employee performance and product issues, and change the company's management policy to address these.

Analytical thinking is also related to the ability to read data and see certain trends. Studying metrics allows you to find out what works well in your business and what doesn't work at all. By making data-driven decisions, businesses can develop more effective strategies tailored to specific challenges. You don't have to rely on your brain alone to do this. Online financial management platforms like Wallester have user-friendly dashboards for quick diagnostics and detailed analytics to break down specific small parts of the problem.

Key takeaway : Cultivating analytical thinking allows businesses to understand problems in depth, ensuring the solutions implemented are relevant and effective.

Creativity: Finding Innovative Solutions

If a problem seems insurmountable, the solution may simply lie elsewhere. To find it, you should think outside the box and come up with innovative solutions that others might overlook. To do this, you should evaluate the problem not only from the traditional perspective of a businessperson but also from other angles — as a customer, an employee, or an independent observer.

For example, if a startup has a problem finding qualified personnel, it can temporarily replace certain positions with artificial intelligence and present it as a test of innovative technologies. With the right marketing, this can turn a negative reaction into a positive one.

Key takeaway : Encourage creativity within your team to explore fresh ideas that can address challenges in ways traditional methods cannot.

Adaptability: Adjusting to Changing Circumstances

Business is a dynamic entity whose development is more like a sinusoidal curve than a straight line. Companies experience ups and downs caused by changes in markets and target audiences. They have to plan for growth but also be prepared for downturns. Being adaptive means developing strategies that include “B,” “C,” and sometimes even “D” plans.

Adaptive leaders can recognize that certain solutions no longer work. They have the strength to abandon old methods in favor of new ones. They use flexible tools that can also adapt to current circumstances. For example, the Wallester platform allows you to instantly close corporate cards that have become unnecessary after the completion of a particular project. This helps reduce company costs and simplify control over the targeted use of funds.

Key takeaway : Cultivate adaptability within your leadership and teams to respond quickly and efficiently to new challenges, ensuring your business remains competitive.

Collaboration: Leveraging Team Expertise

No one can run a large-scale successful business alone. For a company to grow, develop, and improve its performance, you need to delegate authority. Only in this way will it be flexible and dynamic enough to remain competitive.

Teamwork allows you to create a synergistic effect — together, the team has much more knowledge, skills, and experience than each employee individually. And that's not to mention the potential for finding creative, non-standard solutions during brainstorming sessions. The secret to success in collaboration is to be able to trust but maintain invisible threads of control that will help identify the problem in time and take measures to overcome the crisis.

Key takeaway : Foster collaboration within your team to generate innovative, well-rounded solutions that everyone is invested in.

Decision-Making: Acting on Solutions with Confidence

Determining how to grow your company and overcome challenges is only half the battle. You should also make carefully considered but timely and confident decisions about which solutions to implement and how to execute them. Strong decision-making skills are essential for turning insights into actions that drive business growth.

But it's important to understand that decision-making is not about being ready to jump into action when you see the first best way to solve a problem. It's the ability to quickly assess pros and cons, identify risks, and choose methods of hedging them before taking action. This requires critical thinking and the confidence to commit to a course of action, even when faced with uncertainty.

Key takeaway: Develop decision-making skills within your leadership team to implement solutions swiftly, ensuring your business can address problems before they escalate.

Problem-solving is a multifaceted set of skills and abilities that stimulates business development and makes it sustainable. First of all, a manager must be able to analyze problems and break them down into small parts to set specific tasks. They need creativity, adaptability, and the ability to delegate authority. But no less important will be the timely adoption of informed decisions that will make the company competitive by taking into account current circumstances.

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See also: Harnessing Creativity in Problem-Solving: Innovations for Overcoming Challenges How to Create A Small Business Growth Strategy Strategic Planning for Long-Term Business Success

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Open Access

Peer-reviewed

Research Article

The neural dynamics associated with computational complexity

Roles Conceptualization, Data curation, Formal analysis, Investigation, Methodology, Project administration, Software, Visualization, Writing – original draft, Writing – review & editing

Affiliation Centre for Brain, Mind & Markets The University of Melbourne, Melbourne, Victoria, Australia

Roles Conceptualization, Formal analysis, Investigation, Methodology, Software, Supervision, Validation, Writing – original draft, Writing – review & editing

Affiliations Centre for Brain, Mind & Markets The University of Melbourne, Melbourne, Victoria, Australia, Faculty of Economics, Cambridge University, Cambridge, United Kingdom

Roles Conceptualization, Formal analysis, Funding acquisition, Investigation, Methodology, Project administration, Resources, Software, Supervision, Validation, Writing – original draft, Writing – review & editing

* E-mail: [email protected]

Juan Pablo Franco,
Peter Bossaerts,
Carsten Murawski

Published: September 23, 2024
https://doi.org/10.1371/journal.pcbi.1012447
Peer Review
Reader Comments

This is an uncorrected proof.

Many everyday tasks require people to solve computationally complex problems. However, little is known about the effects of computational hardness on the neural processes associated with solving such problems. Here, we draw on computational complexity theory to address this issue. We performed an experiment in which participants solved several instances of the 0-1 knapsack problem, a combinatorial optimization problem, while undergoing ultra-high field (7T) functional magnetic resonance imaging (fMRI). Instances varied in computational hardness. We characterize a network of brain regions whose activation was correlated with computational complexity, including the anterior insula, dorsal anterior cingulate cortex and the intra-parietal sulcus/angular gyrus. Activation and connectivity changed dynamically as a function of complexity, in line with theoretical computational requirements. Overall, our results suggest that computational complexity theory provides a suitable framework to study the effects of computational hardness on the neural processes associated with solving complex cognitive tasks.

Author summary

Humans are frequently faced with complex decisions, ranging from everyday tasks like grocery shopping to more intricate decisions such as selecting an investment portfolio. These decisions require higher-order problem-solving skills, which remain poorly understood, particularly regarding the neural processes that support deliberation. In this study, we introduce a framework that employs computational complexity theory to investigate the neural activity that occurs during complex problem-solving. We suggest that the inherent characteristics of a problem determine its computational difficulty, and that these intrinsic features could be used to identify consistent neural patterns during complex problem-solving. To test this approach, we applied it to the knapsack problem, a standard computational problem. Participants solved several versions of this problem while their brain activity was monitored using an ultra-high field MRI. By leveraging computational complexity theory, we developed generic metrics of computational difficulty and successfully identified the corresponding neural correlates and their dynamics during problem-solving. The results indicate that the proposed framework, grounded in computational complexity theory, offers a promising method for studying the neural processes involved in complex problem-solving. This approach could provide valuable insights into a topic that has previously resisted formal investigation.

Citation: Franco JP, Bossaerts P, Murawski C (2024) The neural dynamics associated with computational complexity. PLoS Comput Biol 20(9): e1012447. https://doi.org/10.1371/journal.pcbi.1012447

Editor: Daniele Marinazzo, Ghent University, BELGIUM

Received: September 26, 2023; Accepted: August 30, 2024; Published: September 23, 2024

Copyright: © 2024 Franco et al. This is an open access article distributed under the terms of the Creative Commons Attribution License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

Data Availability: The data analysis code and the behavioral data are available at the OpenScience Framework (OSF: https://osf.io/g4h7y/ ). The anonymized neuroimaging data are available (in BIDS format) at OpenNeuro ( https://doi.org/10.18112/openneuro.ds005427.v1.1.1 ) and through the OSF project.

Funding: JPF was supported by a University of Melbourne Graduate Research Scholarship from the Faculty of Business and Economics ( https://fbe.unimelb.edu.au ). PB acknowledges financial support through a R@MAP Chair from the University of Melbourne ( https://unimelb.edu.au ). The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.

Competing interests: The authors have declared that no competing interests exist.

1 Introduction

Every day, people make decisions that require solving complex problems. Many of these problems are known to be computationally intractable in the sense that the number of operations that need to be performed to find a solution grows quickly to levels that make solving correctly these problems infeasible. Real-life examples of intractable tasks include attention gating, task scheduling, shopping, routing, bin packing, and gameplay [ 1 , 2 ]. Despite the relevance of intractable problems in daily life, little is known about the effects of complexity of tasks on the neural processes during problem-solving.

