sentences for problem solving

26 Expert-Backed Problem Solving Examples – Interview Answers

Published: February 13, 2023

Interview Questions and Answers

Actionable advice from real experts:

Biron Clark

Former Recruiter

Contributor

Dr. Kyle Elliott

Career Coach

Hayley Jukes

Editor-in-Chief

Biron Clark , Former Recruiter

Kyle Elliott , Career Coach

Hayley Jukes , Editor

As a recruiter , I know employers like to hire people who can solve problems and work well under pressure.

A job rarely goes 100% according to plan, so hiring managers are more likely to hire you if you seem like you can handle unexpected challenges while staying calm and logical.

But how do they measure this?

Hiring managers will ask you interview questions about your problem-solving skills, and they might also look for examples of problem-solving on your resume and cover letter.

In this article, I’m going to share a list of problem-solving examples and sample interview answers to questions like, “Give an example of a time you used logic to solve a problem?” and “Describe a time when you had to solve a problem without managerial input. How did you handle it, and what was the result?”

Problem-solving involves identifying, prioritizing, analyzing, and solving problems using a variety of skills like critical thinking, creativity, decision making, and communication.
Describe the Situation, Task, Action, and Result ( STAR method ) when discussing your problem-solving experiences.
Tailor your interview answer with the specific skills and qualifications outlined in the job description.
Provide numerical data or metrics to demonstrate the tangible impact of your problem-solving efforts.

What are Problem Solving Skills?

Problem-solving is the ability to identify a problem, prioritize based on gravity and urgency, analyze the root cause, gather relevant information, develop and evaluate viable solutions, decide on the most effective and logical solution, and plan and execute implementation.

Problem-solving encompasses other skills that can be showcased in an interview response and your resume. Problem-solving skills examples include:

Critical thinking
Analytical skills
Decision making
Research skills
Technical skills
Communication skills
Adaptability and flexibility

Why is Problem Solving Important in the Workplace?

Problem-solving is essential in the workplace because it directly impacts productivity and efficiency. Whenever you encounter a problem, tackling it head-on prevents minor issues from escalating into bigger ones that could disrupt the entire workflow.

Beyond maintaining smooth operations, your ability to solve problems fosters innovation. It encourages you to think creatively, finding better ways to achieve goals, which keeps the business competitive and pushes the boundaries of what you can achieve.

Effective problem-solving also contributes to a healthier work environment; it reduces stress by providing clear strategies for overcoming obstacles and builds confidence within teams.

Examples of Problem-Solving in the Workplace

Correcting a mistake at work, whether it was made by you or someone else
Overcoming a delay at work through problem solving and communication
Resolving an issue with a difficult or upset customer
Overcoming issues related to a limited budget, and still delivering good work through the use of creative problem solving
Overcoming a scheduling/staffing shortage in the department to still deliver excellent work
Troubleshooting and resolving technical issues
Handling and resolving a conflict with a coworker
Solving any problems related to money, customer billing, accounting and bookkeeping, etc.
Taking initiative when another team member overlooked or missed something important
Taking initiative to meet with your superior to discuss a problem before it became potentially worse
Solving a safety issue at work or reporting the issue to those who could solve it
Using problem solving abilities to reduce/eliminate a company expense
Finding a way to make the company more profitable through new service or product offerings, new pricing ideas, promotion and sale ideas, etc.
Changing how a process, team, or task is organized to make it more efficient
Using creative thinking to come up with a solution that the company hasn’t used before
Performing research to collect data and information to find a new solution to a problem
Boosting a company or team’s performance by improving some aspect of communication among employees
Finding a new piece of data that can guide a company’s decisions or strategy better in a certain area

Problem-Solving Examples for Recent Grads/Entry-Level Job Seekers

Coordinating work between team members in a class project
Reassigning a missing team member’s work to other group members in a class project
Adjusting your workflow on a project to accommodate a tight deadline
Speaking to your professor to get help when you were struggling or unsure about a project
Asking classmates, peers, or professors for help in an area of struggle
Talking to your academic advisor to brainstorm solutions to a problem you were facing
Researching solutions to an academic problem online, via Google or other methods
Using problem solving and creative thinking to obtain an internship or other work opportunity during school after struggling at first

How To Answer “Tell Us About a Problem You Solved”

When you answer interview questions about problem-solving scenarios, or if you decide to demonstrate your problem-solving skills in a cover letter (which is a good idea any time the job description mentions problem-solving as a necessary skill), I recommend using the STAR method.

STAR stands for:

It’s a simple way of walking the listener or reader through the story in a way that will make sense to them.

Start by briefly describing the general situation and the task at hand. After this, describe the course of action you chose and why. Ideally, show that you evaluated all the information you could given the time you had, and made a decision based on logic and fact. Finally, describe the positive result you achieved.

Note: Our sample answers below are structured following the STAR formula. Be sure to check them out!

EXPERT ADVICE

Dr. Kyle Elliott , MPA, CHES Tech & Interview Career Coach caffeinatedkyle.com

How can I communicate complex problem-solving experiences clearly and succinctly?

Before answering any interview question, it’s important to understand why the interviewer is asking the question in the first place.

When it comes to questions about your complex problem-solving experiences, for example, the interviewer likely wants to know about your leadership acumen, collaboration abilities, and communication skills, not the problem itself.

Therefore, your answer should be focused on highlighting how you excelled in each of these areas, not diving into the weeds of the problem itself, which is a common mistake less-experienced interviewees often make.

Tailoring Your Answer Based on the Skills Mentioned in the Job Description

As a recruiter, one of the top tips I can give you when responding to the prompt “Tell us about a problem you solved,” is to tailor your answer to the specific skills and qualifications outlined in the job description.

Once you’ve pinpointed the skills and key competencies the employer is seeking, craft your response to highlight experiences where you successfully utilized or developed those particular abilities.

For instance, if the job requires strong leadership skills, focus on a problem-solving scenario where you took charge and effectively guided a team toward resolution.

By aligning your answer with the desired skills outlined in the job description, you demonstrate your suitability for the role and show the employer that you understand their needs.

Amanda Augustine expands on this by saying:

“Showcase the specific skills you used to solve the problem. Did it require critical thinking, analytical abilities, or strong collaboration? Highlight the relevant skills the employer is seeking.”

Interview Answers to “Tell Me About a Time You Solved a Problem”

Now, let’s look at some sample interview answers to, “Give me an example of a time you used logic to solve a problem,” or “Tell me about a time you solved a problem,” since you’re likely to hear different versions of this interview question in all sorts of industries.

The example interview responses are structured using the STAR method and are categorized into the top 5 key problem-solving skills recruiters look for in a candidate.

1. Analytical Thinking

Situation: In my previous role as a data analyst , our team encountered a significant drop in website traffic.

Task: I was tasked with identifying the root cause of the decrease.

Action: I conducted a thorough analysis of website metrics, including traffic sources, user demographics, and page performance. Through my analysis, I discovered a technical issue with our website’s loading speed, causing users to bounce.

Result: By optimizing server response time, compressing images, and minimizing redirects, we saw a 20% increase in traffic within two weeks.

2. Critical Thinking

Situation: During a project deadline crunch, our team encountered a major technical issue that threatened to derail our progress.

Task: My task was to assess the situation and devise a solution quickly.

Action: I immediately convened a meeting with the team to brainstorm potential solutions. Instead of panicking, I encouraged everyone to think outside the box and consider unconventional approaches. We analyzed the problem from different angles and weighed the pros and cons of each solution.

Result: By devising a workaround solution, we were able to meet the project deadline, avoiding potential delays that could have cost the company $100,000 in penalties for missing contractual obligations.

3. Decision Making

Situation: As a project manager , I was faced with a dilemma when two key team members had conflicting opinions on the project direction.

Task: My task was to make a decisive choice that would align with the project goals and maintain team cohesion.

Action: I scheduled a meeting with both team members to understand their perspectives in detail. I listened actively, asked probing questions, and encouraged open dialogue. After carefully weighing the pros and cons of each approach, I made a decision that incorporated elements from both viewpoints.

Result: The decision I made not only resolved the immediate conflict but also led to a stronger sense of collaboration within the team. By valuing input from all team members and making a well-informed decision, we were able to achieve our project objectives efficiently.

4. Communication (Teamwork)

Situation: During a cross-functional project, miscommunication between departments was causing delays and misunderstandings.

Task: My task was to improve communication channels and foster better teamwork among team members.

Action: I initiated regular cross-departmental meetings to ensure that everyone was on the same page regarding project goals and timelines. I also implemented a centralized communication platform where team members could share updates, ask questions, and collaborate more effectively.

Result: Streamlining workflows and improving communication channels led to a 30% reduction in project completion time, saving the company $25,000 in operational costs.

5. Persistence

Situation: During a challenging sales quarter, I encountered numerous rejections and setbacks while trying to close a major client deal.

Task: My task was to persistently pursue the client and overcome obstacles to secure the deal.

Action: I maintained regular communication with the client, addressing their concerns and demonstrating the value proposition of our product. Despite facing multiple rejections, I remained persistent and resilient, adjusting my approach based on feedback and market dynamics.

Result: After months of perseverance, I successfully closed the deal with the client. By closing the major client deal, I exceeded quarterly sales targets by 25%, resulting in a revenue increase of $250,000 for the company.

Tips to Improve Your Problem-Solving Skills

Throughout your career, being able to showcase and effectively communicate your problem-solving skills gives you more leverage in achieving better jobs and earning more money .

So to improve your problem-solving skills, I recommend always analyzing a problem and situation before acting.

When discussing problem-solving with employers, you never want to sound like you rush or make impulsive decisions. They want to see fact-based or data-based decisions when you solve problems.

Don’t just say you’re good at solving problems. Show it with specifics. How much did you boost efficiency? Did you save the company money? Adding numbers can really make your achievements stand out.

To get better at solving problems, analyze the outcomes of past solutions you came up with. You can recognize what works and what doesn’t.

Think about how you can improve researching and analyzing a situation, how you can get better at communicating, and deciding on the right people in the organization to talk to and “pull in” to help you if needed, etc.

Finally, practice staying calm even in stressful situations. Take a few minutes to walk outside if needed. Step away from your phone and computer to clear your head. A work problem is rarely so urgent that you cannot take five minutes to think (with the possible exception of safety problems), and you’ll get better outcomes if you solve problems by acting logically instead of rushing to react in a panic.

You can use all of the ideas above to describe your problem-solving skills when asked interview questions about the topic. If you say that you do the things above, employers will be impressed when they assess your problem-solving ability.

More Interview Resources

3 Answers to “How Do You Handle Stress?”
How to Answer “How Do You Handle Conflict?” (Interview Question)
Sample Answers to “Tell Me About a Time You Failed”

About the Author

Biron Clark is a former executive recruiter who has worked individually with hundreds of job seekers, reviewed thousands of resumes and LinkedIn profiles, and recruited for top venture-backed startups and Fortune 500 companies. He has been advising job seekers since 2012 to think differently in their job search and land high-paying, competitive positions. Follow on Twitter and LinkedIn .

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39 Best Problem-Solving Examples

problem-solving examples and definition, explained below

Problem-solving is a process where you’re tasked with identifying an issue and coming up with the most practical and effective solution.

This indispensable skill is necessary in several aspects of life, from personal relationships to education to business decisions.

Problem-solving aptitude boosts rational thinking, creativity, and the ability to cooperate with others. It’s also considered essential in 21st Century workplaces.

If explaining your problem-solving skills in an interview, remember that the employer is trying to determine your ability to handle difficulties. Focus on explaining exactly how you solve problems, including by introducing your thoughts on some of the following frameworks and how you’ve applied them in the past.

Problem-Solving Examples

1. divergent thinking.

Divergent thinking refers to the process of coming up with multiple different answers to a single problem. It’s the opposite of convergent thinking, which would involve coming up with a singular answer .

The benefit of a divergent thinking approach is that it can help us achieve blue skies thinking – it lets us generate several possible solutions that we can then critique and analyze .

In the realm of problem-solving, divergent thinking acts as the initial spark. You’re working to create an array of potential solutions, even those that seem outwardly unrelated or unconventional, to get your brain turning and unlock out-of-the-box ideas.

This process paves the way for the decision-making stage, where the most promising ideas are selected and refined.

Go Deeper: Divervent Thinking Examples

2. Convergent Thinking

Next comes convergent thinking, the process of narrowing down multiple possibilities to arrive at a single solution.

This involves using your analytical skills to identify the best, most practical, or most economical solution from the pool of ideas that you generated in the divergent thinking stage.

In a way, convergent thinking shapes the “roadmap” to solve a problem after divergent thinking has supplied the “destinations.”

Have a think about which of these problem-solving skills you’re more adept at: divergent or convergent thinking?

Go Deeper: Convergent Thinking Examples

3. Brainstorming

Brainstorming is a group activity designed to generate a multitude of ideas regarding a specific problem. It’s divergent thinking as a group , which helps unlock even more possibilities.

A typical brainstorming session involves uninhibited and spontaneous ideation, encouraging participants to voice any possible solutions, no matter how unconventional they might appear.

It’s important in a brainstorming session to suspend judgment and be as inclusive as possible, allowing all participants to get involved.

By widening the scope of potential solutions, brainstorming allows better problem definition, more creative solutions, and helps to avoid thinking “traps” that might limit your perspective.

Go Deeper: Brainstorming Examples

4. Thinking Outside the Box

The concept of “thinking outside the box” encourages a shift in perspective, urging you to approach problems from an entirely new angle.

Rather than sticking to traditional methods and processes, it involves breaking away from conventional norms to cultivate unique solutions.

In problem-solving, this mindset can bypass established hurdles and bring you to fresh ideas that might otherwise remain undiscovered.

Think of it as going off the beaten track when regular routes present roadblocks to effective resolution.

5. Case Study Analysis

Analyzing case studies involves a detailed examination of real-life situations that bear relevance to the current problem at hand.

For example, if you’re facing a problem, you could go to another environment that has faced a similar problem and examine how they solved it. You’d then bring the insights from that case study back to your own problem.

This approach provides a practical backdrop against which theories and assumptions can be tested, offering valuable insights into how similar problems have been approached and resolved in the past.

See a Broader Range of Analysis Examples Here

6. Action Research

Action research involves a repetitive process of identifying a problem, formulating a plan to address it, implementing the plan, and then analyzing the results. It’s common in educational research contexts.

The objective is to promote continuous learning and improvement through reflection and action. You conduct research into your problem, attempt to apply a solution, then assess how well the solution worked. This becomes an iterative process of continual improvement over time.

For problem-solving, this method offers a way to test solutions in real-time and allows for changes and refinements along the way, based on feedback or observed outcomes. It’s a form of active problem-solving that integrates lessons learned into the next cycle of action.

Go Deeper: Action Research Examples

7. Information Gathering

Fundamental to solving any problem is the process of information gathering.

This involves collecting relevant data , facts, and details about the issue at hand, significantly aiding in the understanding and conceptualization of the problem.

In problem-solving, information gathering underpins every decision you make.

This process ensures your actions are based on concrete information and evidence, allowing for an informed approach to tackle the problem effectively.

8. Seeking Advice

Seeking advice implies turning to knowledgeable and experienced individuals or entities to gain insights on problem-solving.

It could include mentors, industry experts, peers, or even specialized literature.

The value in this process lies in leveraging different perspectives and proven strategies when dealing with a problem. Moreover, it aids you in avoiding pitfalls, saving time, and learning from others’ experiences.

9. Creative Thinking

Creative thinking refers to the ability to perceive a problem in a new way, identify unconventional patterns, or produce original solutions.

It encourages innovation and uniqueness, often leading to the most effective results.

When applied to problem-solving, creative thinking can help you break free from traditional constraints, ideal for potentially complex or unusual problems.

Go Deeper: Creative Thinking Examples

10. Conflict Resolution

Conflict resolution is a strategy developed to resolve disagreements and arguments, often involving communication, negotiation, and compromise.

When employed as a problem-solving technique, it can diffuse tension, clear bottlenecks, and create a collaborative environment.

Effective conflict resolution ensures that differing views or disagreements do not become roadblocks in the process of problem-solving.

Go Deeper: Conflict Resolution Examples

11. Addressing Bottlenecks

Bottlenecks refer to obstacles or hindrances that slow down or even halt a process.

In problem-solving, addressing bottlenecks involves identifying these impediments and finding ways to eliminate them.

This effort not only smooths the path to resolution but also enhances the overall efficiency of the problem-solving process.

For example, if your workflow is not working well, you’d go to the bottleneck – that one point that is most time consuming – and focus on that. Once you ‘break’ this bottleneck, the entire process will run more smoothly.

12. Market Research

Market research involves gathering and analyzing information about target markets, consumers, and competitors.

In sales and marketing, this is one of the most effective problem-solving methods. The research collected from your market (e.g. from consumer surveys) generates data that can help identify market trends, customer preferences, and competitor strategies.

In this sense, it allows a company to make informed decisions, solve existing problems, and even predict and prevent future ones.

13. Root Cause Analysis

Root cause analysis is a method used to identify the origin or the fundamental reason for a problem.

Once the root cause is determined, you can implement corrective actions to prevent the problem from recurring.

As a problem-solving procedure, root cause analysis helps you to tackle the problem at its source, rather than dealing with its surface symptoms.

Go Deeper: Root Cause Analysis Examples

14. Mind Mapping

Mind mapping is a visual tool used to structure information, helping you better analyze, comprehend and generate new ideas.

By laying out your thoughts visually, it can lead you to solutions that might not have been apparent with linear thinking.

In problem-solving, mind mapping helps in organizing ideas and identifying connections between them, providing a holistic view of the situation and potential solutions.

15. Trial and Error

The trial and error method involves attempting various solutions until you find one that resolves the problem.

It’s an empirical technique that relies on practical actions instead of theories or rules.

In the context of problem-solving, trial and error allows you the flexibility to test different strategies in real situations, gaining insights about what works and what doesn’t.

16. SWOT Analysis

SWOT is an acronym standing for Strengths, Weaknesses, Opportunities, and Threats.

It’s an analytic framework used to evaluate these aspects in relation to a particular objective or problem.

In problem-solving, SWOT Analysis helps you to identify favorable and unfavorable internal and external factors. It helps to craft strategies that make best use of your strengths and opportunities, whilst addressing weaknesses and threats.

Go Deeper: SWOT Analysis Examples

17. Scenario Planning

Scenario planning is a strategic planning method used to make flexible long-term plans.

It involves imagining, and then planning for, multiple likely future scenarios.

By forecasting various directions a problem could take, scenario planning helps manage uncertainty and is an effective tool for problem-solving in volatile conditions.

18. Six Thinking Hats

The Six Thinking Hats is a concept devised by Edward de Bono that proposes six different directions or modes of thinking, symbolized by six different hat colors.

Each hat signifies a different perspective, encouraging you to switch ‘thinking modes’ as you switch hats. This method can help remove bias and broaden perspectives when dealing with a problem.

19. Decision Matrix Analysis

Decision Matrix Analysis is a technique that allows you to weigh different factors when faced with several possible solutions.

After listing down the options and determining the factors of importance, each option is scored based on each factor.

Revealing a clear winner that both serves your objectives and reflects your values, Decision Matrix Analysis grounds your problem-solving process in objectivity and comprehensiveness.

20. Pareto Analysis

Also known as the 80/20 rule, Pareto Analysis is a decision-making technique.