Intractable problems require an extended period of time to solve and involve an extensive search space. These two characteristics defy formal investigation of neural dynamics. Firstly, since solving such tasks requires an extended period of time, one cannot opt for modeling based on discrete choice theories such as those underlying neuroeconomics [ 3 ]. When deciding between, say, an apple and a candy, the neural activation can be modeled in terms of an indicator variable whose level is modulated by the value inferred from choices and kept constant throughout the short (couple of seconds) deliberation time [e.g., 4]. When choice concerns complex alternatives, deliberation times may be an order of magnitude longer, so neural activation can be expected to fluctuate markedly during the course of deliberation. Secondly, because the search space is large, there are a plethora of paths that can be chosen during resolution. Since human approaches to solving a complex problem exhibit substantial heterogeneity, both across individuals and over time [e.g., 5], modeling neural dynamics during deliberation is bound to be challenging if it is to be based on “what people are thinking,” i.e., on individual approaches to solving complex problems. A different strategy is called for.

Here, we propose to focus on “what people are solving,” that is, on features of the computational tasks that are being presented. This has precedent in the analysis of probabilistic tasks, where intrinsic properties of the gamble at hand (such as mean and variance of the uncertain reward) have proven invaluable to deciphering the neural processes leading up to choice [e.g., 6]. Likewise, mathematical characteristics of the stimuli in perceptual tasks, such as signal strength, elucidate neural dynamics during deliberation [e.g., 7, 8]. Drawing on computational complexity theory, we demonstrate here that a mapping exists between intrinsic properties of instances of a problem related to computational hardness and neural dynamics during decision-making. Importantly, these properties represent generic features of computational problems that can be studied across different tasks and, indeed, have been shown to affect human behavior such as accuracy and time-on-task in several tasks [ 9 , 10 ].

We studied the case of a canonical intractable (specifically “NP-complete”; see definition in Materials and methods ) problem, the 0–1 knapsack decision problem (KP). There, the decision-maker is asked to choose whether, given a set of items with differing value and weight, there exists a subset whose total value is at least as high as a given threshold, while the total weight is less than or equal to a capacity constraint. We identified two properties of instances of KP related to an instance’s computational hardness and tested whether these properties elucidated neural signatures during deliberation. The two properties are complexity and proof hardness . Complexity captures the number of computational steps (or time) needed to solve an instance, while proof hardness represents the computational steps needed to verify the correctness of the solution.

In order to measure complexity, we utilized a metric of difficulty that arises from the study of random ensembles of instances (i.e., random cases of the problem). Variation in expected computational complexity, regardless of the algorithm used, has been attributed to specific structural properties of instances [ 11 – 17 ]. The resulting “typical-case complexity” (TCC) has been found to affect human performance and effort in several intractable (NP-complete) problem-solving tasks, including KP [ 9 , 10 ]. Therefore, we hypothesized that TCC would prove useful in characterizing the effects of computational hardness on neural processes. In analogy with work on neural correlates related to deliberation during tractable tasks [ 18 – 21 ], we expected neural correlates of TCC to overlap with the multiple-demand system. Specifically, we hypothesized they would overlap with two networks, (1) the cingulo-opercular network (CON), consisting of the dorsal anterior cingulate cortex (dACC) and the anterior insula (AI), and (2) the frontoparietal network (FPN), composed of the intraparietal sulcus (IPS) and specific regions from the lateral prefrontal cortex including the inferior frontal sulcus and the middle frontal gyrus (MFG) (e.g., [ 18 , 21 – 23 ]). Additionally, we expected the level of complexity to be associated with neural markers of efficacy [ 24 ] and performance [ 25 , 26 ].

We appeal to the theory of proof complexity to measure proof hardness. In the context of an NP-complete problem, such as the KP, there exists an asymmetry in the difficulty of proving that the solution is correct, which depends on the “satisfiability” of the instance. If an instance is satisfiable (the correct choice is ‘yes’), it suffices to find a witness (example assignment of variables) that satisfies all of the constraints; one can then quickly verify that the witness indeed satisfies all the constraints, and this verification is tractable (i.e., can be done in polynomial time). For example, in the KP it suffices to find a subset of items that satisfies the weight capacity and value constraints. In contrast, to confirm that an instance is unsatisfiable (the correct choice is ‘no’) requires proving that no witness exists, which is far more difficult (not tractable): even if a few potential witnesses are found not to satisfy the constraints, there may exist others that do. We thus conjectured that satisfiability would correlate with subjective reliability , that is, the degree to which the result of a calculation can be relied on to be accurate—much like variance modulates subjective beliefs of choice correctness in probabilistic tasks. Therefore, we expected neural correlates of this measure in regions that have been previously shown to encode uncertainty, specifically in CON [ 25 – 28 ].

In our experiment, participants were asked to solve several instances of the knapsack decision problem, while undergoing functional magnetic resonance imaging (fMRI). Instances were drawn randomly but in a way that systematically varied their TCC and their satisfiability. Critically, in order to more precisely localize and track neural signals during deliberation, we employed ultra-high field (7 Tesla) fMRI.

Twenty participants (14 female, 5 male, 1 other; age range = 18–35 years, mean age = 26.6 years) took part in this study. Each participant was asked to solve 56 instances of the knapsack decision task while undergoing ultra-high field MRI brain scanning ( Fig 1a ). Instances varied in their computational complexity (TCC) and their satisfiability (2×2 balanced factorial design; see Materials and methods ). Recall that the latter, satisfiability, captures proof hardness. Specifically, it encapsulates the asymmetry in the difficulty of proving that the solution is correct. Satisfiable instances are considered to have low proof hardness (verifying that a witness satisfies the constraints can be done in polynomial time) while unsatisfiable instances have a high proof hardness (verifying a proof of unsatisfiability might require more than polynomial time).

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(a) Task. The task was composed of three main stages: items stage (3 s), solving stage (22 s) and response stage (2 s). Initially, participants were presented with a set of items of different values and weights. The green circle at the center of the screen indicated the time remaining in this stage of the trial. This stage lasted 3 seconds. Then, both capacity constraint and target profit were shown at the center of the screen. The objective of the task is to decide whether there exists a subset of items for which (1) the sum of weights is lower or equal to the capacity constraint and (2) the sum of values yields at least the target profit. This stage lasted 22 seconds. Finally, participants had 2 seconds to make either a ‘YES’ or ‘NO’ response using the response button box. A fixation cross was shown during the inter-trial interval (jittered between 8 and 12 seconds). (b) Relation between TCC and human performance in the knapsack decision task. Each dot represents an instance; human performance corresponds the proportion of participants that solved the instance correctly. Instances are categorized according to their constrainedness region ( α p ) and their TCC. In the underconstrained region (low TCC) the satisfiability probability is close to one, while in the overconstrained region (low TCC) the probability is close to zero. The region with a high TCC corresponds to a region in which the probability is close to 0.5. Additionally, instances are categorized according to their solution (satisfiability) which is represented by their color. The box-plots represent the median, the interquartile range (IQR) and the whiskers extend to a maximum length of 1.5*IQR. (c) Pictorial representation of complexity and proof hardness. As operationalized in relation to the properties of instances ( α p and satisfiability).

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Additionally, participants performed, outside the scanner, a set of complementary tasks, including a knapsack optimization task and a set of cognitive function tasks. In this section, we report the behavioral results of the knapsack decision task, while the behavioral results from the complementary tasks are reported in Sections 3 and 5 in S1 Appendix .

2.1 Behavioral results

2.1.1 summary statistics..

On average, participants chose the ‘YES’ option 50% of the trials (min = 25%, max = 68%). Mean human performance , measured as the proportion of trials in which a correct response was made, was 0.78 (min = 0.48, max = 0.95, SD = 0.14). Performance increased slightly as the task progressed; however, a negative (or null) effect cannot be fully ruled out with the evidence provided by the current dataset ( β 0.5 = 0.009, HDI 0.95 = [−0.001, 0.021], main effect of trial number on performance, generalized logistic mixed model (GLMM); Table A Model 1 in S1 Appendix ).