It’s based on the principle that 80% of problems are typically caused by 20% of the causes, making it a handy tool for identifying the most significant issues in a situation.

Using this analysis, you’re likely to direct your problem-solving efforts more effectively, tackling the root causes producing most of the problem’s impact.

21. Critical Thinking

Critical thinking refers to the ability to analyze facts to form a judgment objectively.

It involves logical, disciplined thinking that is clear, rational, open-minded, and informed by evidence.

For problem-solving, critical thinking helps evaluate options and decide the most effective solution. It ensures your decisions are grounded in reason and facts, and not biased or irrational assumptions.

Go Deeper: Critical Thinking Examples

22. Hypothesis Testing

Hypothesis testing usually involves formulating a claim, testing it against actual data, and deciding whether to accept or reject the claim based on the results.

In problem-solving, hypotheses often represent potential solutions. Hypothesis testing provides verification, giving a statistical basis for decision-making and problem resolution.

Usually, this will require research methods and a scientific approach to see whether the hypothesis stands up or not.

Go Deeper: Types of Hypothesis Testing

23. Cost-Benefit Analysis

A cost-benefit analysis (CBA) is a systematic process of weighing the pros and cons of different solutions in terms of their potential costs and benefits.

It allows you to measure the positive effects against the negatives and informs your problem-solving strategy.

By using CBA, you can identify which solution offers the greatest benefit for the least cost, significantly improving efficacy and efficiency in your problem-solving process.

Go Deeper: Cost-Benefit Analysis Examples

24. Simulation and Modeling

Simulations and models allow you to create a simplified replica of real-world systems to test outcomes under controlled conditions.

In problem-solving, you can broadly understand potential repercussions of different solutions before implementation.

It offers a cost-effective way to predict the impacts of your decisions, minimizing potential risks associated with various solutions.

25. Delphi Method

The Delphi Method is a structured communication technique used to gather expert opinions.

The method involves a group of experts who respond to questionnaires about a problem. The responses are aggregated and shared with the group, and the process repeats until a consensus is reached.

This method of problem solving can provide a diverse range of insights and solutions, shaped by the wisdom of a collective expert group.

26. Cross-functional Team Collaboration

Cross-functional team collaboration involves individuals from different departments or areas of expertise coming together to solve a common problem or achieve a shared goal.

When you bring diverse skills, knowledge, and perspectives to a problem, it can lead to a more comprehensive and innovative solution.

In problem-solving, this promotes communal thinking and ensures that solutions are inclusive and holistic, with various aspects of the problem being addressed.

27. Benchmarking

Benchmarking involves comparing one’s business processes and performance metrics to the best practices from other companies or industries.

In problem-solving, it allows you to identify gaps in your own processes, determine how others have solved similar problems, and apply those solutions that have proven to be successful.

It also allows you to compare yourself to the best (the benchmark) and assess where you’re not as good.

28. Pros-Cons Lists

A pro-con analysis aids in problem-solving by weighing the advantages (pros) and disadvantages (cons) of various possible solutions.

This simple but powerful tool helps in making a balanced, informed decision.

When confronted with a problem, a pro-con analysis can guide you through the decision-making process, ensuring all possible outcomes and implications are scrutinized before arriving at the optimal solution. Thus, it helps to make the problem-solving process both methodical and comprehensive.

29. 5 Whys Analysis

The 5 Whys Analysis involves repeatedly asking the question ‘why’ (around five times) to peel away the layers of an issue and discover the root cause of a problem.

As a problem-solving technique, it enables you to delve into details that you might otherwise overlook and offers a simple, yet powerful, approach to uncover the origin of a problem.

For example, if your task is to find out why a product isn’t selling your first answer might be: “because customers don’t want it”, then you ask why again – “they don’t want it because it doesn’t solve their problem”, then why again – “because the product is missing a certain feature” … and so on, until you get to the root “why”.

30. Gap Analysis

Gap analysis entails comparing current performance with potential or desired performance.

You’re identifying the ‘gaps’, or the differences, between where you are and where you want to be.

In terms of problem-solving, a Gap Analysis can help identify key areas for improvement and design a roadmap of how to get from the current state to the desired one.

31. Design Thinking

Design thinking is a problem-solving approach that involves empathy, experimentation, and iteration.

The process focuses on understanding user needs, challenging assumptions , and redefining problems from a user-centric perspective.

In problem-solving, design thinking uncovers innovative solutions that may not have been initially apparent and ensures the solution is tailored to the needs of those affected by the issue.

32. Analogical Thinking

Analogical thinking involves the transfer of information from a particular subject (the analogue or source) to another particular subject (the target).

In problem-solving, you’re drawing parallels between similar situations and applying the problem-solving techniques used in one situation to the other.

Thus, it allows you to apply proven strategies to new, but related problems.

33. Lateral Thinking

Lateral thinking requires looking at a situation or problem from a unique, sometimes abstract, often non-sequential viewpoint.

Unlike traditional logical thinking methods, lateral thinking encourages you to employ creative and out-of-the-box techniques.

In solving problems, this type of thinking boosts ingenuity and drives innovation, often leading to novel and effective solutions.

Go Deeper: Lateral Thinking Examples

34. Flowcharting

Flowcharting is the process of visually mapping a process or procedure.

This form of diagram can show every step of a system, process, or workflow, enabling an easy tracking of the progress.

As a problem-solving tool, flowcharts help identify bottlenecks or inefficiencies in a process, guiding improved strategies and providing clarity on task ownership and process outcomes.

35. Multivoting

Multivoting, or N/3 voting, is a method where participants reduce a large list of ideas to a prioritized shortlist by casting multiple votes.

This voting system elevates the most preferred options for further consideration and decision-making.

As a problem-solving technique, multivoting allows a group to narrow options and focus on the most promising solutions, ensuring more effective and democratic decision-making.

36. Force Field Analysis

Force Field Analysis is a decision-making technique that identifies the forces for and against change when contemplating a decision.

The ‘forces’ represent the differing factors that can drive or hinder change.

In problem-solving, Force Field Analysis allows you to understand the entirety of the context, favoring a balanced view over a one-sided perspective. A comprehensive view of all the forces at play can lead to better-informed problem-solving decisions.

TRIZ, which stands for “The Theory of Inventive Problem Solving,” is a problem-solving, analysis, and forecasting methodology.

It focuses on finding contradictions inherent in a scenario. Then, you work toward eliminating the contraditions through finding innovative solutions.

So, when you’re tackling a problem, TRIZ provides a disciplined, systematic approach that aims for ideal solutions and not just acceptable ones. Using TRIZ, you can leverage patterns of problem-solving that have proven effective in different cases, pivoting them to solve the problem at hand.

38. A3 Problem Solving

A3 Problem Solving, derived from Lean Management, is a structured method that uses a single sheet of A3-sized paper to document knowledge from a problem-solving process.

Named after the international paper size standard of A3 (or 11-inch by 17-inch paper), it succinctly records all key details of the problem-solving process from problem description to the root cause and corrective actions.

Used in problem-solving, this provides a straightforward and logical structure for addressing the problem, facilitating communication between team members, ensuring all critical details are included, and providing a record of decisions made.

39. Scenario Analysis

Scenario Analysis is all about predicting different possible future events depending upon your decision.

To do this, you look at each course of action and try to identify the most likely outcomes or scenarios down the track if you take that course of action.

This technique helps forecast the impacts of various strategies, playing each out to their (logical or potential) end. It’s a good strategy for project managers who need to keep a firm eye on the horizon at all times.

When solving problems, Scenario Analysis assists in preparing for uncertainties, making sure your solution remains viable, regardless of changes in circumstances.

How to Answer “Demonstrate Problem-Solving Skills” in an Interview

When asked to demonstrate your problem-solving skills in an interview, the STAR method often proves useful. STAR stands for Situation, Task, Action, and Result.

Situation: Begin by describing a specific circumstance or challenge you encountered. Make sure to provide enough detail to allow the interviewer a clear understanding. You should select an event that adequately showcases your problem-solving abilities.

For instance, “In my previous role as a project manager, we faced a significant issue when our key supplier abruptly went out of business.”

Task: Explain what your responsibilities were in that situation. This serves to provide context, allowing the interviewer to understand your role and the expectations placed upon you.

For instance, “It was my task to ensure the project remained on track despite this setback. Alternative suppliers needed to be found without sacrificing quality or significantly increasing costs.”

Action: Describe the steps you took to manage the problem. Highlight your problem-solving process. Mention any creative approaches or techniques that you used.

For instance, “I conducted thorough research to identify potential new suppliers. After creating a shortlist, I initiated contact, negotiated terms, assessed samples for quality and made a selection. I also worked closely with the team to re-adjust the project timeline.”

Result: Share the outcomes of your actions. How did the situation end? Did your actions lead to success? It’s particularly effective if you can quantify these results.

For instance, “As a result of my active problem solving, we were able to secure a new supplier whose costs were actually 10% cheaper and whose quality was comparable. We adjusted the project plan and managed to complete the project just two weeks later than originally planned, despite the major vendor setback.”

Remember, when you’re explaining your problem-solving skills to an interviewer, what they’re really interested in is your approach to handling difficulties, your creativity and persistence in seeking a resolution, and your ability to carry your solution through to fruition. Tailoring your story to highlight these aspects will help exemplify your problem-solving prowess.

Go Deeper: STAR Interview Method Examples

Benefits of Problem-Solving

Problem-solving is beneficial for the following reasons (among others):

It can help you to overcome challenges, roadblocks, and bottlenecks in your life.
It can save a company money.
It can help you to achieve clarity in your thinking.
It can make procedures more efficient and save time.
It can strengthen your decision-making capacities.
It can lead to better risk management.

Whether for a job interview or school, problem-solving helps you to become a better thinking, solve your problems more effectively, and achieve your goals. Build up your problem-solving frameworks (I presented over 40 in this piece for you!) and work on applying them in real-life situations.

Chris Drew (PhD)

Dr. Chris Drew is the founder of the Helpful Professor. He holds a PhD in education and has published over 20 articles in scholarly journals. He is the former editor of the Journal of Learning Development in Higher Education. [Image Descriptor: Photo of Chris]

Chris Drew (PhD) https://helpfulprofessor.com/author/chris-drew-phd/ Unstructured Play: 13 Pros & Cons for Learning
Chris Drew (PhD) https://helpfulprofessor.com/author/chris-drew-phd/ 17 Types of Play Based Learning in Early Childhood
Chris Drew (PhD) https://helpfulprofessor.com/author/chris-drew-phd/ Bruner’s Spiral Curriculum - The 3 Key Principles
Chris Drew (PhD) https://helpfulprofessor.com/author/chris-drew-phd/ 7 Key Features of 21st Century Learning

PROBLEM SOLVING in a Sentence Examples: 21 Ways to Use Problem Solving

Have you ever found yourself stuck in a situation, trying to figure out the best way to overcome a challenge or obstacle? That’s where the concept of problem solving comes into play. Problem solving refers to the process of identifying issues, brainstorming potential solutions, and selecting the most effective course of action to resolve a problem or achieve a desired outcome.

In various aspects of our lives, from school and work to personal relationships, the ability to problem solve is a valuable skill that can help us navigate through difficulties and make informed decisions. By honing our problem-solving skills, we can approach challenges with confidence and creativity, finding innovative solutions to complex problems.

Table of Contents

7 Examples Of Problem Solving Used In a Sentence For Kids

Problem solving is when we figure out how to fix a tricky situation.
We can use problem solving to help us complete puzzles and games.
Friends can work together to do some problem solving .
It’s fun to use problem solving to come up with new ideas.
Sometimes we need to ask for help with problem solving .
Practice makes us better at problem solving .
We can feel proud when we use problem solving to overcome challenges.

14 Sentences with Problem Solving Examples

Problem solving is essential when faced with complex math equations in engineering classes.
College students often use problem solving skills to navigate group projects and assignments.
Problem solving comes into play when trying to manage time effectively between studying, extracurricular activities, and social life.
Problem solving skills are crucial when dealing with challenging professors or difficult course material.
Balancing a tight budget and finding creative ways to save money requires strong problem solving abilities.
Problem solving is key when troubleshooting technical issues with laptops, smartphones, or other devices.
Effective problem solving can help find innovative solutions to overcome obstacles in research projects or experiments.
Learning to manage stress and anxiety through problem solving techniques can greatly improve academic performance.
Problem solving skills are tested when trying to find internship or job opportunities in a competitive market.
College students may need to use problem solving strategies to resolve conflicts with roommates or classmates.
Implementing problem solving strategies can help improve communication and relationships within student organizations or clubs.
Navigating transportation challenges in crowded cities requires quick thinking and effective problem solving .
Developing problem solving abilities can help students adapt to unexpected changes in their academic schedules or plans.
Utilizing problem solving skills when dealing with cultural differences can enhance the college experience for international students.

How To Use Problem Solving in Sentences?

Problem Solving is the process of identifying problems , finding solutions , and implementing those solutions to resolve the problems . To use “Problem Solving” in a sentence, start by identifying a problem that needs to be addressed. For example, “I am having trouble staying organized with my work schedule.” Next, brainstorm possible solutions to the problem . In this case, one solution could be creating a daily to-do list. Then, choose the most viable solution and implement it. The sentence could be, “I used Problem Solving techniques to create a to-do list and now I am more organized with my work schedule.”

Remember that effective Problem Solving involves critical thinking, analytical skills, and creativity. It is important to break down the problem into smaller components, analyze each part, and come up with innovative solutions . Practice Problem Solving regularly to improve your skills and become more efficient at resolving problems . By mastering Problem Solving , you will be able to tackle challenges more effectively and achieve your goals. So, next time you encounter a problem , remember to apply Problem Solving techniques to find a solution.

In conclusion, problem-solving is a crucial skill that involves identifying, analyzing, and resolving issues or obstacles to achieve a desired outcome. The ability to generate creative solutions, think critically, and make informed decisions is key to effective problem-solving. Examples of problem-solving can be seen in various situations, such as when troubleshooting technical issues, resolving conflicts in the workplace, or finding solutions to complex mathematical problems.

By developing and honing your problem-solving skills, you can enhance your adaptability, resilience, and overall effectiveness in both personal and professional realms. Ultimately, being a proficient problem solver can lead to improved decision-making, increased productivity, and a greater sense of accomplishment in overcoming challenges.

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35 problem-solving techniques and methods for solving complex problems

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How do you identify problems?

How do you identify the right solution.

Tips for more effective problem-solving

Complete problem-solving methods

Problem-solving techniques to identify and analyze problems
Problem-solving techniques for developing solutions

Problem-solving warm-up activities

Closing activities for a problem-solving process.

Before you can move towards finding the right solution for a given problem, you first need to identify and define the problem you wish to solve.

Here, you want to clearly articulate what the problem is and allow your group to do the same. Remember that everyone in a group is likely to have differing perspectives and alignment is necessary in order to help the group move forward.

Identifying a problem accurately also requires that all members of a group are able to contribute their views in an open and safe manner. It can be scary for people to stand up and contribute, especially if the problems or challenges are emotive or personal in nature. Be sure to try and create a psychologically safe space for these kinds of discussions.

Remember that problem analysis and further discussion are also important. Not taking the time to fully analyze and discuss a challenge can result in the development of solutions that are not fit for purpose or do not address the underlying issue.

Successfully identifying and then analyzing a problem means facilitating a group through activities designed to help them clearly and honestly articulate their thoughts and produce usable insight.

With this data, you might then produce a problem statement that clearly describes the problem you wish to be addressed and also state the goal of any process you undertake to tackle this issue.

Finding solutions is the end goal of any process. Complex organizational challenges can only be solved with an appropriate solution but discovering them requires using the right problem-solving tool.

After you’ve explored a problem and discussed ideas, you need to help a team discuss and choose the right solution. Consensus tools and methods such as those below help a group explore possible solutions before then voting for the best. They’re a great way to tap into the collective intelligence of the group for great results!

Remember that the process is often iterative. Great problem solvers often roadtest a viable solution in a measured way to see what works too. While you might not get the right solution on your first try, the methods below help teams land on the most likely to succeed solution while also holding space for improvement.

Every effective problem solving process begins with an agenda . A well-structured workshop is one of the best methods for successfully guiding a group from exploring a problem to implementing a solution.

In SessionLab, it’s easy to go from an idea to a complete agenda . Start by dragging and dropping your core problem solving activities into place . Add timings, breaks and necessary materials before sharing your agenda with your colleagues.

The resulting agenda will be your guide to an effective and productive problem solving session that will also help you stay organized on the day!

Tips for more effective problem solving

Problem-solving activities are only one part of the puzzle. While a great method can help unlock your team’s ability to solve problems, without a thoughtful approach and strong facilitation the solutions may not be fit for purpose.

Let’s take a look at some problem-solving tips you can apply to any process to help it be a success!

Clearly define the problem

Jumping straight to solutions can be tempting, though without first clearly articulating a problem, the solution might not be the right one. Many of the problem-solving activities below include sections where the problem is explored and clearly defined before moving on.

This is a vital part of the problem-solving process and taking the time to fully define an issue can save time and effort later. A clear definition helps identify irrelevant information and it also ensures that your team sets off on the right track.

Don’t jump to conclusions

It’s easy for groups to exhibit cognitive bias or have preconceived ideas about both problems and potential solutions. Be sure to back up any problem statements or potential solutions with facts, research, and adequate forethought.

The best techniques ask participants to be methodical and challenge preconceived notions. Make sure you give the group enough time and space to collect relevant information and consider the problem in a new way. By approaching the process with a clear, rational mindset, you’ll often find that better solutions are more forthcoming.

Try different approaches

Problems come in all shapes and sizes and so too should the methods you use to solve them. If you find that one approach isn’t yielding results and your team isn’t finding different solutions, try mixing it up. You’ll be surprised at how using a new creative activity can unblock your team and generate great solutions.

Don’t take it personally

Depending on the nature of your team or organizational problems, it’s easy for conversations to get heated. While it’s good for participants to be engaged in the discussions, ensure that emotions don’t run too high and that blame isn’t thrown around while finding solutions.

You’re all in it together, and even if your team or area is seeing problems, that isn’t necessarily a disparagement of you personally. Using facilitation skills to manage group dynamics is one effective method of helping conversations be more constructive.

Get the right people in the room

Your problem-solving method is often only as effective as the group using it. Getting the right people on the job and managing the number of people present is important too!

If the group is too small, you may not get enough different perspectives to effectively solve a problem. If the group is too large, you can go round and round during the ideation stages.

Creating the right group makeup is also important in ensuring you have the necessary expertise and skillset to both identify and follow up on potential solutions. Carefully consider who to include at each stage to help ensure your problem-solving method is followed and positioned for success.

Document everything

The best solutions can take refinement, iteration, and reflection to come out. Get into a habit of documenting your process in order to keep all the learnings from the session and to allow ideas to mature and develop. Many of the methods below involve the creation of documents or shared resources. Be sure to keep and share these so everyone can benefit from the work done!

Bring a facilitator

Facilitation is all about making group processes easier. With a subject as potentially emotive and important as problem-solving, having an impartial third party in the form of a facilitator can make all the difference in finding great solutions and keeping the process moving. Consider bringing a facilitator to your problem-solving session to get better results and generate meaningful solutions!

Develop your problem-solving skills

It takes time and practice to be an effective problem solver. While some roles or participants might more naturally gravitate towards problem-solving, it can take development and planning to help everyone create better solutions.

You might develop a training program, run a problem-solving workshop or simply ask your team to practice using the techniques below. Check out our post on problem-solving skills to see how you and your group can develop the right mental process and be more resilient to issues too!

Design a great agenda

Workshops are a great format for solving problems. With the right approach, you can focus a group and help them find the solutions to their own problems. But designing a process can be time-consuming and finding the right activities can be difficult.

Check out our workshop planning guide to level-up your agenda design and start running more effective workshops. Need inspiration? Check out templates designed by expert facilitators to help you kickstart your process!

In this section, we’ll look at in-depth problem-solving methods that provide a complete end-to-end process for developing effective solutions. These will help guide your team from the discovery and definition of a problem through to delivering the right solution.

If you’re looking for an all-encompassing method or problem-solving model, these processes are a great place to start. They’ll ask your team to challenge preconceived ideas and adopt a mindset for solving problems more effectively.

Six Thinking Hats
Lightning Decision Jam
Problem Definition Process
Discovery & Action Dialogue

Design Sprint 2.0

Open Space Technology

1. Six Thinking Hats

Individual approaches to solving a problem can be very different based on what team or role an individual holds. It can be easy for existing biases or perspectives to find their way into the mix, or for internal politics to direct a conversation.

Six Thinking Hats is a classic method for identifying the problems that need to be solved and enables your team to consider them from different angles, whether that is by focusing on facts and data, creative solutions, or by considering why a particular solution might not work.

Like all problem-solving frameworks, Six Thinking Hats is effective at helping teams remove roadblocks from a conversation or discussion and come to terms with all the aspects necessary to solve complex problems.

2. Lightning Decision Jam

Featured courtesy of Jonathan Courtney of AJ&Smart Berlin, Lightning Decision Jam is one of those strategies that should be in every facilitation toolbox. Exploring problems and finding solutions is often creative in nature, though as with any creative process, there is the potential to lose focus and get lost.

Unstructured discussions might get you there in the end, but it’s much more effective to use a method that creates a clear process and team focus.

In Lightning Decision Jam, participants are invited to begin by writing challenges, concerns, or mistakes on post-its without discussing them before then being invited by the moderator to present them to the group.

From there, the team vote on which problems to solve and are guided through steps that will allow them to reframe those problems, create solutions and then decide what to execute on.

By deciding the problems that need to be solved as a team before moving on, this group process is great for ensuring the whole team is aligned and can take ownership over the next stages.

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

3. Problem Definition Process

While problems can be complex, the problem-solving methods you use to identify and solve those problems can often be simple in design.

By taking the time to truly identify and define a problem before asking the group to reframe the challenge as an opportunity, this method is a great way to enable change.

Begin by identifying a focus question and exploring the ways in which it manifests before splitting into five teams who will each consider the problem using a different method: escape, reversal, exaggeration, distortion or wishful. Teams develop a problem objective and create ideas in line with their method before then feeding them back to the group.

This method is great for enabling in-depth discussions while also creating space for finding creative solutions too!

Problem Definition #problem solving #idea generation #creativity #online #remote-friendly A problem solving technique to define a problem, challenge or opportunity and to generate ideas.

4. The 5 Whys

Sometimes, a group needs to go further with their strategies and analyze the root cause at the heart of organizational issues. An RCA or root cause analysis is the process of identifying what is at the heart of business problems or recurring challenges.

The 5 Whys is a simple and effective method of helping a group go find the root cause of any problem or challenge and conduct analysis that will deliver results.

By beginning with the creation of a problem statement and going through five stages to refine it, The 5 Whys provides everything you need to truly discover the cause of an issue.

The 5 Whys #hyperisland #innovation This simple and powerful method is useful for getting to the core of a problem or challenge. As the title suggests, the group defines a problems, then asks the question “why” five times, often using the resulting explanation as a starting point for creative problem solving.

5. World Cafe

World Cafe is a simple but powerful facilitation technique to help bigger groups to focus their energy and attention on solving complex problems.

World Cafe enables this approach by creating a relaxed atmosphere where participants are able to self-organize and explore topics relevant and important to them which are themed around a central problem-solving purpose. Create the right atmosphere by modeling your space after a cafe and after guiding the group through the method, let them take the lead!

Making problem-solving a part of your organization’s culture in the long term can be a difficult undertaking. More approachable formats like World Cafe can be especially effective in bringing people unfamiliar with workshops into the fold.

World Cafe #hyperisland #innovation #issue analysis World Café is a simple yet powerful method, originated by Juanita Brown, for enabling meaningful conversations driven completely by participants and the topics that are relevant and important to them. Facilitators create a cafe-style space and provide simple guidelines. Participants then self-organize and explore a set of relevant topics or questions for conversation.

6. Discovery & Action Dialogue (DAD)

One of the best approaches is to create a safe space for a group to share and discover practices and behaviors that can help them find their own solutions.

With DAD, you can help a group choose which problems they wish to solve and which approaches they will take to do so. It’s great at helping remove resistance to change and can help get buy-in at every level too!

This process of enabling frontline ownership is great in ensuring follow-through and is one of the methods you will want in your toolbox as a facilitator.

Discovery & Action Dialogue (DAD) #idea generation #liberating structures #action #issue analysis #remote-friendly DADs make it easy for a group or community to discover practices and behaviors that enable some individuals (without access to special resources and facing the same constraints) to find better solutions than their peers to common problems. These are called positive deviant (PD) behaviors and practices. DADs make it possible for people in the group, unit, or community to discover by themselves these PD practices. DADs also create favorable conditions for stimulating participants’ creativity in spaces where they can feel safe to invent new and more effective practices. Resistance to change evaporates as participants are unleashed to choose freely which practices they will adopt or try and which problems they will tackle. DADs make it possible to achieve frontline ownership of solutions.

7. Design Sprint 2.0

Want to see how a team can solve big problems and move forward with prototyping and testing solutions in a few days? The Design Sprint 2.0 template from Jake Knapp, author of Sprint, is a complete agenda for a with proven results.

Developing the right agenda can involve difficult but necessary planning. Ensuring all the correct steps are followed can also be stressful or time-consuming depending on your level of experience.

Use this complete 4-day workshop template if you are finding there is no obvious solution to your challenge and want to focus your team around a specific problem that might require a shortcut to launching a minimum viable product or waiting for the organization-wide implementation of a solution.

8. Open space technology

Open space technology- developed by Harrison Owen – creates a space where large groups are invited to take ownership of their problem solving and lead individual sessions. Open space technology is a great format when you have a great deal of expertise and insight in the room and want to allow for different takes and approaches on a particular theme or problem you need to be solved.

Start by bringing your participants together to align around a central theme and focus their efforts. Explain the ground rules to help guide the problem-solving process and then invite members to identify any issue connecting to the central theme that they are interested in and are prepared to take responsibility for.

Once participants have decided on their approach to the core theme, they write their issue on a piece of paper, announce it to the group, pick a session time and place, and post the paper on the wall. As the wall fills up with sessions, the group is then invited to join the sessions that interest them the most and which they can contribute to, then you’re ready to begin!

Everyone joins the problem-solving group they’ve signed up to, record the discussion and if appropriate, findings can then be shared with the rest of the group afterward.

Open Space Technology #action plan #idea generation #problem solving #issue analysis #large group #online #remote-friendly Open Space is a methodology for large groups to create their agenda discerning important topics for discussion, suitable for conferences, community gatherings and whole system facilitation

Techniques to identify and analyze problems

Using a problem-solving method to help a team identify and analyze a problem can be a quick and effective addition to any workshop or meeting.

While further actions are always necessary, you can generate momentum and alignment easily, and these activities are a great place to get started.

We’ve put together this list of techniques to help you and your team with problem identification, analysis, and discussion that sets the foundation for developing effective solutions.

Let’s take a look!

The Creativity Dice
Fishbone Analysis
Problem Tree
SWOT Analysis
Agreement-Certainty Matrix
The Journalistic Six
LEGO Challenge
What, So What, Now What?
Journalists

Individual and group perspectives are incredibly important, but what happens if people are set in their minds and need a change of perspective in order to approach a problem more effectively?

Flip It is a method we love because it is both simple to understand and run, and allows groups to understand how their perspectives and biases are formed.

Participants in Flip It are first invited to consider concerns, issues, or problems from a perspective of fear and write them on a flip chart. Then, the group is asked to consider those same issues from a perspective of hope and flip their understanding.

No problem and solution is free from existing bias and by changing perspectives with Flip It, you can then develop a problem solving model quickly and effectively.

Flip It! #gamestorming #problem solving #action Often, a change in a problem or situation comes simply from a change in our perspectives. Flip It! is a quick game designed to show players that perspectives are made, not born.

10. The Creativity Dice

One of the most useful problem solving skills you can teach your team is of approaching challenges with creativity, flexibility, and openness. Games like The Creativity Dice allow teams to overcome the potential hurdle of too much linear thinking and approach the process with a sense of fun and speed.

In The Creativity Dice, participants are organized around a topic and roll a dice to determine what they will work on for a period of 3 minutes at a time. They might roll a 3 and work on investigating factual information on the chosen topic. They might roll a 1 and work on identifying the specific goals, standards, or criteria for the session.

Encouraging rapid work and iteration while asking participants to be flexible are great skills to cultivate. Having a stage for idea incubation in this game is also important. Moments of pause can help ensure the ideas that are put forward are the most suitable.

The Creativity Dice #creativity #problem solving #thiagi #issue analysis Too much linear thinking is hazardous to creative problem solving. To be creative, you should approach the problem (or the opportunity) from different points of view. You should leave a thought hanging in mid-air and move to another. This skipping around prevents premature closure and lets your brain incubate one line of thought while you consciously pursue another.

11. Fishbone Analysis

Organizational or team challenges are rarely simple, and it’s important to remember that one problem can be an indication of something that goes deeper and may require further consideration to be solved.

Fishbone Analysis helps groups to dig deeper and understand the origins of a problem. It’s a great example of a root cause analysis method that is simple for everyone on a team to get their head around.

Participants in this activity are asked to annotate a diagram of a fish, first adding the problem or issue to be worked on at the head of a fish before then brainstorming the root causes of the problem and adding them as bones on the fish.

Using abstractions such as a diagram of a fish can really help a team break out of their regular thinking and develop a creative approach.

Fishbone Analysis #problem solving ##root cause analysis #decision making #online facilitation A process to help identify and understand the origins of problems, issues or observations.

12. Problem Tree

Encouraging visual thinking can be an essential part of many strategies. By simply reframing and clarifying problems, a group can move towards developing a problem solving model that works for them.

In Problem Tree, groups are asked to first brainstorm a list of problems – these can be design problems, team problems or larger business problems – and then organize them into a hierarchy. The hierarchy could be from most important to least important or abstract to practical, though the key thing with problem solving games that involve this aspect is that your group has some way of managing and sorting all the issues that are raised.

Once you have a list of problems that need to be solved and have organized them accordingly, you’re then well-positioned for the next problem solving steps.

Problem tree #define intentions #create #design #issue analysis A problem tree is a tool to clarify the hierarchy of problems addressed by the team within a design project; it represents high level problems or related sublevel problems.

13. SWOT Analysis

Chances are you’ve heard of the SWOT Analysis before. This problem-solving method focuses on identifying strengths, weaknesses, opportunities, and threats is a tried and tested method for both individuals and teams.

Start by creating a desired end state or outcome and bare this in mind – any process solving model is made more effective by knowing what you are moving towards. Create a quadrant made up of the four categories of a SWOT analysis and ask participants to generate ideas based on each of those quadrants.

Once you have those ideas assembled in their quadrants, cluster them together based on their affinity with other ideas. These clusters are then used to facilitate group conversations and move things forward.

SWOT analysis #gamestorming #problem solving #action #meeting facilitation The SWOT Analysis is a long-standing technique of looking at what we have, with respect to the desired end state, as well as what we could improve on. It gives us an opportunity to gauge approaching opportunities and dangers, and assess the seriousness of the conditions that affect our future. When we understand those conditions, we can influence what comes next.

14. Agreement-Certainty Matrix

Not every problem-solving approach is right for every challenge, and deciding on the right method for the challenge at hand is a key part of being an effective team.

The Agreement Certainty matrix helps teams align on the nature of the challenges facing them. By sorting problems from simple to chaotic, your team can understand what methods are suitable for each problem and what they can do to ensure effective results.

If you are already using Liberating Structures techniques as part of your problem-solving strategy, the Agreement-Certainty Matrix can be an invaluable addition to your process. We’ve found it particularly if you are having issues with recurring problems in your organization and want to go deeper in understanding the root cause.

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.

Organizing and charting a team’s progress can be important in ensuring its success. SQUID (Sequential Question and Insight Diagram) is a great model that allows a team to effectively switch between giving questions and answers and develop the skills they need to stay on track throughout the process.

Begin with two different colored sticky notes – one for questions and one for answers – and with your central topic (the head of the squid) on the board. Ask the group to first come up with a series of questions connected to their best guess of how to approach the topic. Ask the group to come up with answers to those questions, fix them to the board and connect them with a line. After some discussion, go back to question mode by responding to the generated answers or other points on the board.

It’s rewarding to see a diagram grow throughout the exercise, and a completed SQUID can provide a visual resource for future effort and as an example for other teams.

SQUID #gamestorming #project planning #issue analysis #problem solving When exploring an information space, it’s important for a group to know where they are at any given time. By using SQUID, a group charts out the territory as they go and can navigate accordingly. SQUID stands for Sequential Question and Insight Diagram.

16. Speed Boat

To continue with our nautical theme, Speed Boat is a short and sweet activity that can help a team quickly identify what employees, clients or service users might have a problem with and analyze what might be standing in the way of achieving a solution.

Methods that allow for a group to make observations, have insights and obtain those eureka moments quickly are invaluable when trying to solve complex problems.

In Speed Boat, the approach is to first consider what anchors and challenges might be holding an organization (or boat) back. Bonus points if you are able to identify any sharks in the water and develop ideas that can also deal with competitors!

Speed Boat #gamestorming #problem solving #action Speedboat is a short and sweet way to identify what your employees or clients don’t like about your product/service or what’s standing in the way of a desired goal.

17. The Journalistic Six

Some of the most effective ways of solving problems is by encouraging teams to be more inclusive and diverse in their thinking.

Based on the six key questions journalism students are taught to answer in articles and news stories, The Journalistic Six helps create teams to see the whole picture. By using who, what, when, where, why, and how to facilitate the conversation and encourage creative thinking, your team can make sure that the problem identification and problem analysis stages of the are covered exhaustively and thoughtfully. Reporter’s notebook and dictaphone optional.

The Journalistic Six – Who What When Where Why How #idea generation #issue analysis #problem solving #online #creative thinking #remote-friendly A questioning method for generating, explaining, investigating ideas.

18. LEGO Challenge

Now for an activity that is a little out of the (toy) box. LEGO Serious Play is a facilitation methodology that can be used to improve creative thinking and problem-solving skills.

The LEGO Challenge includes giving each member of the team an assignment that is hidden from the rest of the group while they create a structure without speaking.

What the LEGO challenge brings to the table is a fun working example of working with stakeholders who might not be on the same page to solve problems. Also, it’s LEGO! Who doesn’t love LEGO!

LEGO Challenge #hyperisland #team A team-building activity in which groups must work together to build a structure out of LEGO, but each individual has a secret “assignment” which makes the collaborative process more challenging. It emphasizes group communication, leadership dynamics, conflict, cooperation, patience and problem solving strategy.

19. What, So What, Now What?

If not carefully managed, the problem identification and problem analysis stages of the problem-solving process can actually create more problems and misunderstandings.

The What, So What, Now What? problem-solving activity is designed to help collect insights and move forward while also eliminating the possibility of disagreement when it comes to identifying, clarifying, and analyzing organizational or work problems.

Facilitation is all about bringing groups together so that might work on a shared goal and the best problem-solving strategies ensure that teams are aligned in purpose, if not initially in opinion or insight.

Throughout the three steps of this game, you give everyone on a team to reflect on a problem by asking what happened, why it is important, and what actions should then be taken.

This can be a great activity for bringing our individual perceptions about a problem or challenge and contextualizing it in a larger group setting. This is one of the most important problem-solving skills you can bring to your organization.

W³ – What, So What, Now What? #issue analysis #innovation #liberating structures You can help groups reflect on a shared experience in a way that builds understanding and spurs coordinated action while avoiding unproductive conflict. It is possible for every voice to be heard while simultaneously sifting for insights and shaping new direction. Progressing in stages makes this practical—from collecting facts about What Happened to making sense of these facts with So What and finally to what actions logically follow with Now What . The shared progression eliminates most of the misunderstandings that otherwise fuel disagreements about what to do. Voila!

20. Journalists

Problem analysis can be one of the most important and decisive stages of all problem-solving tools. Sometimes, a team can become bogged down in the details and are unable to move forward.

Journalists is an activity that can avoid a group from getting stuck in the problem identification or problem analysis stages of the process.

In Journalists, the group is invited to draft the front page of a fictional newspaper and figure out what stories deserve to be on the cover and what headlines those stories will have. By reframing how your problems and challenges are approached, you can help a team move productively through the process and be better prepared for the steps to follow.

Journalists #vision #big picture #issue analysis #remote-friendly This is an exercise to use when the group gets stuck in details and struggles to see the big picture. Also good for defining a vision.

Problem-solving techniques for developing solutions

The success of any problem-solving process can be measured by the solutions it produces. After you’ve defined the issue, explored existing ideas, and ideated, it’s time to narrow down to the correct solution.

Use these problem-solving techniques when you want to help your team find consensus, compare possible solutions, and move towards taking action on a particular problem.

Improved Solutions
Four-Step Sketch
15% Solutions
How-Now-Wow matrix
Impact Effort Matrix

21. Mindspin

Brainstorming is part of the bread and butter of the problem-solving process and all problem-solving strategies benefit from getting ideas out and challenging a team to generate solutions quickly.

With Mindspin, participants are encouraged not only to generate ideas but to do so under time constraints and by slamming down cards and passing them on. By doing multiple rounds, your team can begin with a free generation of possible solutions before moving on to developing those solutions and encouraging further ideation.

This is one of our favorite problem-solving activities and can be great for keeping the energy up throughout the workshop. Remember the importance of helping people become engaged in the process – energizing problem-solving techniques like Mindspin can help ensure your team stays engaged and happy, even when the problems they’re coming together to solve are complex.

MindSpin #teampedia #idea generation #problem solving #action A fast and loud method to enhance brainstorming within a team. Since this activity has more than round ideas that are repetitive can be ruled out leaving more creative and innovative answers to the challenge.

22. Improved Solutions

After a team has successfully identified a problem and come up with a few solutions, it can be tempting to call the work of the problem-solving process complete. That said, the first solution is not necessarily the best, and by including a further review and reflection activity into your problem-solving model, you can ensure your group reaches the best possible result.

One of a number of problem-solving games from Thiagi Group, Improved Solutions helps you go the extra mile and develop suggested solutions with close consideration and peer review. By supporting the discussion of several problems at once and by shifting team roles throughout, this problem-solving technique is a dynamic way of finding the best solution.