2.1.2 Accuracy and instance properties.

We first studied the effect of TCC on human performance. This measure is based on a prominent framework in computer science that investigates the factors affecting computational hardness in computational problems by studying the difficulty of randomly generated instances of those problems. In the knapsack problem, TCC is explicitly connected to the normalized profit ( α p ) that captures the constrainedness of the problem. Explicitly, α p is defined as the target profit (e.g., $218 in Fig 1a ) divided by the sum of all item values in the instance. [ 9 , 14 ]. This parameter determines the likelihood that a random instance is satisfiable , that is, that the solution is ‘yes’. Specifically, they characterize where typical instances are generally satisfiable (under-constrained region), where they are unsatisfiable (over-constrained region), and where the probability of satisfiability is close to 50% (satisfiability threshold α s ). As an illustration, consider the instance presented in Fig 1a . If the target profit were set to a large value (e.g., $300), the instance would be overconstrained (it is likely that no combination of items satisfies both constraints), whereas if it were set to a very low value (e.g., $20), the instance would be underconstrained. The more extreme these values are, the easier the instance is to solve. Indeed, it has been shown that the computational difficulty of solving the problem is higher when α p is close to α s [ 9 , 14 ]. TCC is then defined based on the distance of α p to the satisfiability threshold α s . Specifically, instances with values of α p near the satisfiability threshold have a high typical-case complexity ( high TCC ) whereas instances further away from it—that is, in the under-constrained and over-constrained regions—have low typical-case complexity ( low TCC ). In line with previous results [ 9 ], we found participants had a better performance on instances with low TCC compared to those with high TCC ( β 0.5 = −1.10, HDI 0.95 = [−1.44, −0.79], main effect of TCC on performance, GLMM; Fig 1b ; Table A Model 2 in S1 Appendix ).

We then studied proof-hardness by investigating satisfiability. Proof-hardness is defined as the computational difficulty of verifying that the certificate of a solution (i.e., proof) is correct. An important driver of proof hardness is the satisfiability of an instance. To verify that an instance is satisfiable, it suffices to check that a candidate set of items (satisfiability-certificate) satisfies the constraints. In contrast, verifying unsatisfiability requires validating a proof of non-existence (unsatisfiability-certificate). For NP-complete problems the former is tractable (P-time) whilst the latter is conjectured to be intractable (follows from the conjecture that coNP ≠ NP ; see Materials and methods ).

Note that proof-hardness is not directly related to the complexity of solving the knapsack problem. Instead, proof hardness characterizes the complexity of a different problem: the one of verifying that a solution to the problem is correct. Strictly speaking, it is mute to the complexity of finding the solution. As such, we hypothesized there would be no effect of satisfiability on performance. As expected, our findings replicate previous results that suggest that there is no effect of satisfiability on human performance in the knapsack decision task ([ 9 ]; β 0.5 = 0.02, HDI 0.95 = [−0.30, 0.30], main effect of satisfiability on performance, GLMM; Table A Model 5 in S1 Appendix ). Moreover, we found no significant interaction effect between TCC and satisfiability on performance ( β 0.5 = 0.26, HDI 0.95 = [−0.37, 0.90], interaction effect of TCC and satisfiability, GLMM; Fig 1b ; Table A Model 6 in S1 Appendix ). Besides studying and replicating previously reported effects of TCC and satisfiability on human performance, we replicated other key findings presented by Franco et al. [ 9 ] (see Section 3 in S1 Appendix ).

Finally, we investigated human performance in a set of related tasks. We explored the relation between performance in the knapsack tasks and core cognitive abilities, including working memory, episodic memory, strategy use, as well as mental arithmetic. For this analysis, we utilized the joined data set from this study together with data collected by Franco et al. [ 9 ]. Our results suggest a weak relation between these cognitive abilities and performance in the knapsack tasks. The only significant correlation (at α = 0.05) shows a link between mental arithmetic ability and performance in the knapsack optimization task (Section 5 in S1 Appendix ).

2.2 Imaging results

2.2.1 whole-brain analysis..

We conducted a whole-brain analysis of the neural correlates of two intrinsic generic properties of problems: TCC and satisfiability. Additionally, we investigated the neural correlates of response accuracy (Section 6 in S1 Appendix ). We did this by fitting GLMs that partitioned the solving stage into four separate periods (5.5 s) with an additional response stage modeled in the analysis (2 s).

Neural correlates of TCC.

We expected to find activation related to complexity in regions in which activation had previously been shown to be correlated with cognitive demand (i.e., multiple-demand system). We explicitly expected to find evidence for the encoding of TCC in the cingulo-opercular network (CON) from early on during the solving stage due to its link with cognitive demand as well as its link with expected performance and reliability. Higher TCC entails, on average, lower performance and lower reliability of finding the solution ( Fig 1b ). Note that the estimation of TCC early on in the trial is feasible because constrainedness (and thus TCC) can be potentially estimated by performing sum and division operations. Explicitly, dividing the target profit by the sum of values.

We found that the neural correlates of TCC varied throughout the duration of the solving stage ( Fig 2a , Table 1 ). Contrary to our expectations, we did not find significant correlations of TCC during the first period of the solving stage. Interestingly, during the second period we did find a set of clusters that showed higher BOLD activity on instances with low TCC. These regions include the angular gyrus (AG) bilaterally, the superior frontal gyrus (SFG), the right middle frontal gyrus (MFG) as well as regions in the orbitofrontal cortex (bilaterally). It is worth noting that the negative pattern found in this period might stem from a different slope in the increased task-related activation and not from differences in the sustained level of activity ( Fig 3 ). This pattern would align with previous results that support that the frontoparietal network (FPN) regions encode evidence accumulation towards a particular decision (see Discussion ).

(a) Brain activation effect estimates ( β ) for the high vs. low TCC contrast ( β highTCC − β lowTCC ). A positive contrast represents a higher BOLD activity on instances with high TCC compared to low TCC. Significant cluster-wise FWE-corrected ( p < 0.05) clusters (with an uncorrected threshold of p < 0.001) are presented for each of the contrasts estimated using the Boxcar analysis. Each panel represents a different period in the solving stage. No significant clusters were found for period S1 nor for the response stage parameters. (b) Brain activation effect estimates ( β ) for the unsatisfiable vs. satisfiable contrast ( β unsatisfiable − β satisfiable ). A positive contrast represents a higher BOLD activity on unsatisfiable instances. Significant cluster-wise FWE-corrected ( p < 0.05) clusters (with an uncorrected threshold of p < 0.001) are presented for each of the contrasts estimated using the Boxcar analysis. Each panel represents a different period in the solving stage. No significant clusters were found in the response stage.

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Mean effect estimate ( β ) for each ROI against time in trial. The effect at each time point represents the mean β FIR over all of the voxels from each ROI: right AI, dACC, and right IPS cluster extending to the angular gyrus. In the top row of panels, the β FIR ’s characterize the coefficients of an FIR regression with four conditions: satisfiability×TCC. The β FIR parameters are aligned to the BOLD signal, which has a lag with respect to the task time. To correct for this, the gray time-markers represent the task-events by assuming a 5-second BOLD signal lag. In the second row, the TCC contrast ( β high − β low ) is presented. The third row displays the satisfiability contrast ( β unsat − β sat ). The bottom row shows the interaction effect between TCC and satisfiability ([ β highTCC , unsat − β highTCC , sat ] − [ β lowTCC , unsat − β lowTCC , sat ]). Red asterisks represent significance at a 0.05 significance level. Significance levels in the gray shaded regions are suggestive only; they represent the time period and contrast from which the ROIs were selected.

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Significant cluster-wise FWE-corrected ( p < 0.05) clusters (using an uncorrected threshold of p < 0.001) from the High TCC—low TCC contrast. Coordinates are in MNI space.

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During the third period of the solving stage, the TCC contrast still showed significant clusters along the FPN, but the pattern overall changed, with respect to period S2. Critically, we found that a different set of regions within the FPN now showed a positive correlation with TCC. Specifically, we found positive clusters in the left SFG, left intraparietal sulcus (IPS), the cerebellum as well as a cluster in the right dorsolateral prefrontal cortex (dlPFC) in between the MFG and the SFG. Interestingly, the right AG kept on displaying a negative correlation with TCC during this period.

Finally, during the fourth, and last, period of the solving stage, a new set of clusters was identified. Markedly, this new set of clusters includes regions from both CON, FPN as well as significant clusters in the occipital lobe. In general, the activation in these clusters is correlated positively with TCC. The only two clusters that correlated negatively with TCC are those located in the ACC, as well as a cluster in the left SFG that overlaps with SFG cluster found in the second period.