Improved Solutions #creativity #thiagi #problem solving #action #team You can improve any solution by objectively reviewing its strengths and weaknesses and making suitable adjustments. In this creativity framegame, you improve the solutions to several problems. To maintain objective detachment, you deal with a different problem during each of six rounds and assume different roles (problem owner, consultant, basher, booster, enhancer, and evaluator) during each round. At the conclusion of the activity, each player ends up with two solutions to her problem.

23. Four Step Sketch

Creative thinking and visual ideation does not need to be confined to the opening stages of your problem-solving strategies. Exercises that include sketching and prototyping on paper can be effective at the solution finding and development stage of the process, and can be great for keeping a team engaged.

By going from simple notes to a crazy 8s round that involves rapidly sketching 8 variations on their ideas before then producing a final solution sketch, the group is able to iterate quickly and visually. Problem-solving techniques like Four-Step Sketch are great if you have a group of different thinkers and want to change things up from a more textual or discussion-based approach.

Four-Step Sketch #design sprint #innovation #idea generation #remote-friendly The four-step sketch is an exercise that helps people to create well-formed concepts through a structured process that includes: Review key information Start design work on paper, Consider multiple variations , Create a detailed solution . This exercise is preceded by a set of other activities allowing the group to clarify the challenge they want to solve. See how the Four Step Sketch exercise fits into a Design Sprint

24. 15% Solutions

Some problems are simpler than others and with the right problem-solving activities, you can empower people to take immediate actions that can help create organizational change.

Part of the liberating structures toolkit, 15% solutions is a problem-solving technique that focuses on finding and implementing solutions quickly. A process of iterating and making small changes quickly can help generate momentum and an appetite for solving complex problems.

Problem-solving strategies can live and die on whether people are onboard. Getting some quick wins is a great way of getting people behind the process.

It can be extremely empowering for a team to realize that problem-solving techniques can be deployed quickly and easily and delineate between things they can positively impact and those things they cannot change.

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.

25. How-Now-Wow Matrix

The problem-solving process is often creative, as complex problems usually require a change of thinking and creative response in order to find the best solutions. While it’s common for the first stages to encourage creative thinking, groups can often gravitate to familiar solutions when it comes to the end of the process.

When selecting solutions, you don’t want to lose your creative energy! The How-Now-Wow Matrix from Gamestorming is a great problem-solving activity that enables a group to stay creative and think out of the box when it comes to selecting the right solution for a given problem.

Problem-solving techniques that encourage creative thinking and the ideation and selection of new solutions can be the most effective in organisational change. Give the How-Now-Wow Matrix a go, and not just for how pleasant it is to say out loud.

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.

26. Impact and Effort Matrix

All problem-solving techniques hope to not only find solutions to a given problem or challenge but to find the best solution. When it comes to finding a solution, groups are invited to put on their decision-making hats and really think about how a proposed idea would work in practice.

The Impact and Effort Matrix is one of the problem-solving techniques that fall into this camp, empowering participants to first generate ideas and then categorize them into a 2×2 matrix based on impact and effort.

Activities that invite critical thinking while remaining simple are invaluable. Use the Impact and Effort Matrix to move from ideation and towards evaluating potential solutions before then committing to them.

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.

27. Dotmocracy

If you’ve followed each of the problem-solving steps with your group successfully, you should move towards the end of your process with heaps of possible solutions developed with a specific problem in mind. But how do you help a group go from ideation to putting a solution into action?

Dotmocracy – or Dot Voting -is a tried and tested method of helping a team in the problem-solving process make decisions and put actions in place with a degree of oversight and consensus.

One of the problem-solving techniques that should be in every facilitator’s toolbox, Dot Voting is fast and effective and can help identify the most popular and best solutions and help bring a group to a decision effectively.

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.

All facilitators know that warm-ups and icebreakers are useful for any workshop or group process. Problem-solving workshops are no different.

Use these problem-solving techniques to warm up a group and prepare them for the rest of the process. Activating your group by tapping into some of the top problem-solving skills can be one of the best ways to see great outcomes from your session.

Check-in/Check-out
Doodling Together
Show and Tell
Constellations
Draw a Tree

28. Check-in / Check-out

Solid processes are planned from beginning to end, and the best facilitators know that setting the tone and establishing a safe, open environment can be integral to a successful problem-solving process.

Check-in / Check-out is a great way to begin and/or bookend a problem-solving workshop. Checking in to a session emphasizes that everyone will be seen, heard, and expected to contribute.

If you are running a series of meetings, setting a consistent pattern of checking in and checking out can really help your team get into a groove. We recommend this opening-closing activity for small to medium-sized groups though it can work with large groups if they’re disciplined!

Check-in / Check-out #team #opening #closing #hyperisland #remote-friendly Either checking-in or checking-out is a simple way for a team to open or close a process, symbolically and in a collaborative way. Checking-in/out invites each member in a group to be present, seen and heard, and to express a reflection or a feeling. Checking-in emphasizes presence, focus and group commitment; checking-out emphasizes reflection and symbolic closure.

29. Doodling Together

Thinking creatively and not being afraid to make suggestions are important problem-solving skills for any group or team, and warming up by encouraging these behaviors is a great way to start.

Doodling Together is one of our favorite creative ice breaker games – it’s quick, effective, and fun and can make all following problem-solving steps easier by encouraging a group to collaborate visually. By passing cards and adding additional items as they go, the workshop group gets into a groove of co-creation and idea development that is crucial to finding solutions to problems.

Doodling Together #collaboration #creativity #teamwork #fun #team #visual methods #energiser #icebreaker #remote-friendly Create wild, weird and often funny postcards together & establish a group’s creative confidence.

30. Show and Tell

You might remember some version of Show and Tell from being a kid in school and it’s a great problem-solving activity to kick off a session.

Asking participants to prepare a little something before a workshop by bringing an object for show and tell can help them warm up before the session has even begun! Games that include a physical object can also help encourage early engagement before moving onto more big-picture thinking.

By asking your participants to tell stories about why they chose to bring a particular item to the group, you can help teams see things from new perspectives and see both differences and similarities in the way they approach a topic. Great groundwork for approaching a problem-solving process as a team!

Show and Tell #gamestorming #action #opening #meeting facilitation Show and Tell taps into the power of metaphors to reveal players’ underlying assumptions and associations around a topic The aim of the game is to get a deeper understanding of stakeholders’ perspectives on anything—a new project, an organizational restructuring, a shift in the company’s vision or team dynamic.

31. Constellations

Who doesn’t love stars? Constellations is a great warm-up activity for any workshop as it gets people up off their feet, energized, and ready to engage in new ways with established topics. It’s also great for showing existing beliefs, biases, and patterns that can come into play as part of your session.

Using warm-up games that help build trust and connection while also allowing for non-verbal responses can be great for easing people into the problem-solving process and encouraging engagement from everyone in the group. Constellations is great in large spaces that allow for movement and is definitely a practical exercise to allow the group to see patterns that are otherwise invisible.

Constellations #trust #connection #opening #coaching #patterns #system Individuals express their response to a statement or idea by standing closer or further from a central object. Used with teams to reveal system, hidden patterns, perspectives.

32. Draw a Tree

Problem-solving games that help raise group awareness through a central, unifying metaphor can be effective ways to warm-up a group in any problem-solving model.

Draw a Tree is a simple warm-up activity you can use in any group and which can provide a quick jolt of energy. Start by asking your participants to draw a tree in just 45 seconds – they can choose whether it will be abstract or realistic.

Once the timer is up, ask the group how many people included the roots of the tree and use this as a means to discuss how we can ignore important parts of any system simply because they are not visible.

All problem-solving strategies are made more effective by thinking of problems critically and by exposing things that may not normally come to light. Warm-up games like Draw a Tree are great in that they quickly demonstrate some key problem-solving skills in an accessible and effective way.

Draw a Tree #thiagi #opening #perspectives #remote-friendly With this game you can raise awarness about being more mindful, and aware of the environment we live in.

Each step of the problem-solving workshop benefits from an intelligent deployment of activities, games, and techniques. Bringing your session to an effective close helps ensure that solutions are followed through on and that you also celebrate what has been achieved.

Here are some problem-solving activities you can use to effectively close a workshop or meeting and ensure the great work you’ve done can continue afterward.

One Breath Feedback
Who What When Matrix
Response Cards

How do I conclude a problem-solving process?

All good things must come to an end. With the bulk of the work done, it can be tempting to conclude your workshop swiftly and without a moment to debrief and align. This can be problematic in that it doesn’t allow your team to fully process the results or reflect on the process.

At the end of an effective session, your team will have gone through a process that, while productive, can be exhausting. It’s important to give your group a moment to take a breath, ensure that they are clear on future actions, and provide short feedback before leaving the space.

The primary purpose of any problem-solving method is to generate solutions and then implement them. Be sure to take the opportunity to ensure everyone is aligned and ready to effectively implement the solutions you produced in the workshop.

Remember that every process can be improved and by giving a short moment to collect feedback in the session, you can further refine your problem-solving methods and see further success in the future too.

33. One Breath Feedback

Maintaining attention and focus during the closing stages of a problem-solving workshop can be tricky and so being concise when giving feedback can be important. It’s easy to incur “death by feedback” should some team members go on for too long sharing their perspectives in a quick feedback round.

One Breath Feedback is a great closing activity for workshops. You give everyone an opportunity to provide feedback on what they’ve done but only in the space of a single breath. This keeps feedback short and to the point and means that everyone is encouraged to provide the most important piece of feedback to them.

One breath feedback #closing #feedback #action This is a feedback round in just one breath that excels in maintaining attention: each participants is able to speak during just one breath … for most people that’s around 20 to 25 seconds … unless of course you’ve been a deep sea diver in which case you’ll be able to do it for longer.

34. Who What When Matrix

Matrices feature as part of many effective problem-solving strategies and with good reason. They are easily recognizable, simple to use, and generate results.

The Who What When Matrix is a great tool to use when closing your problem-solving session by attributing a who, what and when to the actions and solutions you have decided upon. The resulting matrix is a simple, easy-to-follow way of ensuring your team can move forward.

Great solutions can’t be enacted without action and ownership. Your problem-solving process should include a stage for allocating tasks to individuals or teams and creating a realistic timeframe for those solutions to be implemented or checked out. Use this method to keep the solution implementation process clear and simple for all involved.

Who/What/When Matrix #gamestorming #action #project planning With Who/What/When matrix, you can connect people with clear actions they have defined and have committed to.

35. Response cards

Group discussion can comprise the bulk of most problem-solving activities and by the end of the process, you might find that your team is talked out!

Providing a means for your team to give feedback with short written notes can ensure everyone is head and can contribute without the need to stand up and talk. Depending on the needs of the group, giving an alternative can help ensure everyone can contribute to your problem-solving model in the way that makes the most sense for them.

Response Cards is a great way to close a workshop if you are looking for a gentle warm-down and want to get some swift discussion around some of the feedback that is raised.

Response Cards #debriefing #closing #structured sharing #questions and answers #thiagi #action It can be hard to involve everyone during a closing of a session. Some might stay in the background or get unheard because of louder participants. However, with the use of Response Cards, everyone will be involved in providing feedback or clarify questions at the end of a session.

Save time and effort discovering the right solutions

A structured problem solving process is a surefire way of solving tough problems, discovering creative solutions and driving organizational change. But how can you design for successful outcomes?

With SessionLab, it’s easy to design engaging workshops that deliver results. Drag, drop and reorder blocks to build your agenda. When you make changes or update your agenda, your session timing adjusts automatically , saving you time on manual adjustments.

Collaborating with stakeholders or clients? Share your agenda with a single click and collaborate in real-time. No more sending documents back and forth over email.

Explore how to use SessionLab to design effective problem solving workshops or watch this five minute video to see the planner in action!

Over to you

The problem-solving process can often be as complicated and multifaceted as the problems they are set-up to solve. With the right problem-solving techniques and a mix of creative exercises designed to guide discussion and generate purposeful ideas, we hope we’ve given you the tools to find the best solutions as simply and easily as possible.

Is there a problem-solving technique that you are missing here? Do you have a favorite activity or method you use when facilitating? Let us know in the comments below, we’d love to hear from you!

thank you very much for these excellent techniques

Certainly wonderful article, very detailed. Shared!

Your list of techniques for problem solving can be helpfully extended by adding TRIZ to the list of techniques. TRIZ has 40 problem solving techniques derived from methods inventros and patent holders used to get new patents. About 10-12 are general approaches. many organization sponsor classes in TRIZ that are used to solve business problems or general organiztational problems. You can take a look at TRIZ and dwonload a free internet booklet to see if you feel it shound be included per your selection process.

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What Are Problem-Solving Skills? (Examples Included)

Mike Simpson 0 Comments

By Mike Simpson

Problem-solving skills are important not just for work. In the words of Karl Popper , “All life is problem-solving.”

What on earth does that mean? Simply that being alive means facing challenges. With problem-solving skills, you can navigate issues with greater ease, making hard times, well, less hard.

But what are problem-solving skills? How do you know if you have them or not? Why do they matter to your job search? And what should you do if you don’t feel yours are up to snuff? Luckily, we’re about to get into all of that.

If you’re curious about the world of problem-solving skills, here’s what you need to know.

What Are Problem-Solving Skills?

Before we dig into any examples, let’s focus first on an important question: what are problem-solving skills.

To answer that question, let’s start with the barebones basics. According to Merriam-Webster , problem-solving is “the process or act of finding a solution to a problem.” Why does that matter? Well, because it gives you insight into what problem-solving skills are.

Any skill that helps you find solutions to problems can qualify. And that means problem-solving skills aren’t just one capability, but a toolbox filled with soft skills and hard skills that come together during your time of need.

The ability to solve problems is relevant to any part of your life. Whether your writing a grocery list or dealing with a car that won’t start, you’re actually problem-solving.

The same is true at work, too. Most tasks actually involve a degree of problem-solving. Really? Really.

Think about it this way; when you’re given an assignment, you’re being asked, “Can you do this thing?” Doing that thing is the problem.

Then, you have to find a path that lets you accomplish what you need to do. That is problem-solving.

Yes, sometimes what you need to handle isn’t “challenging” in the difficulty sense. But that doesn’t mean it doesn’t count.

Besides, some of what you need to do will legitimately be hard. Maybe you’re given a new responsibility, or something goes wrong during a project. When that happens, you’ll have to navigate unfamiliar territory, gather new information, and think outside of the box. That’s problem-solving, too.

That’s why hiring managers favor candidates with problem-solving skills. They make you more effective in your role, increasing the odds that you can find solutions whenever the need arises.

How Are Problem-Solving Skills Relevant to a Job Search?

Alright, you probably have a good idea of what problem-solving skills are. Now, it’s time to talk about why they matter to your job search.

We’ve already touched on one major point: hiring managers prefer candidates with strong problem-solving skills. That alone makes these capabilities a relevant part of the equation. If you don’t show the hiring manager you’ve got what it takes to excel, you may struggle to land a position.

But that isn’t the only reason these skills matter. Problem-solving skills can help you during the entire job search process. After all, what’s a job search but a problem – or a series of problems – that needs an answer.

You need a new job; that’s the core problem you’re solving. But every step is its own unique challenge. Finding an opening that matches your skills, creating a resume that resonates with the hiring manager, nailing the interview, and negotiating a salary … those are all smaller problems that are part of the bigger one.

So, problem-solving skills really are at the core of the job search experience. By having strong capabilities in this area, you may find a new position faster than you’d expect.

Okay, you may be thinking, “If hiring managers prefer candidates with problem-solving skills, which ones are they after? Are certain problem-solving capabilities more important today? Is there something I should be going out of my way to showcase?”

While any related skills are worth highlighting, some may get you further than others. Analysis, research, creativity, collaboration , organization, and decision-making are all biggies. With those skills, you can work through the entire problem-solving process, making them worthwhile additions to your resume.

But that doesn’t mean you have to focus there solely. Don’t shy away from showcasing everything you bring to the table. That way, if a particular hiring manager is looking for a certain capability, you’re more likely to tap on what they’re after.

How to Highlight Problem-Solving Skills for Job Search

At this point, it’s ridiculously clear that problem-solving skills are valuable in the eyes of hiring managers. So, how do you show them that you’ve got all of the capabilities they are after? By using the right approach.

When you’re writing your resume or cover letter , your best bet is to highlight achievements that let you put your problem-solving skills to work. That way, you can “show” the hiring manager you have what it takes.

Showing is always better than telling. Anyone can write down, “I have awesome problem-solving skills.” The thing is, that doesn’t really prove that you do. With a great example, you offer up some context, and that makes a difference.

How do you decide on which skills to highlight on your resume or cover letter? By having a great strategy. With the Tailoring Method , it’s all about relevancy. The technique helps you identify skills that matter to that particular hiring manager, allowing you to speak directly to their needs.

Plus, you can use the Tailoring Method when you answer job interview questions . With that approach, you’re making sure those responses are on-point, too.

But when do you talk about your problem-solving capabilities during an interview? Well, there’s a good chance you’ll get asked problem-solving interview questions during your meeting. Take a look at those to see the kinds of questions that are perfect for mentioning these skills.

However, you don’t have to stop there. If you’re asked about your greatest achievement or your strengths, those could be opportunities, too. Nearly any open-ended question could be the right time to discuss those skills, so keep that in mind as you practice for your interview.

How to Develop Problem-Solving Skills If You Don’t Have Them

Developing problem-solving skills may seem a bit tricky on the surface, especially if you think you don’t have them. The thing is, it doesn’t actually have to be hard. You simply need to use the right strategy.

First, understand that you probably do have problem-solving skills; you simply may not have realized it. After all, life is full of challenges that you have to tackle, so there’s a good chance you’ve developed some abilities along the way.

Now, let’s reframe the question and focus on how to improve your problem-solving skills. Here’s how to go about it.

Understand the Problem-Solving Process

In many cases, problem-solving is all about the process. You:

Identify the problem
Analyze the key elements
Look for potential solutions
Examine the options for viability and risk
Decide on an approach
Review the outcome for lessons

By understanding the core process, you can apply it more effectively. That way, when you encounter an issue, you’ll know how to approach it, increasing the odds you’ll handle the situation effectively.

Try Puzzles and Games

Any activity that lets you take the steps listed above could help you hone your problem-solving skills. For example, brainteasers, puzzles, and logic-based games can be great places to start.

Whether it’s something as straightforward – but nonetheless challenging – as Sudoku or a Rubik’s Cube, or something as complex as Settlers of Catan, it puts your problem-solving skills to work. Plus, if you enjoy the activity, it makes skill-building fun, making it a win-win.

Look for Daily Opportunities

If you’re looking for a practical approach, you’re in luck. You can also look at the various challenges you face during the day and think about how to overcome them.

For example, if you always experience a mid-day energy slump that hurts your productivity, take a deep dive into that problem. Define what’s happening, think about why it occurs, consider various solutions, pick one to try, and analyze the results.

By using the problem-solving approach more often in your life, you’ll develop those skills further and make using these capabilities a habit. Plus, you may find ways to improve your day-to-day living, which is a nice bonus.

Volunteer for “Stretch” Projects

If you’re currently employed, volunteering for projects that push you slightly outside of your comfort zone can help you develop problem-solving skills, too. You’ll encounter the unknown and have to think outside of the box, both of which can boost critical problem-solving-related skills.

Plus, you may gain other capabilities along the way, like experience with new technologies or tools. That makes the project an even bigger career booster, which is pretty awesome.

List of Problem-Solving Skills

Alright, we’ve taken a pretty deep dive into what problem-solving skills are. Now, it’s time for some problem-solving skills examples.

As we mentioned above, there are a ton of capabilities and traits that can support better problem-solving. By understanding what they are, you can showcase the right abilities during your job search.

So, without further ado, here is a quick list of problem-solving skill examples:

Collaboration
Organization
Decision-Making
Troubleshooting
Self-Reliance
Self-Motivation
Communication
Attention to Detail
Brainstorming
Forecasting
Active Listening
Accountability
Open-Mindedness
Critical Thinking
Flexibility

Do you have to showcase all of those skills during your job search individually? No, not necessarily. Instead, you want to highlight a range of capabilities based on what the hiring manager is after. If you’re using the Tailoring Method, you’ll know which ones need to make their way into your resume, cover letter, and interview answers.

Now, are there other skills that support problem-solving? Yes, there certainly can be.

Essentially any skill that helps you go from the problem to the solution can, in its own right, be a problem-solving skill.

All of the skills above can be part of the equation. But, if you have another capability that helps you flourish when you encounter an obstacle, it can count, too.

Reflect on your past experience and consider how you’ve navigated challenges in the past. If a particular skill helped you do that, then it’s worth highlighting during a job search.

If you would like to find out more about skills to put on a resume , we’ve taken a close look at the topic before. Along with problem-solving skills, we dig into a variety of other areas, helping you choose what to highlight so that you can increase your odds of landing your perfect job.

Putting It All Together

Ultimately, problem-solving skills are essential for professionals in any kind of field. By honing your capabilities and showcasing them during your job search, you can become a stronger candidate and employee. In the end, that’s all good stuff, making it easier for you to keep your career on track today, tomorrow, and well into the future.

Co-Founder and CEO of TheInterviewGuys.com. Mike is a job interview and career expert and the head writer at TheInterviewGuys.com.

His advice and insights have been shared and featured by publications such as Forbes , Entrepreneur , CNBC and more as well as educational institutions such as the University of Michigan , Penn State , Northeastern and others.

Learn more about The Interview Guys on our About Us page .

About The Author

Mike simpson.

Co-Founder and CEO of TheInterviewGuys.com. Mike is a job interview and career expert and the head writer at TheInterviewGuys.com. His advice and insights have been shared and featured by publications such as Forbes , Entrepreneur , CNBC and more as well as educational institutions such as the University of Michigan , Penn State , Northeastern and others. Learn more about The Interview Guys on our About Us page .

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How to Nail your next Technical Interview

You may be missing out on a 66.5% salary hike*, nick camilleri, how many years of coding experience do you have, free course on 'sorting algorithms' by omkar deshpande (stanford phd, head of curriculum, ik).

What are problem-solving skills? (Examples included!)

Last updated by Swaminathan Iyer on Apr 01, 2024 at 01:09 PM | Reading time: 13 minutes

Life in the 21st century is all about efficiency and development. The unending quench of discovering the unknown, materializing one dream after another, has helped push the limits through the sky. But have you ever thought what the key to all of these astronomical successes is?

It is the zeal to solve a problem with the resources available to generate the best possible results.

Here's what this article will cover:

What are problem-solving skills , how do problem-solving skills help or act as your pillars of success, how do employers assess your problem-solving skills , steps to execute problem-solving skills, skills to hone for an apt solution-finder, examples of problem-solving techniques.

Dos and Don'ts in interviews

How to improve your problem-solving skills ?

How to highlight problem-solving skills .

Problem-solving is hunting; it is a savage pleasure, and we are born to it." –Thomas Harris .

The truth is, problem-solving skills are acquirable for some people while others adapt to it like fish in the water. Working in IT, web development, coding, machine learning, and the likes demand the ability to make decisions at a moment's notice.

So, do you want to back off when the time comes or take it up as a challenge?

Brush up your problem-solving skills or better, enhance them, and make them your forte by reading this article. No technical interview preparation guide is complete without tips to improve such problem-solving skills.

Also read: Why do FAANG companies test for problem-solving skills in their interviews.

Larry and his team suddenly face a major crisis. Not a single developer in his team who is good with String is coming to the office, but there is an urgent client requirement. Larry asks his team if anybody is confident enough to pull it through, and surprisingly, he sees one solitary hand of Jim in the mix. But it is a 4-men job, at least. Realizing that there is no way out other than working with another team(s), he wastes no time. He sends out emails to other teams asking for at least two more developers, counting himself and Jim. 4 more fellow coders came to the rescue and delivered the project before the deadline!

Problem-solving skills enable you to observe the situation and determine the contributing factors of the issue. Identifying the root cause and the ability to take necessary steps with available resources are integral in finessing your problem-solving ability.

All technical interview preparation courses , therefore, cover this crucial aspect.

Employers seek problem-solving skills in their employees . And why not?

Who wouldn't want to have an efficient employee like Larry? The knack of not backing down from a challenge is the perfect catalyst for business expansion.

Problem-solving skills help you attain insight into the source of the problem and figuring out an ideal solution. However, several skills and their correct implementation are essential, which are listed below.

Patient listener : To identify a problem, you must first be all ears to gain information about the situation.
Eye for detail : Once you start listening minutely, you now need to identify the data's discrepancies and have an intuitive eye for detail.
Thorough research : Background research and data verification is bread and butter for efficient problem-solvers.
Innovative approach : It is not just about getting it done. It's about taking a challenging approach in a mission to maximize results.
Communication skills: Flawless communication skills are necessary to negate any misunderstanding and ensure conveying the message with clarity. You can indeed consider this as a great time saver!
Composure : Your ability to remain calm even in a demanding situation will always earn you dividends in the path to success. It is not a quality that you can imbibe easily, but rigorous practice can do the trick for you.
Decision-making ability : Having a knack for making the right decisions under pressure is a highly sought-after attribute by employers when hiring people. Taking quick decisions in dire straits is the reason why the company is paying you the big bucks.
Team player : Understanding the strengths and weaknesses of your team is instrumental in maintaining team spirit. Higher the team spirit, the better the performance!

Employers today prioritize hiring people with soft skills like problem-solving abilities to maximize business output even when the going gets tough. Your problem-solving ability is judged based on:

If you have accomplished any remarkable feat in a taxing situation. This gives an insight into the upper benchmark of your performance.
Presenting hypothetical problems for the interviewee to solve is another commonly used trick to ascertain your productivity metrics and creative problem-solving techniques in tough conditions.
Some organizations may even line up some challenging tests and exercises to have a firsthand look at the execution and effectiveness of your technical skills in the approach to problem-solving.

"We cannot solve a problem with the same level of thinking that created them." – Albert Einstein

Analyze contributing factors

James was getting an error code during the execution of specific UI updates. He started analyzing the code and rechecking the repository for any possible mistake. To his delight, his hunch turned out to be accurate. He immediately made the necessary changes, and the updates were successfully executed.

Analysis of contributing factors and its repercussions in the ebb and flow of the task is a preliminary attribute of an able problem-solver. To acquire perfection in analysis and problem-solving skills, you must ensure a thorough:

Gathering of data
Diligent study of the collected data
Scrutiny to filter relevant data
Historical analysis
Generate interventions

Working at a software development firm, Donald is perturbed by the lack of advancement in the deep learning project. Lack of idea and innovation is leading to nowhere. He decided that enough is enough. He asked for a group session to brainstorm in the hope of generating some leads. The session was a huge success, and Donald was finally able to catch a breather.

It is not an unknown fact that 'we' is always more productive than 'I' under any circumstance.

Utilizing the versatility of your available resources with the help of various sessions can work miracles. Such sessions can be for:

Creative thinking
Brainstorming
Planning a project
Forecasting future trends
Prediction of possible outcomes
Designing your project with originality, etc.
Evaluate solutions

This is more up the alley for managers and team leads. To become adept at evaluating solutions, one must gain prolonged experience in corporate decision-making. The evaluation process needs to consider potential costs, available resources, and possible hurdles of project completion.

Remember Donald?

Yes, he is a team lead, and therefore, he had the authority to initiate a brainstorming session with multiple teams to bring in new ideas.

The secret to evaluating solutions?

Corroboration
Identifying change in trends
Prioritization
Implement a plan

Choosing the right course of action is the preliminary step to solve the problems. The success of the execution is streamlined with the help of quality benchmarks to indicate its effectiveness.

"A problem is a chance for you to do the best!" – Duke Ellington .

Knowing the right people to do it for you is essential for successful implementation. It is also crucial that you are accustomed to your organization's operating procedures before you formulate the best possible strategy.

Skills you need are:

Project management
Implementation of project strategy
Collaboration
Time management
Developing appropriate quality benchmark
Assess the solution's effectiveness

An ideal way to detect whether a solution is effective or not is to check if the problem still exists after applying the solution. Benchmarks need to be set as per organizational standards to help them assess the situation and if any further changes are required in the interim.

Data analysis
Communication
Close follow-ups
Troubleshooting

"A problem well stated is a problem half solved." –John Dewey

Research: Problem-solving is not complete without extensive research. It is otherwise impossible to identify the problem without gathering enough data on the errors and their analysis. Consulting with your team gives you an edge to find the solution quicker.
Analysis: Analysis of the situation is a must. Analytical skills further assist you in identifying the discrepancies and the possible actions which can resolve the issue.
Decision-making: The ability to make decisions in hours of need defines your mettle. The onus is on you to be proactive and choose the right course of action.
Communication: Are you great at conversations? If so, communication skills can help you garner much-required assistance for the project. Communication of the issues and how you want the project done are critical for the problem-solving process's smooth flow.
Dependability: Having dependable members boosts the morale of the team. If you are a problem-solver, taking responsibility and taking it on the chin to solve the issues needs to be your forte.
Select an example or situation that you can handle without any issue.
Do not stray off topic and stay on track.
Do not use jargon in your interview. So, choose your example and words wisely.
Do not choose a redundant issue.

Sam has come to an interview for a team-lead profile. The recruiter asks a situation-based problem in regards to machine learning software. Though tricky, Sam knew the exact way around for the problem and answered it precisely to the point. The recruiter is delighted and hires Sam for the position.

Thirst for knowledge : An insatiable thirst for knowledge is the secret door to success in problem-solving skills. If Sam was unaware of the tweaks needed to solve the problem, do you think the manager would have been impressed? No, managers at companies like Google and Facebook are looking for people who can act independently with their available resources. The question is, are you the problem solver who can be a catch to any company?
An intuition for challenge : You need to be intuitive and have a sharp nose for challenges. The more you take up difficult situations and handle them with panache and ease, the more you can hone your problem-solving skills .
Practice and more practice: Practice makes a man perfect – truer words have never been said. Effective problem solving is achieved not by slacking off but by acquainting yourself with various situations and applying your skills to resolve them. Remember, experience can never be substituted, and you have to take the long route to success!
Keen and observant eyes : Do you have an eye for detail, and are you quick to point out discrepancies in data analysis? If yes, you are already one step towards becoming a valued problem solver in your company. Also, if you are a person who observes closely what is being done and why others do it, it helps develop your decision-making skills in future. Don't forget to mention this in your resume.

Tom has been applying frantically for a job since he moved to Arizona but seemed unable to find just the right one. When he sees his attempts are futile, he decides to add some of his previous company's achievements, thinking it might help. Oh, boy, did it help! Tom writes about when he was asked to handle a team of 12 single-handedly while his manager suddenly went on a sabbatical. Tom had no prior experience of leading a team but appeared to come out of this fix with flying colors.

Megan is currently looking for a step up in her career. She carefully drafts a cover letter that entails her achievements with clarity. The cover letter explained her contributions in reviving team spirit in the office after her predecessor, with his poor man-management, had successfully built a wall of distrust among the employees.

Problem-solving skills for resume : You can convey your achievements or even your hobbies to the person sitting in front of you, or not, depending on his/her nature. But you cannot afford to miss the chance to showcase your best achievement. It is in your best interest to build your CV around the achievements to give it maximum traction and attention. Mention the problem you faced and jot down the course of action you took to nullify the situation. Nobody can stop you if this is done right!
Problem-solving skills for cover letter : Use it as an opportunity to let the company delve into your success story so far and the factors leading to it. If you have done your research on the organization you're applying for, it will not hurt your chances of identifying some challenges of the company and suggesting some solutions. It goes down a long way if you indeed join forces!

If you are adequately seasoned with problem-solving skills with dedication and practice, you're already almost there. Proper interview preparation tips can further help you in this regard.

Swaminathan Iyer

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Problem-Solving Strategies and Obstacles

Kendra Cherry, MS, is a psychosocial rehabilitation specialist, psychology educator, and author of the "Everything Psychology Book."

Sean is a fact-checker and researcher with experience in sociology, field research, and data analytics.

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From deciding what to eat for dinner to considering whether it's the right time to buy a house, problem-solving is a large part of our daily lives. Learn some of the problem-solving strategies that exist and how to use them in real life, along with ways to overcome obstacles that are making it harder to resolve the issues you face.

What Is Problem-Solving?

In cognitive psychology , the term 'problem-solving' refers to the mental process that people go through to discover, analyze, and solve problems.

A problem exists when there is a goal that we want to achieve but the process by which we will achieve it is not obvious to us. Put another way, there is something that we want to occur in our life, yet we are not immediately certain how to make it happen.

Maybe you want a better relationship with your spouse or another family member but you're not sure how to improve it. Or you want to start a business but are unsure what steps to take. Problem-solving helps you figure out how to achieve these desires.

The problem-solving process involves:

Discovery of the problem
Deciding to tackle the issue
Seeking to understand the problem more fully
Researching available options or solutions
Taking action to resolve the issue

Before problem-solving can occur, it is important to first understand the exact nature of the problem itself. If your understanding of the issue is faulty, your attempts to resolve it will also be incorrect or flawed.

Problem-Solving Mental Processes

Several mental processes are at work during problem-solving. Among them are:

Perceptually recognizing the problem
Representing the problem in memory
Considering relevant information that applies to the problem
Identifying different aspects of the problem
Labeling and describing the problem

Problem-Solving Strategies

There are many ways to go about solving a problem. Some of these strategies might be used on their own, or you may decide to employ multiple approaches when working to figure out and fix a problem.

An algorithm is a step-by-step procedure that, by following certain "rules" produces a solution. Algorithms are commonly used in mathematics to solve division or multiplication problems. But they can be used in other fields as well.

In psychology, algorithms can be used to help identify individuals with a greater risk of mental health issues. For instance, research suggests that certain algorithms might help us recognize children with an elevated risk of suicide or self-harm.

One benefit of algorithms is that they guarantee an accurate answer. However, they aren't always the best approach to problem-solving, in part because detecting patterns can be incredibly time-consuming.

There are also concerns when machine learning is involved—also known as artificial intelligence (AI)—such as whether they can accurately predict human behaviors.

Heuristics are shortcut strategies that people can use to solve a problem at hand. These "rule of thumb" approaches allow you to simplify complex problems, reducing the total number of possible solutions to a more manageable set.

If you find yourself sitting in a traffic jam, for example, you may quickly consider other routes, taking one to get moving once again. When shopping for a new car, you might think back to a prior experience when negotiating got you a lower price, then employ the same tactics.

While heuristics may be helpful when facing smaller issues, major decisions shouldn't necessarily be made using a shortcut approach. Heuristics also don't guarantee an effective solution, such as when trying to drive around a traffic jam only to find yourself on an equally crowded route.

Trial and Error

A trial-and-error approach to problem-solving involves trying a number of potential solutions to a particular issue, then ruling out those that do not work. If you're not sure whether to buy a shirt in blue or green, for instance, you may try on each before deciding which one to purchase.

This can be a good strategy to use if you have a limited number of solutions available. But if there are many different choices available, narrowing down the possible options using another problem-solving technique can be helpful before attempting trial and error.

In some cases, the solution to a problem can appear as a sudden insight. You are facing an issue in a relationship or your career when, out of nowhere, the solution appears in your mind and you know exactly what to do.

Insight can occur when the problem in front of you is similar to an issue that you've dealt with in the past. Although, you may not recognize what is occurring since the underlying mental processes that lead to insight often happen outside of conscious awareness .

Research indicates that insight is most likely to occur during times when you are alone—such as when going on a walk by yourself, when you're in the shower, or when lying in bed after waking up.

How to Apply Problem-Solving Strategies in Real Life

If you're facing a problem, you can implement one or more of these strategies to find a potential solution. Here's how to use them in real life:

Create a flow chart . If you have time, you can take advantage of the algorithm approach to problem-solving by sitting down and making a flow chart of each potential solution, its consequences, and what happens next.
Recall your past experiences . When a problem needs to be solved fairly quickly, heuristics may be a better approach. Think back to when you faced a similar issue, then use your knowledge and experience to choose the best option possible.
Start trying potential solutions . If your options are limited, start trying them one by one to see which solution is best for achieving your desired goal. If a particular solution doesn't work, move on to the next.
Take some time alone . Since insight is often achieved when you're alone, carve out time to be by yourself for a while. The answer to your problem may come to you, seemingly out of the blue, if you spend some time away from others.

Obstacles to Problem-Solving

Problem-solving is not a flawless process as there are a number of obstacles that can interfere with our ability to solve a problem quickly and efficiently. These obstacles include:

Assumptions: When dealing with a problem, people can make assumptions about the constraints and obstacles that prevent certain solutions. Thus, they may not even try some potential options.
Functional fixedness : This term refers to the tendency to view problems only in their customary manner. Functional fixedness prevents people from fully seeing all of the different options that might be available to find a solution.
Irrelevant or misleading information: When trying to solve a problem, it's important to distinguish between information that is relevant to the issue and irrelevant data that can lead to faulty solutions. The more complex the problem, the easier it is to focus on misleading or irrelevant information.
Mental set: A mental set is a tendency to only use solutions that have worked in the past rather than looking for alternative ideas. A mental set can work as a heuristic, making it a useful problem-solving tool. However, mental sets can also lead to inflexibility, making it more difficult to find effective solutions.

How to Improve Your Problem-Solving Skills

In the end, if your goal is to become a better problem-solver, it's helpful to remember that this is a process. Thus, if you want to improve your problem-solving skills, following these steps can help lead you to your solution:

Recognize that a problem exists . If you are facing a problem, there are generally signs. For instance, if you have a mental illness , you may experience excessive fear or sadness, mood changes, and changes in sleeping or eating habits. Recognizing these signs can help you realize that an issue exists.
Decide to solve the problem . Make a conscious decision to solve the issue at hand. Commit to yourself that you will go through the steps necessary to find a solution.
Seek to fully understand the issue . Analyze the problem you face, looking at it from all sides. If your problem is relationship-related, for instance, ask yourself how the other person may be interpreting the issue. You might also consider how your actions might be contributing to the situation.
Research potential options . Using the problem-solving strategies mentioned, research potential solutions. Make a list of options, then consider each one individually. What are some pros and cons of taking the available routes? What would you need to do to make them happen?
Take action . Select the best solution possible and take action. Action is one of the steps required for change . So, go through the motions needed to resolve the issue.
Try another option, if needed . If the solution you chose didn't work, don't give up. Either go through the problem-solving process again or simply try another option.

You can find a way to solve your problems as long as you keep working toward this goal—even if the best solution is simply to let go because no other good solution exists.

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By Kendra Cherry, MSEd Kendra Cherry, MS, is a psychosocial rehabilitation specialist, psychology educator, and author of the "Everything Psychology Book."