Markedly, correlates of TCC on period four include the dACC and right anterior insula (AI) from CON as well as the precentral gyrus and IPS from FPN. The right IPS activation is segregated into two clusters, one medial and superior that overlaps with the precuneus and one more lateral that overlaps with the AG. These clusters were also found when using an alternative metric of complexity (instance complexity) that is closely related to TCC (see Sections 3 and 4 in S1 Appendix ).

We did not find any significant clusters during the response stage.

Neural correlates of satisfiability.

We expected the asymmetry between satisfiable and unsatisfiable instances to reflect differences in control signals associated with reliability (i.e., how much the result of a calculation can be relied on to be accurate). Specifically, we hypothesized that satisfiable instances would be associated with higher reliability, given that once a solution witness is found, verifying that the proposed solution is correct is a polynomial-time operation (tractable problem). In contrast, for unsatisfiable instances, verifying a proof of non-existence is conjectured to be intractable, and thus, computationally harder to verify.

Therefore, we expected regions that have been linked to monitoring of uncertainty to be more active during a trial with an unsatisfiable instance compared to a satisfiable one. In particular, we conjectured higher activation of the CON, on unsatisfiable instances, during late stages of the trial [ 25 – 28 ].

Interestingly, and contrary to our expectations, we found significant clusters from the first period of the solving stage ( Fig 2b , Table 2 ). Moreover, significant clusters did not extend to the response screen, which was also in opposition to our conjecture. Most of the clusters during the solving stage showed a lower BOLD activity for unsatisfiable instances. These clusters extended from period one to period four of the solving stage. Notably, the posterior cingulate showed a lower sustained activation on unsatisfiable instances throughout the solving stage (periods two, three and four). Similarly, different clusters in the SFG had significant clusters throughout the solving stage. Additionally, similar to the clusters found for the TCC contrast, the AG showed bilateral activation during the second period of the solving stage. Interestingly, a bigger AG cluster was found on the left hemisphere compared to the right, in contrast to the right laterality predominance of AG found in the TCC contrast.

Significant cluster-wise FWE-corrected ( p < 0.05) clusters (using an uncorrected threshold of p < 0.001) from the Unsatisfiable-Satisfiable contrast. Coordinates are in MNI space.

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The only two clusters that showed significantly higher activity on unsatisfiable instances were the right AI and the occipital superior cortex, both present only during period four of the solving stage. The significant cluster found in the AI is in line with our hypothesis that unsatisfiable instances are related to higher markers of uncertainty, a signal that we expected to find in the CON. However, in disagreement with our hypothesis, we did not find a significant satisfiability cluster in the dACC. This may be due to insufficient statistical power of the whole brain analysis (see Fig 3b ).

Neural correlates of accuracy.

Although participants did not receive any feedback during the task, we expected to see error-related signals late in the trial. Although these signals would not represent the integration of novel exogenous information (since there was no feedback), we conjectured that participants would hold a subjective belief of the expected accuracy (or reward) of their answer (e.g, [ 29 ]). In line with our hypothesis, we found that activity in both FPN and CON was positively correlated with erring during the response stage (Section 6 in S1 Appendix ).

2.2.2 ROI dynamics.

Three ROIs were selected (see Section 4.9.3) to investigate more closely the neural dynamics associated with computational complexity. We included in our analysis the dACC due to its proposed involvement in the allocation of control [ 30 – 35 ] as well as the right AI because of its involvement in encoding control signals and uncertainty in particular [ 25 – 28 ]. In order to compare the neural activity in these regions, which are generally attributed to control, with relevant processing units, we selected a region associated with mathematical calculations, the right IPS [ 36 – 38 ].

We explored the BOLD effect estimates ( β FIR ) for the 2×2 balanced factorial design (satisfiability×TCC) employing Finite Impulse Response (FIR) analysis at a two-second resolution (see Section 4.9.4). We found similar patterns in AI and dACC. In both regions, the BOLD signal rose throughout the task and quickly decreased around the time the solving stage ended ( Fig 3 ). The activity pattern in the IPS showed a different pattern to that of CON regions. In this region, the BOLD signal increased quickly early on in the trial and was sustained until it started decreasing later on in the trial. The moment at which the decrease started was modulated by TCC and satisfiability ( Fig 3 ).

We were also interested in studying the interaction effect between TCC and satisfiability. Conceptually, we predicted an interaction effect between complexity and proof hardness. This follows from the definition of proof hardness, which relates to the length of verifying a valid proof (be it proof of existence or proof of non-existence). Consequently, proof hardness is only directly informative for cases in which a participant has found (the correct) solution to verify. This entails that in instances where finding a valid witness is harder (e.g., high TCC), the effect of proof hardness should be lower on average. Specifically, we expected that instances with high TCC would have a lower differential effect on BOLD activity between unsatisfiable and satisfiable instances. This is exactly what we found on all three ROIs, although this effect was only consistently significant in the AI and IPS ( Fig 3 ; fourth row of panels).

When contrasting the effect of TCC in each of the ROIs, we find that there is a significant positive effect of TCC from mid-way through the trial in the right IPS/AG ( Fig 3 second row of panels). This differs from the results obtained in the whole brain analysis. Similarly, when estimating the effect of satisfiability ( Fig 3 ; third row of panels), the results marginally differ from those of the whole-brain analysis. Firstly, the ROI analysis reveals that there is an effect of satisfiability on all three regions late in the solving-stage. Secondly, the effect of satisfiability starts in the AI and dACC mid-way through the trial. Interestingly, the effect of TCC seems to precede that of satisfiability in the IPS, whereas in the dACC the effect of satisfiability seems to precede that of TCC.

Altogether, these results suggest that both satisfiability and TCC correlate with activity in all three regions, but that their effect might have different temporal signatures. Importantly, the sign of the effect was in line with our hypothesis: a higher signal in these regions was generally related to higher TCC and unsatisfiability. The only exceptions happen briefly early on in the trial.

Finally, we explored the interaction between neural markers of accuracy and the proposed metrics of computational difficulty. We first analyzed the interaction effect between correctness and TCC on neural dynamics. We found that for instances with low TCC, there was a significant effect of correctness of the instance from early on in the trial in the IPS. Similarly, midway through the trial a significant accuracy neural marker appeared in the AI for instances with low TCC ( Fig 4 ; top panels). This effect was mainly due to a significantly lower BOLD signal on incorrect instances with low TCC. Similarly, when studying the interaction effect between correctness and satisfiability we found a consistent significant effect of accuracy but only during satisfiable instances in the IPS, which was driven, as well, by a lower BOLD activity on incorrect instances ( Fig 4 ; bottom panels). Importantly, this significant contrast showed from the moment the trial started.

Mean effect estimate ( β ) of each ROI against time in trial. The effect at each time point represents the mean β FIR over all of the voxels from each ROI: right AI (a) , dACC (b) , and right IPS cluster extending to the angular gyrus (c) . The β FIR ’s characterize the coefficients of an FIR regression with four conditions: accuracy×TCC in the top panels, and accuracy×satisfiability in the bottom panels. The β FIR parameters are aligned to the BOLD signal, which has a lag with respect to the task time. The gray vertical lines represent the task events assuming a 5-second BOLD signal lag. Below the mean ROI effects, the second and fourth rows of figures show the accuracy contrasts ( β correct − β incorrect ) for different levels of TCC or satisfiability. Red stars represent significance at a 0.05 significance level.

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Overall, our results suggest a link between neural markers of accuracy and metrics of computational difficulty. This relation was particularly evident in the IPS and marginally in the AI. Importantly, the differential effects of accuracy in the IPS showed from early on in the trial, suggesting that for instances associated with low computational difficulty (i.e., low proof hardness and low complexity), the accuracy could be predicted from early on in the trial from BOLD activity in the IPS.

2.2.3 Connectivity analysis.

The results so far implicate a dynamic collection of brain regions that correlate with different properties of the target computational problem at different stages of deliberation. An important open question that remains is how these regions coordinate with each other to orchestrate the intricate sequence of computations to solve the knapsack problem. In order to shed light on this coordination of computations, we studied how connectivity changes throughout the problem-solving task and how these fluctuations in connectivity relate to computational difficulty (details in Section 7 in S1 Appendix ).