50 Problem-Solving and Critical Thinking Examples

Critical thinking and problem solving are essential skills for success in the 21st century. Critical thinking is the ability to analyze information, evaluate evidence, and draw logical conclusions. Problem solving is the ability to apply critical thinking to find effective solutions to various challenges. Both skills require creativity, curiosity, and persistence. Developing critical thinking and problem solving skills can help students improve their academic performance, enhance their career prospects, and become more informed and engaged citizens.

Sanju Pradeepa

Problem-Solving and Critical Thinking Examples

In today’s complex and fast-paced world, the ability to think critically and solve problems effectively has become a vital skill for success in all areas of life. Whether it’s navigating professional challenges, making sound decisions, or finding innovative solutions, critical thinking and problem-solving are key to overcoming obstacles and achieving desired outcomes. In this blog post, we will explore problem-solving and critical thinking examples.

Developing the skills needed for critical thinking and problem solving.

It is not enough to simply recognize an issue; we must use the right tools and techniques to address it. To do this, we must learn how to define and identify the problem or task at hand, gather relevant information from reliable sources, analyze and compare data to draw conclusions, make logical connections between different ideas, generate a solution or action plan, and make a recommendation.

The first step in developing these skills is understanding what the problem or task is that needs to be addressed. This requires careful consideration of all available information in order to form an accurate picture of what needs to be done. Once the issue has been identified, gathering reliable sources of data can help further your understanding of it. Sources could include interviews with customers or stakeholders, surveys, industry reports, and analysis of customer feedback.

After collecting relevant information from reliable sources, it’s important to analyze and compare the data in order to draw meaningful conclusions about the situation at hand. This helps us better understand our options for addressing an issue by providing context for decision-making. Once you have analyzed the data you collected, making logical connections between different ideas can help you form a more complete picture of the situation and inform your potential solutions.

Once you have analyzed your options for addressing an issue based on all available data points, it’s time to generate a solution or action plan that takes into account considerations such as cost-effectiveness and feasibility. It’s also important to consider the risk factors associated with any proposed solutions in order to ensure that they are responsible before moving forward with implementation. Finally, once all the analysis has been completed, it is time to make a recommendation based on your findings, which should take into account any objectives set out by stakeholders at the beginning of this process as well as any other pertinent factors discovered throughout the analysis stage.

By following these steps carefully when faced with complex issues, one can effectively use critical thinking and problem-solving skills in order to achieve desired outcomes more efficiently than would otherwise be possible without them, while also taking responsibility for decisions made along the way.

What Does Critical Thinking Involve: 5 Essential Skill

Problem-solving and critical thinking examples.

Problem-solving and critical thinking are key skills that are highly valued in any professional setting. These skills enable individuals to analyze complex situations, make informed decisions, and find innovative solutions. Here, we present 25 examples of problem-solving and critical thinking. problem-solving scenarios to help you cultivate and enhance these skills.

Ethical dilemma: A company faces a situation where a client asks for a product that does not meet quality standards. The team must decide how to address the client’s request without compromising the company’s credibility or values.

Brainstorming session: A team needs to come up with new ideas for a marketing campaign targeting a specific demographic. Through an organized brainstorming session, they explore various approaches and analyze their potential impact.

Troubleshooting technical issues : An IT professional receives a ticket indicating a network outage. They analyze the issue, assess potential causes (hardware, software, or connectivity), and solve the problem efficiently.

Negotiation : During contract negotiations, representatives from two companies must find common ground to strike a mutually beneficial agreement, considering the needs and limitations of both parties.

Project management: A project manager identifies potential risks and develops contingency plans to address unforeseen obstacles, ensuring the project stays on track.

Decision-making under pressure: In a high-stakes situation, a medical professional must make a critical decision regarding a patient’s treatment, weighing all available information and considering potential risks.

Conflict resolution: A team encounters conflicts due to differing opinions or approaches. The team leader facilitates a discussion to reach a consensus while considering everyone’s perspectives.

Data analysis: A data scientist is presented with a large dataset and is tasked with extracting valuable insights. They apply analytical techniques to identify trends, correlations, and patterns that can inform decision-making.

Customer service: A customer service representative encounters a challenging customer complaint and must employ active listening and problem-solving skills to address the issue and provide a satisfactory resolution.

Market research : A business seeks to expand into a new market. They conduct thorough market research, analyzing consumer behavior, competitor strategies, and economic factors to make informed market-entry decisions.

Creative problem-solvin g: An engineer faces a design challenge and must think outside the box to come up with a unique and innovative solution that meets project requirements.

Change management: During a company-wide transition, managers must effectively communicate the change, address employees’ concerns, and facilitate a smooth transition process.

Crisis management: When a company faces a public relations crisis, effective critical thinking is necessary to analyze the situation, develop a response strategy, and minimize potential damage to the company’s reputation.

Cost optimization : A financial analyst identifies areas where expenses can be reduced while maintaining operational efficiency, presenting recommendations for cost savings.

Time management : An employee has multiple deadlines to meet. They assess the priority of each task, develop a plan, and allocate time accordingly to achieve optimal productivity.

Quality control: A production manager detects an increase in product defects and investigates the root causes, implementing corrective actions to enhance product quality.

Strategic planning: An executive team engages in strategic planning to define long-term goals, assess market trends, and identify growth opportunities.

Cross-functional collaboration: Multiple teams with different areas of expertise must collaborate to develop a comprehensive solution, combining their knowledge and skills.

Training and development : A manager identifies skill gaps in their team and designs training programs to enhance critical thinking, problem-solving, and decision-making abilities.

Risk assessment : A risk management professional evaluates potential risks associated with a new business venture, weighing their potential impact and developing strategies to mitigate them.

Continuous improvement: An operations manager analyzes existing processes, identifies inefficiencies, and introduces improvements to enhance productivity and customer satisfaction.

Customer needs analysis: A product development team conducts extensive research to understand customer needs and preferences, ensuring that the resulting product meets those requirements.

Crisis decision-making: A team dealing with a crisis must think quickly, assess the situation, and make timely decisions with limited information.

Marketing campaign analysis : A marketing team evaluates the success of a recent campaign, analyzing key performance indicators to understand its impact on sales and customer engagement.

Constructive feedback: A supervisor provides feedback to an employee, highlighting areas for improvement and offering constructive suggestions for growth.

Conflict resolution in a team project: Team members engaged in a project have conflicting ideas on the approach. They must engage in open dialogue, actively listen to each other’s perspectives, and reach a compromise that aligns with the project’s goals.

Crisis response in a natural disaster: Emergency responders must think critically and swiftly in responding to a natural disaster, coordinating rescue efforts, allocating resources effectively, and prioritizing the needs of affected individuals.

Product innovation : A product development team conducts market research, studies consumer trends, and uses critical thinking to create innovative products that address unmet customer needs.

Supply chain optimization: A logistics manager analyzes the supply chain to identify areas for efficiency improvement, such as reducing transportation costs, improving inventory management, or streamlining order fulfillment processes.

Business strategy formulation: A business executive assesses market dynamics, the competitive landscape, and internal capabilities to develop a robust business strategy that ensures sustainable growth and competitiveness.

Crisis communication: In the face of a public relations crisis, an organization’s spokesperson must think critically to develop and deliver a transparent, authentic, and effective communication strategy to rebuild trust and manage reputation.

Social problem-solving: A group of volunteers addresses a specific social issue, such as poverty or homelessness, by critically examining its root causes, collaborating with stakeholders, and implementing sustainable solutions for the affected population.

Problem-Solving Mindset: How to Achieve It (15 Ways)

Risk assessment in investment decision-making: An investment analyst evaluates various investment opportunities, conducting risk assessments based on market trends, financial indicators, and potential regulatory changes to make informed investment recommendations.

Environmental sustainability: An environmental scientist analyzes the impact of industrial processes on the environment, develops strategies to mitigate risks, and promotes sustainable practices within organizations and communities.

Adaptation to technological advancements : In a rapidly evolving technological landscape, professionals need critical thinking skills to adapt to new tools, software, and systems, ensuring they can effectively leverage these advancements to enhance productivity and efficiency.

Productivity improvement: An operations manager leverages critical thinking to identify productivity bottlenecks within a workflow and implement process improvements to optimize resource utilization, minimize waste, and increase overall efficiency.

Cost-benefit analysis: An organization considering a major investment or expansion opportunity conducts a thorough cost-benefit analysis, weighing potential costs against expected benefits to make an informed decision.

Human resources management : HR professionals utilize critical thinking to assess job applicants, identify skill gaps within the organization, and design training and development programs to enhance the workforce’s capabilities.

Root cause analysis: In response to a recurring problem or inefficiency, professionals apply critical thinking to identify the root cause of the issue, develop remedial actions, and prevent future occurrences.

Leadership development: Aspiring leaders undergo critical thinking exercises to enhance their decision-making abilities, develop strategic thinking skills, and foster a culture of innovation within their teams.

Brand positioning : Marketers conduct comprehensive market research and consumer behavior analysis to strategically position a brand, differentiating it from competitors and appealing to target audiences effectively.

Resource allocation: Non-profit organizations distribute limited resources efficiently, critically evaluating project proposals, considering social impact, and allocating resources to initiatives that align with their mission.

Innovating in a mature market: A company operating in a mature market seeks to innovate to maintain a competitive edge. They cultivate critical thinking skills to identify gaps, anticipate changing customer needs, and develop new strategies, products, or services accordingly.

Analyzing financial statements : Financial analysts critically assess financial statements, analyze key performance indicators, and derive insights to support financial decision-making, such as investment evaluations or budget planning.

Crisis intervention : Mental health professionals employ critical thinking and problem-solving to assess crises faced by individuals or communities, develop intervention plans, and provide support during challenging times.

Data privacy and cybersecurity : IT professionals critically evaluate existing cybersecurity measures, identify vulnerabilities, and develop strategies to protect sensitive data from threats, ensuring compliance with privacy regulations.

Process improvement : Professionals in manufacturing or service industries critically evaluate existing processes, identify inefficiencies, and implement improvements to optimize efficiency, quality, and customer satisfaction.

Multi-channel marketing strategy : Marketers employ critical thinking to design and execute effective marketing campaigns across various channels such as social media, web, print, and television, ensuring a cohesive brand experience for customers.

Peer review: Researchers critically analyze and review the work of their peers, providing constructive feedback and ensuring the accuracy, validity, and reliability of scientific studies.

Project coordination : A project manager must coordinate multiple teams and resources to ensure seamless collaboration, identify potential bottlenecks, and find solutions to keep the project on schedule.

These examples highlight the various contexts in which problem-solving and critical-thinking skills are necessary for success. By understanding and practicing these skills, individuals can enhance their ability to navigate challenges and make sound decisions in both personal and professional endeavors.

Conclusion:

Critical thinking and problem-solving are indispensable skills that empower individuals to overcome challenges, make sound decisions, and find innovative solutions. By honing these skills, one can navigate through the complexities of modern life and achieve success in both personal and professional endeavors. Embrace the power of critical thinking and problem-solving, and unlock the door to endless possibilities and growth.

Problem solving From Wikipedia, the free encyclopedia
Critical thinking From Wikipedia, the free encyclopedia
The Importance of Critical Thinking and Problem Solving Skills for Students (5 Minutes)

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31 examples of problem solving performance review phrases

Jump to section

You're doing great

You should think of improving

Tips to improve

Use these practical examples of phrases, sample comments, and templates for your performance review , 360-degree feedback survey, or manager appraisal.

The following examples not only relate to problem-solving but also conflict management , effective solutions, selecting the best alternatives, decision making , problem identification, analyzing effectively, and generally becoming an effective problem-solving strategist. Start using effective performance review questions to help better guide your workforce's development.

Problem solving appraisal comments: you're doing great

You always maintain an effective dialogue with clients when they have technical problems. Being clear and articulate makes sure our customers' faults are attended to promptly.
You constantly make sure to look beyond the obvious you never stop at the first answer. You’re really good at exploring alternatives. Well done!
Keeping the supervisors and managers informed of status changes and requests is important. You’re really good at communicating the changes to the projects at all times. Keep it up!
You stay cool and collected even when things aren’t going according to plan or up in the air. This is a great trait to possess. Well done!
You’re excellent at giving an honest and logical analysis. Keep it up! Effectively diagnosing complex problems and reaching sustainable solutions is one of your strong points.
Your ability to ability to make complex systems into simple ones is truly a unique skill to possess. Well done!
You often identify practical solutions to every roadblock. You’re a real asset to the team! Great job.
You always listen actively and attentively to make sure you understand what the exact problem is and you come up with solutions in an effective manner.
You have an amazing ability to clearly explain options and solutions effectively and efficiently. Well done!
When driving projects, you can shift to other areas comfortably and easily. making sure the project runs smoothly. Great job!

problem-solving-performance-review-phrases-person-at-work-talking-to-boss

Problem solving performance review phrases: you should think of improving

You always seem too overwhelmed when faced with multiple problems. Try to think of ways to make problems more manageable so that they can be solved in a timely and effective manner.
Avoiding conflicts constantly with people is not a good idea as you will only build up personal frustration and nothing will be done to remedy the situation. Try to face people when there are problems and rectify problems when they occur.
Don’t allow demanding customers to rattle your cage too much. If they become too demanding, take a step back, regulate your emotions , and try to make use of online support tools to help you rectify problems these tools can help a lot!
It’s necessary that you learn from your past mistakes . You cannot keep making the same mistakes , as this is not beneficial to the company.
You tend to ask the same questions over and over again. Try to listen more attentively or take notes when colleagues are answering!
Providing multiple solutions in an indirect and creative approach will allow you to be more effective at problem-solving . if you struggle with this typically through viewing the problem in a new and unusual light.
You fail to provide staff with the appropriate amount of structure and direction. They must know the direction you wish them to go in to achieve their goals .
You need to be able to recognize repetitive trends to solve problems promptly.
You tend to have problems troubleshooting even the most basic of questions. As a problem solver and customer support person, it’s imperative that you can answer these questions easily.
Read through your training manual and make sure you fully understand it before attempting questions again.

problem-solving-performance-review-phrases-person-talking-at-work

Performance review tips to improve problem solving

Try to complain less about problems and come up with solutions to the problems more often. Complaining is not beneficial to progression and innovation.
As a problem solver, it’s important to be able to handle multiple priorities under short deadlines.
You need to be able to effectively distinguish between the cause and the symptoms of problems to solve them in an efficient and timely manner.
Try to anticipate problems in advance before they become major roadblocks down the road.
Try to view obstacles as opportunities to learn and thrive at the challenge of solving the problem.
Remember to prioritize problems according to their degree of urgency. It's important that you spend the majority of your time on urgent tasks over menial ones.
When putting plans into place, stick to them and make sure they are completed.
When solving problems, try to allocate appropriate levels of resources when undertaking new projects. It is important to become as efficient and as effective as possible.
Try to learn to pace yourself when solving problems to avoid burnout . You’re a great asset to the team and we cannot afford to lose at this point.
Meeting regularly with your staff to review results is vital to the problem-solving process.
Staff that has regular check-ins understand what it is that is required of them, what they are currently achieving, and areas they may need to improve. Try to hold one-on-one meetings every week.

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Madeline Miles

Madeline is a writer, communicator, and storyteller who is passionate about using words to help drive positive change. She holds a bachelor's in English Creative Writing and Communication Studies and lives in Denver, Colorado. In her spare time, she's usually somewhere outside (preferably in the mountains) — and enjoys poetry and fiction.

How a performance review template improves the feedback process

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7 Problem Solving Skills That Aren’t Just Buzzwords (+ Resume Example)

Julia Mlcuchova ,
Updated April 8, 2024 9 min read

Problem-solving skills are something everybody should include on their resume, yet only a few seem to understand what these skills actually are. If you've always felt that the term "problem-solving skills" is rather vague and wanted to know more, you've come to the right place.

In this article, we're going to explain what problem-solving skills really mean. We'll talk about what makes up good problem-solving skills and give you tips on how to get better at them. You'll also find out how to make your problem-solving abilities look more impressive to those who might want to hire you.

Sounds good, right? Curious to learn more?

In this article we’ll show you:

What are problem solving skills;
Why are they important;
Specific problem solving skills examples;
How to develop your problem solving skills;
And, how to showcase them on your resume.

Click on a section to skip

What are problem solving skills?

Why are problem solving skills important, the best 7 problem solving skills examples, how to develop problem solving skills, problem solving skills resume example, key takeaways: problem solving skills.

First of all, they're more than just a buzzword!

Problem-solving skills are a set of specific abilities that allow you to deal with unexpected situations in the workplace, whether it be job related or team related.

It's a complex process that involves several “sub skills” or “sub steps,” namely:

Recognizing and identifying the issue at hand.
Breaking the problem down into smaller parts and analyzing how they relate to one another.
Creating potential solutions to the problem, evaluating them and picking the best one.
Applying the chosen solution and assessing its outcome.
Learning from the whole process to deal with future problems more effectively.

As you can see, it's not just about solving problems that are right in front of us, but also about predicting potential issues and being prepared to deal with them before they arise.

Despite what you may believe, problem-solving skills aren't just for managers .

Think about it this way: Why do employers hire employees in the first place? To solve problems for them!

And, as we all know, problems don't discriminate. In other words, it doesn't matter whether you're just an intern, an entry-level professional, or a seasoned veteran, you'll constantly face some kind of challenges. And the only difference is in how complex they will get.

This is also reflected in the way employers assess suitability of potential job candidates.

In fact, research shows that the ability to deal with unexpected complications is prioritized by an overwhelming 60% of employers across all industries, making it one of the most compelling skills on your resume.

So, regardless of your job description or your career level, you're always expected to find solutions for problems, either independently or as a part of a team.

And that's precisely what makes problem-solving skills so invaluable and universal !

Wondering how good is your resume?

Find out with our AI Resume Checker! Just upload your resume and see what can be improved.

As we've said before, problem-solving isn't really just one single skill.

Instead, your ability to handle workplace issues with composure depends on several different “sub-skills”.

So, which specific skills make an employee desirable even for the most demanding of recruiters?

In no particular order, you should focus on these 7 skills :

Analytical skills
Research skills
Critical thinking
Decision-making
Collaboration
Having a growth mindset

Let's have a look at each of them in greater detail!

#1 Analytical skills

Firstly, to truly understand complex problems, you need to break them down into more manageable parts . Then, you observe them closely and ask yourself: “ Which parts work and which don't,” How do these parts contribute to the problem as a whole,” and "What exactly needs to be fixed?” In other words, you gather data , you study it, and compare it - all to pinpoint the cause of the issue as closely as possible.

#2 Research skills

Another priceless tool is your research skills (sometimes relying on just one source of information isn't enough). Besides, to make a truly informed decision , you'll have to dig a little deeper. Being a good researcher means looking for potential solutions to a problem in a wider context. For example: going through team reports, customer feedback, quarterly sales or current market trends.

#3 Critical thinking

Every employer wants to hire people who can think critically. Yet, the ability to evaluate situations objectively and from different perspectives , is actually pretty hard to come by. But as long as you stay open-minded, inquisitive, and with a healthy dose of skepticism, you'll be able to assess situations based on facts and evidence more successfully. Plus, critical thinking comes in especially handy when you need to examine your own actions and processes.

#4 Creativity

Instead of following the old established processes that don't work anymore, you should feel comfortable thinking outside the box. The thing is, problems have a nasty habit of popping up unexpectedly and rapidly. And sometimes, you have to get creative in order to solve them fast. Especially those that have no precedence. But this requires a blend of intuition, industry knowledge, and quick thinking - a truly rare combination.

#5 Decision-making

The analysis, research, and brainstorming are done. Now, you need to look at the possible solutions, and make the final decision (informed, of course). And not only that, you also have to stand by it ! Because once the train gets moving, there's no room for second guessing. Also, keep in mind that you need to be prepared to take responsibility for all decisions you make. That's no small feat!

#6 Collaboration

Not every problem you encounter can be solved by yourself alone. And this is especially true when it comes to complex projects. So, being able to actively listen to your colleagues, take their ideas into account, and being respectful of their opinions enables you to solve problems together. Because every individual can offer a unique perspective and skill set. Yes, democracy is hard, but at the end of the day, it's teamwork that makes the corporate world go round.

#7 Having a growth mindset

Let's be honest, no one wants their work to be riddled with problems. But facing constant challenges and changes is inevitable. And that can be scary! However, when you're able to see these situations as opportunities to grow instead of issues that hold you back, your problem solving skills reach new heights. And the employers know that too!

Now that we've shown you the value problem-solving skills can add to your resume, let's ask the all-important question: “How can I learn them?”

Well…you can't. At least not in the traditional sense of the word.

Let us explain: Since problem-solving skills fall under the umbrella of soft skills , they can't be taught through formal education, unlike computer skills for example. There's no university course that you can take and graduate as a professional problem solver.

But, just like other interpersonal skills, they can be nurtured and refined over time through practice and experience.

Unfortunately, there's no one-size-fits-all approach, but the following tips can offer you inspiration on how to improve your problem solving skills:

Cultivate a growth mindset. Remember what we've said before? Your attitude towards obstacles is the first step to unlocking your problem-solving potential.
Gain further knowledge in your specialized field. Secondly, it's a good idea to delve a little deeper into your chosen profession. Because the more you read on a subject, the easier it becomes to spot certain patterns and relations.
Start with small steps. Don't attack the big questions straight away — you'll only set yourself up for failure. Instead, start with more straightforward tasks and work your way up to more complex problems.
Break problems down into more digestible pieces. Complex issues are made up of smaller problems. And those can be further divided into even smaller problems, and so on. Until you're left with only the basics.
Don't settle for a single solution. Instead, keep on exploring other possible answers.
Accept failure as a part of the learning process. Finally, don't let your failures discourage you. After all, you're bound to misstep a couple of times before you find your footing. Just keep on practicing.

How to improve problem solving skills with online courses

While it’s true that formal education won’t turn you into a master problem solver, you can still hone your skills with courses and certifications offered by online learning platforms :

Analytical skills. You can sharpen your analytical skills with Data Analytics Basics for Everyone from IBM provided by edX (Free); or Decision Making and Analytical Thinking: Fortune 500 provided by Udemy (＄21,74).
Creativity. And, to unlock your inner creative mind, you can try Creative Thinking: Techniques and Tools for Success from the Imperial College London provided by Coursera (Free).
Critical thinking. Try Introduction to Logic and Critical Thinking Specialization from Duke University provided by Coursera (Free); or Logical and Critical Thinking offered by The University of Auckland via FutureLearn.
Decision-making. Or, you can learn how to become more confident when it's time to make a decision with Decision-Making Strategies and Executive Decision-Making both offered by LinkedIn Learning (1 month free trial).
Communication skills . Lastly, to improve your collaborative skills, check out Communicating for Influence and Impact online at University of Cambridge.

The fact that everybody and their grandmothers put “ problem-solving skills ” on their CVs has turned the phrase into a cliche.

But there's a way to incorporate these skills into your resume without sounding pretentious and empty. Below, we've prepared a mock-up resume that manages to do just that.

FYI, if you like this design, you can use the template to create your very own resume. Just click the red button and fill in your information (or let the AI do it for you).

Problem solving skills on resume example

This resume was written by our experienced resume writers specifically for this profession.

Why this example works?

Firstly, the job description itself is neatly organized into bullet points .
Instead of simply listing soft skills in a skills section , you can incorporate them into the description of your work experience entry.
Also, the language here isn't vague . This resume puts each problem-solving skill into a real-life context by detailing specific situations and obstacles.
And, to highlight the impact of each skill on your previous job position, we recommend quantifying your results whenever possible.
Finally, starting each bullet point with an action verb (in bold) makes you look more dynamic and proactive.

To sum it all up, problem-solving skills continue gaining popularity among employers and employees alike. And for a good reason!

Because of them, you can overcome any obstacles that stand in the way of your professional life more efficiently and systematically.

In essence, problem-solving skills refer to the ability to recognize a challenge, identify its root cause, think of possible solutions , and then implement the most effective one.

Believing that these skills are all the same would be a serious misconception. In reality, this term encompasses a variety of different abilities , including:

In short, understanding, developing, and showcasing these skills, can greatly boost your chances at getting noticed by the hiring managers. So, don't hesitate and start working on your problem-solving skills right now!

Julia has recently joined Kickresume as a career writer. From helping people with their English to get admitted to the uni of their dreams to advising them on how to succeed in the job market. It would seem that her career is on a steadfast trajectory. Julia holds a degree in Anglophone studies from Metropolitan University in Prague, where she also resides. Apart from creative writing and languages, she takes a keen interest in literature and theatre.

Project manager skills: boss up your resume with these 7 key skills (+resume example), should you write your resume in 1st or 3rd person, share this article, join our newsletter.

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Problem Solving Skills: 25 Performance Review Phrases Examples

By Status.net Editorial Team on July 21, 2023 — 4 minutes to read

Problem solving is an important skill in any work environment: it includes the ability to identify, understand, and develop solutions to complex issues while maintaining a focus on the end goal. Evaluating this skill in employees during performance reviews can be highly beneficial for both the employee and the organization.

Questions that can help you determine an employee’s rating for problem solving skills:

How well does the employee define the problem and identify its root cause?
How creative is the employee in generating potential solutions?
How effective is the employee in implementing the chosen solution?
How well does the employee evaluate the effectiveness of the solution and adjust it if necessary?

Related: Best Performance Review Examples for 48 Key Skills

2000+ Performance Review Phrases: The Complete List (Performance Feedback Examples)

Performance Review Phrases and Paragraphs Examples For Problem Solving

5 – outstanding.

Phrases examples:

Consistently demonstrates exceptional problem-solving abilities
Proactively identifies issues and offers innovative solutions
Quickly adapts to unforeseen challenges and finds effective resolutions
Exceptional problem-solving ability, consistently providing innovative solutions
Regularly goes above and beyond to find creative solutions to complicated issues
Demonstrates a keen understanding of complex problems and quickly identifies effective solutions

Paragraph Example 1

“Jane consistently demonstrates outstanding problem-solving skills. She proactively identifies issues in our department and offers innovative solutions that have improved processes and productivity. Her ability to quickly adapt to unforeseen challenges and find effective resolutions is commendable and has proven invaluable to the team.”

Paragraph Example 2

“Sarah has demonstrated an outstanding ability in problem solving throughout the year. Her innovative solutions have significantly improved our department’s efficiency, and she consistently goes above and beyond expectations to find creative approaches to complicated issues.”

4 – Exceeds Expectations

Demonstrates a strong aptitude for solving complex problems
Often takes initiative in identifying and resolving issues
Effectively considers multiple perspectives and approaches before making decisions
Displayed a consistently strong ability to tackle challenging problems efficiently
Often takes the initiative to solve problems before they escalate
Demonstrates a high level of critical thinking when resolving issues

“John exceeds expectations in problem-solving. He has a strong aptitude for solving complex problems and often takes initiative in identifying and resolving issues. His ability to consider multiple perspectives and approaches before making decisions has led to valuable improvements within the team.”

“Sam consistently exceeded expectations in problem solving this year. His efficient handling of challenging issues has made a positive impact on our team, and he often takes the initiative to resolve problems before they escalate. Sam’s critical thinking ability has been a valuable asset to our organization, and we appreciate his efforts.”

3 – Meets Expectations

Displays adequate problem-solving skills when faced with challenges
Generally able to identify issues and propose viable solutions
Seeks assistance when necessary to resolve difficult situations
Demonstrates a solid understanding of problem-solving techniques
Capable of resolving everyday issues independently
Shows perseverance when facing difficult challenges

“Mary meets expectations in her problem-solving abilities. She displays adequate skills when faced with challenges and is generally able to identify issues and propose viable solutions. Mary also seeks assistance when necessary to resolve difficult situations, demonstrating her willingness to collaborate and learn.”

“Sarah meets expectations in her problem-solving abilities. She demonstrates a solid understanding of problem-solving techniques and can resolve everyday issues independently. We value her perseverance when facing difficult challenges and encourage her to continue developing these skills.”

2 – Needs Improvement

Struggles to find effective solutions to problems
Tends to overlook critical details when evaluating situations
Reluctant to seek help or collaborate with others to resolve issues
Struggles to find effective solutions when faced with complex issues
Often relies on assistance from others to resolve problems
May lack confidence in decision-making when solving problems

“Tom’s problem-solving skills need improvement. He struggles to find effective solutions to problems and tends to overlook critical details when evaluating situations. Tom should work on being more willing to seek help and collaborate with others to resolve issues, which will ultimately strengthen his problem-solving abilities.”

“Mark’s problem-solving skills need improvement. He often struggles to find effective solutions for complex issues and seeks assistance from others to resolve problems. We encourage Mark to build his confidence in decision-making and focus on developing his problem-solving abilities.”

1 – Unacceptable

Fails to identify and resolve problems in a timely manner
Lacks critical thinking skills necessary for effective problem-solving
Often creates additional issues when attempting to resolve problems
Demonstrates a consistent inability to resolve even basic issues
Often avoids responsibility for problem-solving tasks
Fails to analyze problems effectively, leading to poor decision-making

“Sally’s problem-solving skills are unacceptable. She consistently fails to identify and resolve problems in a timely manner, and her lack of critical thinking skills hinders her ability to effectively solve challenges. Additionally, her attempts to resolve problems often create additional issues, resulting in a negative impact on the team’s overall performance.”

“Susan’s problem-solving performance has been unacceptable this year. She consistently demonstrates an inability to resolve basic issues and avoids taking responsibility for problem-solving tasks. Her ineffectiveness in analyzing problems has led to poor decision-making. It is crucial that Susan improve her problem-solving skills to succeed in her role.”

Job Knowledge Performance Review Phrases (Examples)
Cooperation Skills: 25 Performance Review Phrases Examples
100 Performance Review Phrases for Job Knowledge, Judgment, Listening Skills
What Are Analytical Skills? [Examples]
Collaboration Skills: 25 Performance Review Phrases Examples
Critical Thinking: 25 Performance Review Phrases Examples

Critical Thinking

Ai generator.

In today’s dynamic and fast-paced world, critical thinking stands out as an essential competency, seamlessly bridging the gap between soft and hard skills . As we navigate complex challenges and make informed decisions, the ability to think critically enhances our overall skill set. Critical thinking stands at the core of effective decision-making and problem-solving in today’s complex world. It involves analyzing information, evaluating evidence, and considering multiple perspectives to make informed judgments. In a society flooded with information, the ability to think critically ensures that individuals can distinguish between credible sources and misinformation. It empowers people to approach challenges logically and creatively, fostering innovation and resilience. By honing critical thinking skills, individuals enhance their capacity to navigate personal and professional landscapes with clarity and confidence.

What is Critical Thinking?

Critical thinking is the process of actively and skillfully analyzing, evaluating, and synthesizing information gathered from various sources, including observations , experiences, and communication. It involves using logic and reasoning to identify connections, draw conclusions, and make informed decisions, while remaining open-minded and aware of potential biases.

Critical Thinking Examples

Analyzing News Reports : Evaluating the credibility of sources, checking for biases, and verifying facts before accepting news stories as true.
Problem-Solving in the Workplace : Identifying the root cause of a problem, considering multiple solutions, and weighing the pros and cons before deciding on the best course of action.
Scientific Research : Formulating hypotheses, designing experiments to test them, analyzing data objectively, and drawing conclusions based on evidence.
Budgeting : Assessing income and expenses, prioritizing spending, and making informed decisions to stay within budget while saving for future needs.
Reading Literature : Interpreting themes, symbols, and character motivations in a novel or poem, and considering how they relate to broader societal issues.
Debating : Constructing logical arguments, anticipating counterarguments, and using evidence to support one’s position while also listening to and understanding opposing views.
Medical Diagnosis : Doctors evaluating symptoms, considering possible conditions, ordering tests, and interpreting results to make accurate diagnoses and treatment plans.
Educational Assessment : Teachers designing fair and effective assessments that measure student understanding and skills, and using the results to improve teaching strategies.
Ethical Decision-Making : Weighing the moral implications of actions, considering the impact on stakeholders, and making choices that align with ethical principles.
Legal Analysis : Lawyers analyzing case law, statutes, and evidence to build strong legal arguments and anticipate the strategies of opposing counsel.
Marketing Strategy : Analyzing market trends, customer needs, and competitor actions to develop effective marketing campaigns that resonate with target audiences.
Programming : Writing efficient code by understanding the problem, breaking it into smaller parts, and testing and debugging to ensure it works correctly.
Urban Planning : Evaluating the needs of a community, considering environmental impact, and planning sustainable and functional urban spaces.
Historical Analysis : Examining historical events, considering the context, and understanding the causes and effects while avoiding presentism (judging the past by today’s standards).
Personal Decision-Making : Weighing the benefits and drawbacks of significant life choices, such as career changes or moving to a new city, and making decisions based on careful consideration and long-term goals.

For Students

Activity : Organize debates on current events or controversial topics.
Example : Have students debate the pros and cons of renewable energy sources versus fossil fuels.
Activity : Present students with complex problems to solve in groups.
Example : Task students with designing a plan to reduce plastic waste in their school.
Activity : Analyze case studies relevant to their subjects.
Example : In a business class, analyze a company’s decision-making process during a crisis.
Activity : Conduct Socratic seminars where students discuss philosophical or ethical questions.
Example : Discuss the ethical implications of artificial intelligence in society.
Activity : Facilitate brainstorming sessions to generate creative solutions to problems.
Example : Brainstorm ideas for a community service project to help local residents.
Activity : Assign research projects requiring critical analysis of sources.
Example : Research the impact of social media on teenage mental health and present findings.
Activity : Engage students in role-playing exercises to explore different perspectives.
Example : Role-play a historical event, with each student taking on the role of a key figure.
Activity : Use logic puzzles and games to develop reasoning skills.
Example : Solve Sudoku puzzles or play strategy games like chess.
Activity : Encourage students to write reflectively about their learning experiences.
Example : Write an essay on how their views on a topic have changed after a class discussion.
Activity : Analyze the techniques used in advertisements to influence consumers.
Example : Evaluate an advertisement’s claims and discuss the strategies used to persuade the audience.

In the Workplace

Problem Solving : Analyzing the root cause of a recurring issue in production and developing a sustainable solution.
Decision Making : Evaluating the pros and cons of two potential suppliers based on cost, quality, and reliability.
Strategic Planning : Assessing market trends to develop a new product line that meets future consumer demands.
Conflict Resolution : Mediating a disagreement between team members by understanding both perspectives and finding common ground.
Process Improvement : Reviewing workflow inefficiencies and implementing new procedures to increase productivity.
Risk Management : Identifying potential risks in a project and devising strategies to mitigate them.
Customer Service : Addressing a customer complaint by understanding the underlying issue and providing a satisfactory resolution.
Innovation : Brainstorming and evaluating new ideas for improving a product or service.
Performance Evaluation : Analyzing employee performance data to provide constructive feedback and development plans.
Budgeting : Reviewing and adjusting the department budget to ensure financial efficiency without compromising quality.

In the Classroom

Critical Reading : Analyzing a text to understand the author’s argument, purpose, and use of evidence.
Scientific Inquiry : Designing and conducting experiments to test hypotheses and draw conclusions based on data.
Mathematical Problem Solving : Applying logical reasoning to solve complex math problems and explaining the solution process.
Historical Analysis : Evaluating historical events and their impact from multiple perspectives.
Debate : Constructing and defending arguments on various topics using evidence and reasoning.
Project-Based Learning : Developing a research project by identifying a problem, gathering information, and presenting findings.
Creative Writing : Critiquing peers’ work to provide constructive feedback and suggestions for improvement.
Ethical Dilemmas : Discussing moral questions and justifying decisions based on ethical principles.
Literary Analysis : Interpreting themes, symbols, and character development in literature.
Collaborative Learning : Working in groups to solve problems, share ideas, and reach consensus.

In Everyday Life

Financial Planning : Creating a budget to manage expenses, savings, and investments.
Nutrition and Health : Analyzing dietary choices to improve overall health and wellness.
Time Management : Prioritizing tasks and activities to make efficient use of time.
Consumer Decisions : Comparing product reviews and prices before making a purchase.
Home Maintenance : Troubleshooting and fixing household issues, such as plumbing or electrical problems.
Travel Planning : Researching destinations, comparing travel options, and creating itineraries.
Parenting : Making informed decisions about children’s education, health, and activities.
Conflict Resolution : Resolving disputes with family or friends by understanding different viewpoints and finding compromises.
Personal Development : Setting and pursuing personal goals, such as learning a new skill or improving fitness.
Community Involvement : Analyzing community issues and participating in local initiatives to address them.

In Healthcare

Diagnosis : Interpreting patient symptoms and medical history to diagnose conditions accurately.
Treatment Planning : Developing individualized treatment plans based on patient needs and evidence-based practices.
Ethical Decision-Making : Addressing ethical dilemmas in patient care, such as end-of-life decisions.
Patient Communication : Explaining complex medical information to patients and families clearly and compassionately.
Interdisciplinary Collaboration : Working with other healthcare professionals to provide comprehensive care.
Medical Research : Designing and conducting research studies to advance medical knowledge and treatments.
Healthcare Policy Analysis : Evaluating healthcare policies and their impact on patient care and outcomes.
Clinical Judgment : Assessing and prioritizing patient care needs in emergency situations.
Quality Improvement : Implementing strategies to improve patient safety and care quality.
Continuing Education : Staying updated on medical advancements and integrating new knowledge into practice.

In Business

Market Analysis : Evaluating market trends and consumer behavior to make informed business decisions.
Strategic Planning : Developing long-term goals and strategies to achieve business objectives.
Financial Management : Analyzing financial statements to make sound investment and budgeting decisions.
Risk Assessment : Identifying and mitigating potential business risks.
Negotiation : Using persuasive arguments and data to negotiate contracts and deals.
Product Development : Assessing customer needs and market gaps to create new products.
Customer Feedback Analysis : Collecting and analyzing customer feedback to improve products and services.
Supply Chain Management : Optimizing supply chain processes to reduce costs and increase efficiency.
Leadership : Making decisions that motivate and guide employees toward achieving company goals.
Corporate Social Responsibility : Evaluating the social and environmental impact of business practices and implementing sustainable strategies.
Research Projects : Conducting independent research, analyzing data, and presenting findings.
Critical Essays : Writing essays that critically analyze texts, arguments, and ideas.
Group Projects : Collaborating with classmates to complete assignments and solve problems.
Class Discussions : Participating in discussions by presenting well-reasoned arguments and listening to others.
Case Studies : Analyzing real-world scenarios to understand complex issues and propose solutions.
Exam Preparation : Developing study plans and strategies to prepare for exams effectively.
Internships : Applying classroom knowledge to real-world situations during internships and reflecting on experiences.
Time Management : Balancing academic, social, and personal responsibilities.
Library Research : Using library resources to find credible sources for research papers.
Extracurricular Activities : Engaging in activities that develop leadership, teamwork, and problem-solving skills.