We first studied the effect of TCC and satisfiability on functional connectivity . To do this, we conducted a PPI analysis to gauge the functional synchronization between each of the ROIs and other regions in the brain. Explicitly, we performed whole-brain PPI analyses employing the three considered ROIs (dACC, rAG and rAI) as seed regions. For these regressions, we modeled the task (items and solving stages together) with two boxcar functions of equal length (12.5s) (Fig G in S1 Appendix ). This allowed us to study PPI task interactions separately for an early period (PPI-1: first 12.5 seconds of the task) and a late period (PPI-2: last 12.5 seconds). We found a similar and generalized pattern of connectivity for all three ROIs and both periods when contrasting the PPI effect compared to baseline (Fig F in S1 Appendix ). This suggests that the task has a similar effect on the BOLD synchronization between the three ROIs and several regions.

When comparing the connectivity between instances with high and low TCC, we found one significant cluster with differential connectivity. This cluster, located along the rAG and the supramarginal gyrus, showed a change in connectivity to the rAI (seed region) between high and low TCC instances during the second PPI period (Fig Ga and Table F in S1 Appendix ). We also explored the differences in the PPI connectivity between unsatisfiable and satisfiable instances. We observed a significant PPI effect of satisfiability between the right IPS/AG (seed) and the left MFG, as well as with the left AG, during the second PPI period (Fig Gb and Table F in S1 Appendix ). Overall, these results suggest that instance properties have an effect on the synchronicity between the ROIs and a limited collection of clusters. However, this effect is only significant during the later part of the solving stage. PPI analysis, however, only explores temporal connectivity. A closer inspection of the time courses in Fig 3 suggests that there may be inter-temporal relationships in activation. We turn to a study of those next.

Critical for this study, we expected the underlying neural processes of problem-solving to be internally driven. Specifically, we expected the connectivity patterns to be linked to neural processes whose timing could vary stochastically across trials and participants (e.g., the burst of neural activity does not have to coincide with an experimental intervention such as the initial display of items). In order to explore this inter-temporal connectivity (i.e., effective connectivity ), we performed a Granger Causality (GC) analysis on the BOLD signal in these three ROIs.

We found that, throughout the experiment, there was bi-directional effective connectivity between dACC, AI and IPS (see Fig H in S1 Appendix ). Additionally, during the solving stage, we found that there was a significant change in GC from dACC to rAG. However, we did not find any significant changes in the effective connectivity between high and low TCC instances nor between unsatisfiable and satisfiable instances. Notice, however, that Granger causality only measures intertemporal correlation but not intensity. For instance, even if communication flow from, say, dACC to, say, IPS increases as a function of TCC, this will not translate into increased correlation as long as activation attributed to dACC itself increases as a function of TCC (as in Period S4 of the solving stage; see Table 1 ). Taken together, these results suggest that the effects of TCC and satisfiability on neural activity propagate through the ROIs via baseline effective connectivity (present during the solving stage) and not through a direct effect on the effective connectivity.

3 Discussion

The study of the neural underpinnings of problem-solving has, to date, been centered on tractable problems. This line of research has led to the characterization of networks and processes that support problem-solving. A critical shortcoming of existing studies, however, is the absence of a generic theoretical framework to study the neural underpinnings of problem-solving that can be extended to intractable problems. Here, we present a framework, grounded in computational complexity theory, to study the neural underpinnings of problem-solving that overcomes previous limitations. Importantly, this theoretical framework can be applied across tasks and without knowledge of the cognitive strategies employed.

We empirically test this framework in the knapsack decision task using ultra-high field fMRI. Our findings shed light on the neural processes supporting problem-solving. Firstly, our findings not only extend but solidify the research on the neural correlates of cognitive demand by exploring the processes associated with one specific dimension of cognitive demand: computational complexity. Importantly, this is done in a task-independent way in the sense that these metrics can be applied to a whole class of problems (i.e., NP-complete). Secondly, rather than studying cognitive demand starting from “what people are thinking,’’ we rely on the theory of computational complexity to identify intrinsic properties of a problem to delineate cognitive requirements. These intrinsic properties allowed us to discover relevant neural markers and their dynamics, similar to how risk and variance have been shown to affect decisions in probabilistic tasks [ 6 ]. Finally, the results presented provide evidence in support of the theoretical framework put forward here, which can contribute to the study of cognitive control, especially in those tasks that involve intractable problems. Critically, cognitive control involves the dynamic allocation of cognitive resources that stem from an interaction between the cognitive requirements of a task and the resources available. The framework presented here provides a theoretical foundation for the characterization of cognitive requirements that can be applied to intractable problems, which are generally understudied in the field of cognitive control.

Extensive research has studied the neural correlates of cognitive demand. This program has characterized the multiple-demand system, a network of regions that respond robustly to cognitive demand regardless of the task at hand [ 18 – 21 ]. This has been done using several tasks including perceptual target detection and memory retrieval, among many others. Notably, most of the tasks employed to date have been based on tractable problems. Moreover, many of the tasks modulate the cognitive demand of the task by tuning the amount of processing needed on one specific dimension of cognitive processing. For instance, in perceptual tasks, signal to noise ratio is modulated [e.g., 8 , 7 , 39 , 40 ]; in memory retrieval tasks, the amount of information to be stored/retrieved is tuned [e.g., 18 , 41 ]. The lack of a generic (problem-independent) definition of cognitive demand hinders the generalization of this approach to new problems. Here, we propose a way forward, grounded in the assumption that hardness is, at least partially, an intrinsic characteristic of the problem at hand, which can be studied across tasks employing an overarching theoretical framework.

Following this approach, we operationalized cognitive demand via TCC and found that the neural correlates of TCC overlapped with those associated with the multiple-demand system. In particular, the positively correlated clusters (higher activation in high TCC instances) in the FPN and CON resembled those of the multiple-demand system. Notably, we found clusters in the AI, the dACC, the precentral gyrus and the IPS, which have been associated with the multiple-demand system [ 18 ]. Importantly, our results display a dynamic process in which the neural correlates of TCC vary throughout the different stages of the task. This suggests that the multiple-demand system can be construed as a heterogeneous set of regions that play a dynamic and varying role at different stages in problem-solving.

It is worth highlighting that we are not arguing for the proposed framework to replace other methodological approaches in the study of cognitive demand. Instead, we assert that both approaches complement each other. Critically, complex tasks involve the interplay of several computational processing units such as working memory, logical operations, processing of numerical magnitudes among many others. Our approach, as it stands, is not able to differentiate among these sub-processes. A proper understanding of problem-solving requires both the study of these sub-processes independently, like in more classical approaches [e.g., 41 ], as well as in tandem in order to understand how they interact to support computationally hard problem-solving, as done in this study.

A related effect of these properties on neural processes is through the encoding of relevant task markers that could be employed during problem-solving [ 3 , 42 ]. These neural markers include markers of performance such as expected error [ 25 , 26 ], variance in this expectation (uncertainty) [ 25 – 27 ], as well as markers that encode the evidence towards a particular response [ 7 , 43 ] or even the merit of alternative strategies [ 29 , 44 ]. Critically, we made three conjectures with regards to these neural markers. First, we hypothesized to see markers of performance, related to TCC, from early on in the trial. Second, we conjectured we would see markers of reliability (i.e., how much can the result of a calculation be relied on to be accurate), related to satisfiability, in regions shown to encode uncertainty. Third, we expected to find neural correlates of accuracy late in the trial, which would be associated to expected performance.

With regards to our first hypothesis, we argue that TCC is a feasible metric that can be related to markers of performance and efficacy of effort from early on in the trial. Firstly, TCC has been shown to be correlated with human performance [ 9 ]. Secondly, TCC can be potentially estimated from early on in the solving stage without the need to know the solution to the problem. Indeed, TCC could be estimated by performing a straightforward summation followed by a division (add all item values and divide the result by the target profit). As such, we expected to see neural correlates of TCC from early on in the trial. Specifically, we expected to see markers of TCC from early on in the solving stage in the CON [ 26 , 27 , 30 ]. Contrary to our expectations, we only found significant clusters in the CON starting from the third period of the solving stage. These might reflect markers of expected performance, but other explanations cannot be excluded. For instance, this effect might reflect differences in time-on-task between TCC conditions [ 45 ]; indeed, previous work has shown that TCC affects time-on-task in other computational problems [ 10 ]. This explanation, however, would still allow these activation patterns to represent differences in neural markers such as reliability and expected performance. This follows from the fact that time-on-task is an endogenous variable of the system. That is, the agent decides when to stop reasoning about the problem, and as such, this decision would likely follow from a subjective belief on how well they can expect to perform given the current candidate solution. Therefore, differences in time-on-task between high and low TCC instances may be related to differences in subjective beliefs of both expected performance and reliability. Future work is needed to explore how and when people decide to stop deliberating, as well as the role of computational difficulty in this process.

In addition to the reported clusters that correlated positively with computational complexity, we found a set of clusters that correlated negatively with TCC. These clusters are concentrated in the second period of the solving stage, but are also found in the third and fourth periods of the solving stage. These results might be explained by the encoding of evidence accumulation signals [ 7 , 43 ]. Arguably, evidence toward a solution can be accumulated faster in low TCC compared to high TCC instances. This follows directly from the theoretical prediction that the time needed to reach the solution is, on average, higher for instances with high TCC than low TCC. The difference in rate accumulation would imply that regions that encode evidence accumulation would show a higher activation on low TCC instances early in the trial, in accordance with the pattern found in the second period of the solving stage.

Turning now to our second conjecture regarding the neural markers of reliability, we explored the correlates of satisfiability during problem-solving. We expected to see activation related to satisfiability in regions previously associated with uncertainty encoding, specifically in the CON. In line with our hypothesis, we found a significant positive relation between unsatisfiability and activity in the CON that started halfway through the solving stage. In line with our conjecture, we found that the neural markers of satisfiability overlap with regions that encode probabilistic uncertainty. This suggests that reliability and uncertainty might constitute analogous constructs that are encoded similarly across tasks and that could serve a generic role in decision-making. While our findings provide a potential explanation for the observed neural activity, further work would be needed to categorically connect these constructs across tasks. The CON is associated with a multitude of cognitive processes, and the activity we observed could be linked to any number of these. Therefore, our interpretation, while supported by our data, should not be seen as definitive. Further research is necessary to connect these constructs across various tasks definitively and to explore other potential explanations for the observed neural activity.

Contrary to our expectations, we found several regions that displayed an increase in activity during satisfiable instances from early on in the solving stage. This result is perplexing because knowing the satisfiability of the problem equates to having solved the problem, which would not be expected early on in the trial. A possible explanation for this is that the clusters found encode evidence accumulation [ 7 , 43 ] and that accumulating evidence towards the solution in satisfiable instances occurs at a different rate than in unsatisfiable instances. However, this is not directly supported by theory. The computational difficulty of finding a solution is determined by TCC, and the selection of instances in this study ensured that TCC remained balanced between satisfiable and unsatisfiable instances. This entails that, on average, the expected level of complexity (and evidence accumulation rate) would be the same for both satisfiable and unsatisfiable instances. Alternatively, these activation patterns might reflect the use of different strategies. For example, if an individual predicts that a given instance could potentially be satisfiable, they could search for a subset of items that meets the defined constraints. However, if the perception is that the given instance might be unsatisfiable, then the individual may start a search for proof of infeasibility, like verifying (in an extreme case) whether fitting even a single item into the knapsack is impossible due to all the item weights surpassing the allowed weight capacity. However, this account would still require participants to implement different strategies, based on satisfiability, as early as during the first few seconds of the solving stage. Overall, future research should attempt to disentangle the effect of proof hardness from that of satisfiability and complexity. This could be done, for instance, through experiments aimed at testing more nuanced metrics of proof hardness beyond worst-case complexity classes.

Moving on now to consider our conjecture related to the neural markers associated with erring, we explored the effect of accuracy on neural activation throughout the task. It has been proposed that FPN and CON regions encode task signals related to error detection and error expectation [ 25 , 27 , 31 ]. We hypothesized that participants would represent a subjective belief on the expected accuracy (or reward) of their answer (e.g, [ 29 ]). In line with our conjecture, we found that activity in both the FPN and CON was positively correlated with erring during the response stage, even in the absence of feedback, as was the case in our design (Section 6 in S1 Appendix ).

A puzzling finding in this regard is the fact that neural correlates of accuracy are identified early on in the trial in the ROIs, especially in instances with low computational difficulty (i.e., low proof hardness and low complexity). One possible explanation for this is attentional engagement on the task. If a participant does not actively engage in the task, they are more likely to have an incorrect solution. In turn, the likelihood of reaching an incorrect answer due to inattention is higher among instances with low computational difficulty. Together, these patterns would partially explain the marked difference in BOLD activity between correct and incorrect trials in the IPS. However, other alternative explanations are possible. Further work is needed to fully identify the dynamics of effort and attention allocation in computationally complex tasks.

Overall, we found evidence that suggests the existence of neural markers related to computational complexity, proof hardness and performance. Taken together, the framework put forward here provides a way to study neural markers associated to subjective beliefs during problem-solving. It is worth noting, however, that while we modulated complexity and proof hardness, many other complexity-related features might be relevant, including, for example, the size of the problem at hand [e.g., 46 – 51 ]. Further work in this area is needed to understand the interaction between different sources of computational difficulty in human problem-solving.

Finally, to explore the dynamics related to control during complex problem-solving, we analyzed the functional interaction during problem-solving of three ROIs, two of which have been associated with cognitive control (i.e., CON) and one region which has been associated with processes that were deemed highly relevant for the task at hand (i.e., IPS). We studied synchronization of signals (employing PPI analysis) and explored their effective connectivity (using GC analysis).

Our results support the view that there is a generalized change in signal synchronization during the solving stage compared to baseline. Moreover, when exploring the link between instance properties and synchronicity between regions, we found several clusters whose connectivity was modulated by either satisfiability or TCC. These effects were only present late in the trial. Specifically, we found that TCC modulated the synchronicity between the rAI and the rIPS. Additionally, satisfiability modulated the functional connectivity between the right IPS and two clusters in the left hemisphere, one in the AG and one in the MFG. Overall, these results suggest a differential recruitment of regions during the task, partially modulated by task properties late in the trial. Interestingly, the significant clusters identified in this analysis have been implicated in the performance of mathematical calculations [ 38 , 52 ], suggesting that they could support moment-to-moment implementation of strategies. Further work would be needed in order to assess whether the relation, found here, between instance properties and functional synchronization is associated to the implementation of different strategies.

Humans are constantly solving problems that vary in complexity, ranging from perceptual tasks, such as motion detection and face recognition, to reasoning tasks, such as choosing an investment portfolio. Understanding how the complexity of these problems affects the neural processes involved in problem-solving is of crucial importance for the understanding of human decision-making. Here, we present a framework that allows for the study of the computational difficulty of human problem-solving. We applied this framework and identified a dynamic set of regions in which activation was modulated by different properties related to computational complexity. Overall, our findings provide support to the premise that computational complexity theory, as applied here, provides a useful characterization of cognitive demand and reliability for the study of problem-solving in neuroscience.

4 Materials and methods

4.1 ethics statement.

The experimental protocol was approved by the University of Melbourne Human Research Ethics Committee (Ethics ID 1749616.3). Written informed consent was obtained from all participants prior to the commencement of the experimental sessions. Experiments were performed in accordance with all relevant guidelines and regulations.

4.2 Participants

Twenty right-handed volunteers from Melbourne University and the surrounding community took part in the study (14 female, 5 male, 1 other; age range = 18–35 years, mean age = 26.6 years). Inclusion was based on age (minimum = 18 years, maximum = 40 years) and on right-handedness. Each participant performed the knapsack decision task in the scanner and performed outside the scanner the knapsack optimization task and a set of basic cognitive function tasks.

4.3 Knapsack decision task

In this task, participants were asked to solve a number of instances of the (0–1) knapsack decision problem ( Fig 1a ). In each trial, they were shown a set of items with different values and weights, as well as a capacity constraint and a target profit. Participants had to decide whether there exists a subset of those items for which (1) the sum of weights is lower or equal to the capacity constraint and (2) the sum of values yields at least the target profit.

Each trial had four stages. In the first stage (items stage; 3 seconds), only the items were presented. Item values, in dollars, were displayed using dollar bills and weights, in grams, were shown inside a black weight symbol. The larger the value of an item, the larger the dollar bill was in size. Similarly, the larger the weight of an item, the larger its weight symbol was in size. At the center of the screen, a green circle indicated the time remaining in this stage. In the second stage (solving stage; 22 seconds), target profit and capacity constraint were added to the screen inside the green timer circle. In the third stage (response stage; 2 seconds), participants saw a ‘YES’ and a ‘NO’ button on the screen, in addition to the timer circle, and made a response using the keyboard ( Fig 1a ). Finally, a jittered inter-trial rest period of 8, 10 or 12 seconds was shown before the start of the next trial.

Participants completed 56 trials (7 blocks of 8 trials), each showing a different instance of the knapsack decision problem. The order of instances was randomized across participants. The side of the ‘YES’ and ‘NO’ buttons was also randomized.

4.4 Complexity, proof hardness and instance sampling

We modulate proof hardness using insights from canonical computational complexity classes. For NP-complete problems (like the knapsack decision problem), this theory predicts that it is easier to prove that a solution is correct if the instance is satisfiable than if it is unsatisfiable. For example, in the case of the knapsack, for a satisfiable instance (the correct choice is ‘yes’), it suffices to find a subset of items that satisfies the weight capacity and value constraints. Subsequently, verification that this subset of items satisfies the constraints can be done in polynomial time. In contrast, to confirm that an instance is unsatisfiable (the correct choice is ‘no’) requires proving that no subset of items exists that satisfies the constraints. It is conjectured and broadly accepted that verifying such a proof is not in P (the polynomial time complexity class). Theoretically, the asymmetry reflects the conjectured null intersection between complexity classes NP-complete and co-NP-Complete ( Fig 5 ).

The knapsack decision problem belongs to the class NP-Complete (NPC) because it satisfies the dual-qualifying criteria of NP and NP-hard. It is NP, given that it fulfills the NP defining condition: a YES-certificate of a satisfiable instance can be verified in Polynomial Time (P). It is NP-hard since it is at least as hard as any other problem in NP. It is conjectured that P≠NP, which entails that the NPC problems are not solvable in Polynomial time (i.e., they are harder and require more computational resources—time—to solve than problems in P). Within the class of NPC problems, there are instances that are harder than others. A key discriminator factoring instances by the respective computational resources needed for their resolution is their Typical-case Complexity (TCC). The class noted as co-NP-Complete (co-NPC) comprehends problems such as the co-knapsack. The aim of this problem is to determine if the existence of a subset of items that satisfy the constraints is infeasible. Every satisfiable knapsack instance has a counterpart unsatisfiable co-knapsack instance. It is conjectured that co-NPC is not in NP, thereby implying that verifying a proof of non-existence for an unsatisfiable knapsack instance is not in P; it is harder.

https://doi.org/10.1371/journal.pcbi.1012447.g005

Instances were sampled following a 2×2 balanced factorial design ( Fig 6 ) for the factors TCC (high and low) and satisfiability (satisfiable and unsatisfiable). Specifically, instances selected were sub-sampled from those employed in a previous behavioral study [ 9 ]. Instances in their study were selected such that α c was fixed ( α c ∈ [0.40, 0.45]) and the instance constrainedness varied according to α p . 18 satisfiable instances were selected from the under-constrained region ( α p ∈ [0.35, 0.4]; low TCC ) and 18 unsatisfiable instances from the over-constrained region ( α p ∈ [0.85, 0.9]; low TCC ). Note that, by definition, sampling from the underconstrained region is unlikely to generate unsatisfiable instances, and analogously, sampling from the overconstrained region is unlikely to generate satisfiable instances. We leveraged this fact to obtain a balanced design in which half of the instances were satisfiable and half unsatisfiable. Additionally, 18 satisfiable instances and 18 unsatisfiable instances were sampled near the satisfiability threshold ( α p ∈ [0.6, 0.65]; high TCC ). Half of the instances with high TCC were forced to have high/low computational requirements (top/bottom 50%), according to an algorithm-specific ex-post complexity measure of a widely-used algorithm (Gecode [ 53 ]). All instances in the experiment had N = 6 items and w i , v i , c and p were integers.

Instances were sampled using a 2x2 factorial design, ensuring that each participant answered an equal number of instances for each of the four possible categories of TCC and Proof Hardness. Each category presents a distinct profile of proof hardness (the computational difficulty of validating a solution) and complexity (the computational difficulty of solving the instance).

https://doi.org/10.1371/journal.pcbi.1012447.g006

In the current study, we randomly selected 56 of the 72 instances sampled in Franco et al. [ 9 ]. Sub-sampling without replacement was done ensuring that the same number of instances were selected across TCC and satisfiability conditions. Moreover, instances with high TCC were balanced to require high/low computational requirements according to the same algorithm-specific complexity measure employed in their study (i.e., Gecode propagations).

4.5 Complementary tasks

Participants were presented with a set of complementary tasks outside of the scanner. They were asked to solve a number of instances of the (0–1) knapsack optimization problem. Similar to the knapsack decision task, participants were shown a set of items with different weights and values as well as a capacity constraint. However, unlike the decision variant, no target profit was presented. Participants had to find the subset of items that maximized total value subject to the capacity constraint (see Section 3 in S1 Appendix ).

We also tested participants’ performance on five aspects of cognitive function that we considered relevant for the knapsack tasks, namely, working memory, episodic memory, strategy use, processing and psychomotor speed, as well as mental arithmetic. To do so, we administered a set of tasks from the Cambridge Neuropsychological Test Automated Battery (CANTAB; see Section 5 in S1 Appendix ). Specifically, we asked participants to perform the Reaction Time (RTI), Paired Associates Learning (PAL), Spatial Working Memory (SWM) and Spatial Span (SSP). In addition, participants were presented with a set of mental arithmetic problems (Section 5 in S1 Appendix ).

4.6 Procedure

Participants were asked to fill in an MRI screening form before attending the experiment. Once at the experiment, participants were presented with a plain language statement and a consent form. After reading these and providing written informed consent, participants were instructed in the tasks and completed a practice session of the knapsack decision task. Participants then underwent an MRI safety check and debriefing.

Before being scanned, participants solved the CANTAB RTI task outside of the scanner. This was followed by the scan session in which they performed the knapsack decision task. Afterwards, outside of the scanner, they completed the CANTAB RTI task again, followed by the knapsack optimization task. Subsequently, they completed the remaining CANTAB tasks in the following order: PAL, SWM and SSP. Finally, they performed the mental arithmetic task and completed a set of demographic and debriefing questionnaires. Altogether, the experimental session lasted around three hours.

Participants received a show-up fee of A$10, as well as monetary compensation based on performance. They earned A$1.2 for each correct answer in the knapsack decision task and for each correct answer in the knapsack optimization task.

4.7 Behavioral statistical analyses

The R programming language was used to analyze the behavioral data. All of the linear mixed models (LMM), generalized logistic mixed models (GLMM) and censored linear mixed models (CLMM) included random effects on the intercept for participants (unless otherwise stated). Different models were selected according to the data structure. GLMM were used for models with binary dependent variables, LMM were used for continuous dependent variables and CLMM were used for censored continuous dependent variables (e.g., time-on-task).

All of the models were fitted using a Bayesian framework implemented using the probabilistic programming language Stan via the R package ‘brms’ [ 54 ]. Default priors were used. All population-level effects of interest had uninformative priors; i.e., an improper flat prior over the reals. Intercepts had a student-t prior with 3 degrees of freedom and a scale parameter that depended on the standard deviation of the dependent variable after applying the link function. The t-student distribution was centered around the mean of the dependent variable. Sigma values, in the case of Gaussian-link models, had a half student-t prior (restricted to positive values) with 3 degrees of freedom and a scale parameter that depended on the standard deviation of the dependent variable after applying the link function. Standard deviations of the participant-level intercept had a half student-t prior that was scaled in the same way as the sigma priors.

Statistical tests were performed based on the 95% credible interval estimated using the highest density interval (HDI) of the posterior distributions calculated via the R package ‘parameters’ [ 55 ]. For each statistical test we report both the median ( β 0.5 ) of the posterior distribution and its corresponding credible interval ( HDI 0.95 ).

No participant nor trial was excluded from the data analysis of the knapsack decision task.

4.8 MRI data acquisition

We collected the fMRI images using a 7 Tesla Siemens MAGNETOM scanner located at the Melbourne Brain Centre (Parkville, Victoria) with a 32-channel radio frequency coil.

The BOLD signal was measured using a multiband echo-planar imaging sequence (TR = 800 ms, TE = 22.2 ms, FA = 45°). We acquired 84 interleaved slices (thickness = 1.6 mm, gap = 0 mm, FOV = 208 mm, matrix = 130x130, multi-band factor = 6, voxel size = 1.6 × 1.6×1.6mm 3 ) per volume. 380 volumes were acquired on each run while recording cardiac and respiratory traces.

After five functional runs (one resting state run followed by four task runs), a high resolution (0.7 mm isotropic) anatomical image was acquired using an MP2RAGE pulse sequence (TR = 5000 ms, TE = 3.07 ms, TI1 = 700ms, FA1 = 4°, TI2 = 2700ms, FA1 = 5°, matrix = 330×330, voxel size = 0.73×0.73×0.73mm 3 , FOV = 240 mm, 224 slices, slice thickness = 0.73). Afterwards, another three functional runs were performed, followed by a diffusion weighted imaging (DWI) multi-band sequence (TR = 7000 ms, TE = 72.4 ms, FA = 90°, FoV = 210 mm, matrix = 170x170, slice thickness = 1.24, voxel size = 1.24 m 3 , 128 slices, multi-band factor = 2).

4.9 Imaging statistical analyses

4.9.1 preprocessing..

Initial preprocessing of the data was performed using AFNI [ 56 ] and the Advanced Normalization Tools (ANTs) software. For each subject, pulse and cardiac noise was regressed out from the functional scans. These were then slice-time corrected and the volumes were motion-corrected by registering them to the first volume of the first functional run. The mean image of the first run was co-registered to the anatomical scan (down-sampled) and this transformation was applied to all of the functional volumes. Afterwards, each participant’s anatomical scan was used for calculation of transformation parameters to normalize the functional images into the Montreal Neurological Institute (MNI) space (see Section 1 in S1 Appendix for more details).

4.9.2 Whole-brain analysis (boxcar).

Whole-brain analyses were performed by fitting generalized linear models (GLM) using AFNI [ 56 ]. Before the regressions were implemented, we spatially smoothed the functional volumes with a 4.8mm FWHM Gaussian kernel. Additionally, volumes with motion or signal outliers were censored from each of the regressions.

Group level analyses were performed using mixed effects multilevel modeling [ 57 ]. All whole-brain analysis results are reported with a clusterwise threshold of p < 0.05 corrected for multiple comparisons across the whole brain, using an uncorrected voxelwise threshold of p < 0.001.

4.9.3 ROI specification.

We were particularly interested in how control and subjective beliefs of cognitive demand and reliability were involved in complex problem-solving. To study these dynamic processes we selected three regions of interest (ROIs) that have been implicated in the processes of interest. Firstly, we included in our analysis the CON (dACC and AI) due to its proposed involvement in the allocation of control [ 30 – 35 ] and uncertainty encoding [ 25 – 27 ], which we conjectured would be highly related to encoding of reliability. Secondly, we included a region that has been involved in moment-to-moment processing operations during problem-solving. We expected the knapsack task to engage processing units associated with number processing and mathematical calculations. Therefore, we selected a region that has been widely connected to ‘processing’ in mathematical problem-solving, the right IPS [ 36 – 38 ].

The three ROIs were selected from the clusters found when contrasting high and low TCC in the last boxcar during the solving stage (period S4). We chose the contrast for the fourth boxcar for a few reasons. We expected that during this last period of the solving stage we would be able to see a marked differentiation in the cognitive demand between instances with high and low TCC. We expected instances with low TCC to require less computational time and thus, we hypothesized that, on average, participants would be still making calculations during the period S4 for high TCC instance, but not for low TCC instances. This was further indicated by a parallel pilot study that found that participants spent on average 17.9s solving an instance with low TCC and 21.2s on those with high TCC (period S3 ends at 19.5s of solving stage). Importantly, we believed that these differences in cognitive demand would be reflected as well in a differentiation in the control activity in the system. Critically, we expected the monitoring of control variables such as expected performance would differ between types of instances. For instance, we expected the subjective markers of performance would converge to actual performance levels in the late stages of the solving stage ([ 9 ]; Fig 1 ), which would imply higher subjective beliefs of expected performance for low TCC. Additionally, we expected that this contrast would allow us to control for task-set signals [ 23 ]. We conjectured that the task-set signals would be maintained during the whole solution-stage, so the proposed contrast would not capture task-set signals encoding goals nor the underlying structure of the task.

Among the significant clusters found around the right IPS, we chose the IPS (AG) cluster (peak: x = 32, y = -65, z = 47) because of its overlap with the regions that were found to be associated with mathematical calculations in a meta-analysis [ 38 ].

4.9.4 ROI temporal dynamics.

We explored the dynamics in these ROIs by fitting generalized linear models (GLM) using AFNI [ 56 ]. Analogous to the whole brain GLM analysis (i.e., boxcar analysis), we spatially smoothed the signal and censored outliers from the regression. In this case, in contrast to the whole brain analysis GLMs, we modeled the trial time using a Finite Impulse Response (FIR) approach, in which each trial was modeled using 17 simple basis functions (tents).

This approach allowed us to take advantage of the short TRs (0.8s) used for the functional acquisition sequence, which were possible due to the ultra-high-field MRI used in the experiment. Modeling the BOLD signal using FIR allowed us to obtain 17 beta estimates β FIR for each voxel for each of the conditions considered. Note that these estimates model the hemodynamic response directly and, therefore, they do not factor in the lag of the BOLD signal. In order to link each β FIR to a time in the task, we assumed a lag of 5 seconds in the hemodynamic response.

We obtained a 2×2 β FIR -estimates for the factors TCC (high and low) and satisfiability (satisfiable and unsatisfiable). We explored the dynamics of each ROI by estimating the average β FIR over all of the voxels from each ROI for each condition. The ROI signal aggregation was performed using python 3.7 and the nilearn library.

Supporting information

S1 appendix. supplementary methods and results..

https://doi.org/10.1371/journal.pcbi.1012447.s001

Acknowledgments

The authors would like to acknowledge Rebecca Glarin and Scott Kolbe for their assistance in the planning and successful execution of the MRI scans.

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What is Problem Solving? (Steps, Techniques, Examples)

What Is Problem Solving?

Problem-Solving Steps

Defining the Problem

Generating Solutions

Evaluating and Selecting Solutions

Implementing and Monitoring the Solution

Problem-Solving Techniques

Brainstorming

Root Cause Analysis

SWOT Analysis

Mind Mapping

Examples of Problem Solving in Various Contexts

Effective Decision Making Techniques for Every Situation

What is a Decision Making Technique?

6 Decision Making Techniques for Better Decisions

​​1. Pugh Matrix

Brainstorming

The Heuristic Method

Tiered Voting

SWOT Analysis

Game Theory

Scenario Planning

Priority Matrix

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What is decision-making?

What are the benefits of using decision-making techniques?

Make sure all voices are heard

Pave the way for easy implementation

Reduce uncertaint y

Increase trust

Better decisions!

The most effective decision-making techniques

Decision-making techniques for ranking and prioritization

Impact and Effort Matrix

How-Now-Wow Matrix

20/20 Vision

Cost Benefit Analysis

The 100$ Test

Decision-making techniques that mitigate the risk of groupthink

The six thinking hats

Affinity Map

Decision-making techniques to converge upon a solution

Agreement-Certainty Matrix

Let’s Check Resistance

Feedback Frames

Gradients of Agreement

Fist to Five

Closing activities to turn a decision into action

Start, Stop, Continue

Backcasting

3 Action Steps

15% Solutions

Training activities to learn about decision-making

Delegation levels

Escape hopeland

Decisions, decisions

The trolley dilemma

The cushions game

Activity flows designed for taking collective decision making

Lighting Decision Jam

Sociocratic “Consent” Decision Making

How to Facilitate a Quarterly Planning Process (detailed guide)

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Problem Solving and Decision Making: Key Differences & Applications

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What do you understand by Decision Making?

Understanding Problem Solving

What are the differences between Problem Solving and Decision Making?

1) Definition

2) Objective

3) Nature

4) Process

5) Tools and techniques

6) Skills required

1. Pugh Matrix