Critical Thinking scenarios

Here are some critical thinking scenarios along with questions and answers to help you practice and enhance your critical thinking skills:

Scenario 1: Workplace Conflict

Scenario: You are a manager at a company. Two of your team members, John and Lisa, have been having frequent disagreements. These conflicts are starting to affect the team’s productivity and morale.

What steps would you take to address the conflict between John and Lisa?
How would you ensure that the resolution is fair and satisfactory for both parties?
What strategies would you implement to prevent similar conflicts in the future?
Schedule a private meeting with John and Lisa to discuss the issue.
Listen to both sides without taking sides to understand the root cause of the conflict.
Facilitate a mediation session where both parties can express their concerns and work towards a resolution.
Agree on specific actions that both parties will take to avoid future conflicts.
Ensure that both John and Lisa feel heard and respected during the mediation process.
Identify common ground and mutual interests to build a foundation for resolution.
Set clear expectations and follow-up actions for both parties.
Monitor the situation and provide support to ensure the conflict does not resurface.
Foster an open and inclusive team culture where concerns can be raised early.
Provide regular team-building activities to strengthen relationships.
Implement conflict resolution training for all team members.
Establish clear communication channels and protocols for addressing grievances.

Scenario 2: Ethical Dilemma

Scenario: You are a journalist working on a high-profile story. You discover that one of your sources has provided you with information that could harm their reputation if published. However, this information is crucial to your story and serves the public interest.

What factors would you consider before deciding whether to publish the information?
How would you balance the public interest with the potential harm to your source?
What steps would you take to verify the accuracy of the information before publication?
The significance of the information to the public interest.
The potential consequences for the source if the information is published.
The ethical guidelines and professional standards of journalism.
Any possible legal implications of publishing the information.
Evaluate whether the public’s right to know outweighs the potential harm to the source.
Consider anonymizing the source or redacting sensitive details to protect their identity.
Seek advice from colleagues or an ethics committee to make an informed decision.
Cross-check the information with other reliable sources.
Review any documentation or evidence provided by the source.
Conduct interviews with other individuals who can corroborate the information.
Ensure that the information is presented in context to avoid misrepresentation.

Scenario 3: Environmental Impact

Scenario: Your company is planning to build a new factory in a rural area. This project promises economic growth and job creation but also raises concerns about environmental impact and the displacement of local wildlife.

What are the potential environmental impacts of the new factory?
How would you address the concerns of the local community and environmental groups?
What measures would you implement to minimize the environmental impact of the factory?
Air and water pollution from factory emissions and waste.
Habitat destruction and displacement of local wildlife.
Increased traffic and noise pollution in the area.
Strain on local resources such as water and energy.
Organize community meetings to discuss the project and listen to concerns.
Collaborate with environmental groups to assess the impact and find solutions.
Provide transparent information about the factory’s operations and mitigation plans.
Offer compensation or relocation assistance to affected residents if necessary.
Implement eco-friendly technologies and practices to reduce emissions and waste.
Develop a comprehensive environmental management plan.
Create buffer zones and wildlife corridors to protect local habitats.
Invest in renewable energy sources to power the factory.
Improved Problem Solving: Critical thinking helps in analyzing problems systematically and making better decisions.
Enhanced Communication: It allows for clear expression and understanding of ideas.
Better Decision Making: Critical thinking leads to more informed and logical choices.
Adaptability: It enables individuals to adapt to new situations and challenges effectively.
Informed Opinions: Critical thinkers can form well-grounded opinions and defend them logically.

What are the critical thinking skills?

Analysis: Breaking down complex information into smaller parts to understand it better.
Interpretation: Understanding and explaining the meaning of information or an event.
Inference: Drawing logical conclusions from available information.
Evaluation: Assessing the credibility and relevance of information and arguments.
Explanation: Clearly and concisely articulating your reasoning and evidence.
Self-Regulation: Reflecting on and adjusting one’s own thought processes and biases.

Concepts of critical thinking

Clarity: Ensuring that the information and arguments are clear and understandable.
Accuracy: Ensuring that information is true and free from errors.
Precision: Providing enough detail to understand the specific context.
Relevance: Ensuring that information and arguments are directly related to the issue at hand.
Depth: Addressing the complexities and underlying factors of an issue.
Breadth: Considering different perspectives and alternatives.
Logic: Ensuring that the reasoning is coherent and follows a logical sequence.
Fairness: Being open-minded and impartial in evaluating information and arguments.
Identify the Problem or Question: Clearly define what you are trying to solve or understand.
Gather Information: Collect relevant data, evidence, and viewpoints.
Analyze the Information: Break down the information to understand the relationships and implications.
Evaluate the Evidence: Assess the quality, credibility, and relevance of the evidence.
Formulate Conclusions: Draw reasoned conclusions based on the analysis and evaluation.
Communicate the Conclusion: Clearly express your findings and reasoning.
Reflect and Reassess: Continuously reflect on the process and outcomes to improve your critical thinking skills.

Basics of critical thinking

Open-Mindedness: Being willing to consider new ideas and perspectives.
Curiosity: Having a strong desire to learn and understand.
Skepticism: Questioning the validity of information and not taking things at face value.
Objectivity: Striving to remain unbiased and impartial.
Rationality: Basing decisions on logical reasoning rather than emotions.
Socratic Questioning: Asking a series of probing questions to explore complex ideas and uncover underlying assumptions.
Mind Mapping: Visually organizing information to see connections and relationships.
Brainstorming: Generating a wide range of ideas and solutions without immediate judgment.
Role Playing: Considering different perspectives by imagining oneself in another person’s position.
SWOT Analysis: Evaluating the strengths, weaknesses, opportunities, and threats related to a particular situation or decision.
Thought Experiments: Imagining hypothetical scenarios to explore potential outcomes and implications.

How to Practice and Use Critical Thinking

The critical thinking process incorporates various other logical soft skills that will help you analyze and interpret all the information to create an informed decision. These soft skills include observational skills, problem-solving, communication skills, and analytical thinking. If you sharpen all of these elements and characteristics you will inadvertently enhance your critical thinking.

Step 1: Practice One’s Observational and Perception Skills

We use our senses to perceive the world around us, whether it would be sight, smell, a, and sensations. One should practice utilizing these senses to create logical inferences and deductions that will help out brain unconsciously absorb and analyze these types of information. The more one practices their senses the better their thinking process will be.

Step 2: Enhance One’s Problem-Solving Skills

Logic and problem-solving allow the person to deduce and connect information that the environment or circumstance presents to the said person. You need to practice your problem-solving skills via puzzles, logical reasoning tests, and ethical dilemmas. Practicing one’s problem-solving skills will allow the person to efficiently establish cause-and-effect reasoning or properly create logical decisions.

Step 3: Prepare and Practice One’s Communication Skills

Communication is a pivotal skill we often use when interacting with other people. This type of skill includes body language , assertive communication , concise language, and other communication skills. In critical thinking, a person must be able to properly communicate their thoughts and thinking process to other people, which will create a collaborative environment. Other times, the perfect solution might not be present without the need for communication.

Step 4: Practice Analysis of the Situation

One’s analytical thinking skills allow the person to take note of various elements and characteristics of the situation and analyze these elements’ contribution to the current situation or circumstance. You need to practice your analytical thinking to properly process the current situation or circumstance you find yourself in.

Why Do Employers Value Critical Thinking Skills?

Employers value critical thinking skills because they enable employees to analyze situations, make informed decisions, and solve problems effectively. Critical thinkers can evaluate information from various sources, identify logical connections, and foresee potential consequences, which leads to better strategic planning and innovation. These skills also enhance communication and collaboration, as critical thinkers can present their ideas clearly and consider different perspectives. Ultimately, critical thinking contributes to improved productivity, adaptability, and competitiveness in the workplace.

What is critical thinking?

Critical thinking involves analyzing and evaluating information to make reasoned, logical decisions, and judgments. It emphasizes evidence-based reasoning and problem-solving.

Why is critical thinking important?

Critical thinking enhances decision-making, problem-solving, and the ability to analyze complex situations. It is crucial for personal and professional growth.

How can I improve my critical thinking skills?

Improve critical thinking by questioning assumptions, seeking diverse perspectives, practicing problem-solving, and engaging in reflective thinking regularly.

What are the key components of critical thinking?

Key components include analysis, evaluation, inference, explanation, and self-regulation. These skills help in understanding and assessing arguments and evidence.

How does critical thinking benefit students?

Students benefit from critical thinking by improving academic performance, enhancing research skills, and fostering independent thinking and creativity.

What role does critical thinking play in the workplace?

In the workplace, critical thinking aids in decision-making, innovation, conflict resolution, and improving productivity and efficiency.

Can critical thinking be taught?

Yes, critical thinking can be taught through targeted educational programs, exercises, and practice that focus on developing analytical and evaluative skills.

What is an example of critical thinking in everyday life?

An example is evaluating news sources for credibility before accepting information as true. This involves analyzing evidence and assessing biases.

How does critical thinking relate to problem-solving?

Critical thinking is integral to problem-solving as it involves analyzing the problem, evaluating options, and making reasoned decisions based on evidence.

What are common barriers to critical thinking?

Common barriers include cognitive biases, emotional influences, lack of relevant information, and social pressures. Overcoming these requires awareness and deliberate practice.

Text prompt

Instructive
Professional

10 Examples of Public speaking

20 Examples of Gas lighting

Team Building Problem-Solving Activities Drive Performance

T eam building activities are essential for fostering a collaborative and cohesive work environment. Among the various types of team-building exercises, problem-solving activities stand out as particularly effective. They not only enhance critical thinking and creativity but also improve communication and build trust among team members.

Executed effectively, engaging team activities can have a dramatic impact on business performance, culture, and job satisfaction. In this blog post, we'll explore the numerous benefits of team-building problem-solving activities, highlighting several examples, including the increasingly popular escape rooms.

Why Team Building Problem-Solving Activities Matter

Enhances critical thinking and creativity.

Problem-solving activities require team members to think critically and come up with innovative solutions. This stimulates the brain and encourages out-of-the-box thinking, which can translate to more creative problem-solving in the workplace.

Improves Communication

Effective communication is the backbone of any successful team. Problem-solving activities force team members to communicate their ideas clearly and listen to others. This practice helps in breaking down communication barriers and enhances overall team interaction.

Builds Trust and Collaboration

Trust is built when team members rely on each other to overcome challenges. Dynamic team-building events and activities require collaboration, where each member's input is valued. This mutual dependence fosters a sense of trust and strengthens team bonds.

Develops Leadership Skills

These activities often present opportunities for team members to step up and lead. It helps identify potential leaders and allows them to develop their leadership skills in a supportive environment.

Boosts Morale and Engagement

Engaging in fun and challenging activities outside the regular work routine can boost team morale. It provides a refreshing break and can reignite enthusiasm and motivation among team members.

Examples of Effective Problem-Solving Activities

1. escape rooms.

Escape rooms have become a popular choice for team-building activities. In an escape room, a team is locked in a themed room and must solve a series of puzzles and riddles to "escape" within a set time limit. The immersive and high-pressure environment encourages teamwork, sharpens problem-solving skills, and enhances communication.

Benefits of Escape Rooms:

Enhanced Cooperation: Teams must work together to solve puzzles, ensuring everyone's input is considered.
Improved Time Management: With a ticking clock, teams learn to prioritize tasks and manage their time effectively.
Increased Engagement: The thrilling and immersive experience keeps team members engaged and invested in the outcome.

2. Treasure/Scavenger Hunts

Treasure hunts involve teams following clues to find a hidden "treasure." This activity can be conducted indoors or outdoors and requires strategic planning and teamwork.

Benefits of Treasure/Scavenger Hunts:

Strategic Thinking: Teams must plan their route and approach to find the treasure efficiently.
Collaboration: Clues often require combined knowledge and skills, promoting teamwork.
Fun and Physical Activity: It combines mental and physical challenges, making it a well-rounded activity.

3. Problem-Solving Workshops

Workshops focused on specific problem-solving techniques can be highly beneficial. These workshops often involve case studies, role-playing, and group discussions to tackle real-world problems.

Benefits of Problem-Solving Workshops:

Skill Development: Team members learn new problem-solving techniques and strategies.
Real-World Application: Workshops often address actual workplace issues, providing immediate value.
Knowledge Sharing: Participants share their experiences and insights, fostering a collaborative learning environment.

4. Puzzle Challenges

Puzzle challenges can range from jigsaw puzzles to more complex logic puzzles. Teams must work together to complete the puzzle within a time limit.

Benefits of Puzzle Challenges:

Enhanced Focus: Solving puzzles requires concentration and attention to detail.
Patience and Persistence: Team members learn the value of persistence and patience in overcoming challenges.
Team Synergy: Successful completion often requires understanding each team member's strengths and leveraging them effectively.

5. Simulation Games

Simulation games create realistic scenarios where teams must solve problems or make decisions under pressure. These can range from business simulations to survival scenarios.

Benefits of Simulation Games:

Realistic Experience: Teams face realistic challenges, making the learning experience more impactful.
Decision-Making Skills: Participants must make quick, informed decisions, improving their decision-making abilities.
Crisis Management: Teams learn to manage stress and work efficiently under pressure.

A Powerful Tool to Drive Performance in Modern Business

Team-building problem-solving activities are a powerful tool for enhancing team dynamics and fostering a positive work environment. Whether it's the excitement of an escape room or the strategic planning of a treasure hunt, these activities offer numerous benefits that translate to improved performance and collaboration in the workplace. By investing in such activities, organizations can build stronger, more cohesive teams ready to tackle any challenge that comes their way.

Team building activities are essential for fostering a collaborative and cohesive work environment. Among the various ty

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Open access
Published: 30 May 2024

Critical-edge based tabu search algorithm for solving large-scale multi-vehicle Chinese postman problem

Jizhou Tang 1 , 2 ,
Lili He 1 , 2 ,
Yinghui Cao 1 , 2 &
Hongtao Bai 1 , 2

Scientific Reports volume 14 , Article number: 12437 ( 2024 ) Cite this article

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Computational science
Computer science

The min–max multi-vehicle Chinese postman problem is an NP-hard problem, which is widely used in path planning problems based on road network graphs, such as urban road structure probing planning, urban road underground cavity detection planning, high-voltage line inspection planning, and so on. With the rapid increase in the number of nodes and connections of road network graph, the solution time and path equilibrium constraints pose new challenges to the problem solving. In this paper, we propose a critical-edge tabu search algorithm, CTA-kroutes, for solving the min–max multi-vehicle postman problem for large-scale road networks. First, the initial solution with balanced path lengths is obtained by segmenting the Eulerian paths; second, the critical edges are moved in the initial solution to construct the neighborhood solution, and the tabu search algorithm is used to find the optimal solution iteratively; and lastly, the solution optimization algorithm is used at the end of each iteration to de-duplicate and optimally reconstruct the current search result. Experiments show that the CTA-kroutes algorithm can effectively improve the equalization of multi-vehicle paths and its applicability to large-scale road networks.

Vehicle logistics intermodal route optimization based on Tabu search algorithm

Search graph structure and its implications for multi-graph constrained routing and scheduling problems

Dynamic Signal priority of the self-driving bus at an isolated intersection considering private vehicles

Introduction.

The multi-vehicle Chinese postman problem (KCPP) is an important Arc Routing Problem (ARP) problem, which is a multi-vehicle version of the Chinese postman problem (CPP) 1 , 2 . The KCPP problem involves finding k optimal closed paths within a network under specific constraints, with the requirement that each edge in the network is traversed by at least one path. Currently, scholars have studied for many different constraints, and the relevant constraints are: mixed road network constraints 3 , capacity constraints 4 and time constraints 5 . In the tasks of road exploration, security patrol, snowplow street clearing and street photography 6 , 7 , 8 , the main constraints of KCPP are the large-scale road network and the target loop equilibrium. The KCPP problem with constraints on the goal loop equalization is also known as the Min–Max k Chinese Postman Problem (MMKCPP).

MMKCPP, based on KCPP, requires to find k balanced shortest circuits in an undirected graph to ensure the balance of task allocation and improve the efficiency of task completion. Since MMKCPP is an NP-hard problem, the research for this problem is dominated by approximation algorithms. Shuhe Wang proposed a dedicated right-handed passing KPCPP algorithm for right-handed passing environments 9 , but this algorithm is only for the case where the road conforms to the right-handed passing, and is not generalized. Frederickson GN et al. proposed the approximation algorithm K-POSTMEN 10 based on the Eulerian loop construction algorithm of Edmonds and Johnson, which formed k equalization loops by segmentation. However, the loop length obtained by this method is far from the ideal optimal length. Dino Ahr et al. proposed Augment-Merge algorithm 11 , which is solved by continuously adjusting the longest and shortest loop paths. Subsequently, they introduced the Tabu Search algorithm 12 , which relies on an initial solution and a moving strategy to find the optimal solution. All of these methods are able to find k equalization loops, but the computational effort increases significantly when facing a large-scale road network. Rong Fei et al. proposed a solution method using dynamic programming 13 , 14 , 15 , which first interchanges point edges on the road map and constructs a dynamic programming model from it, which is more complex and the overall computational length of the algorithm increases dramatically with the increase of the complexity of the road network. Wei Yu et al. also proposed an improved approximation algorithm, 4-approximation algorithm for MMKCPP 16 , 17 , 18 , 19 , and the equalization loop length obtained by the method is four times of the ideal optimal length.

Most of the existing methods have been studied for small-scale road networks. In the actual task, there often exists the constraint of large-scale road networks, and it is usually difficult for the existing methods to find the balanced multiple paths under large-scale road networks. Meanwhile, the gap between the longest path lengths obtained by existing methods and the ideal optimal value increases with the increase of the road network size. Therefore, in order to solve this difficulty and improve the applicability of the methods to large-scale road networks, this paper studies the MMKCPP problem. A solution method (Critical tabu ant k-routes method, CTA-kroutes) based on the idea of critical edges and using the tabu search algorithm and ant colony algorithm is proposed. The method itself employs heuristic and solution optimization steps, using the tabu search algorithm to continuously search for the optimal solution from within the neighborhood formed by the movement of critical edges. And an ant colony algorithm for solving RPP (Rural Postman Problem, Rural postman problem) is used to optimize the solution for each search.

The remaining part of this article is organized as follows: In Section " MMKCPP problem definition and mathematical model ", the MMKCPP problem and its mathematical model are described; In Section " CTA-kroutes algorithmic framework ", the CTA-kroutes algorithm and its main contributions are introduced; In Section " Experimental results and analysis ", the results and improvements of the CTA-kroutes method are presented; Finally, a summary is provided in Section " Conclusion ".

MMKCPP problem definition and mathematical model

Problem definition.

MMKCPP is defined as follows: given an undirected connected graph G = (V, E), each edge has weights w: E → R + , starting point v 1 , number of vehicles k (k ≥ 2), find k strip of loops S = (RL 1 , RL 2 , …, RL k ) such that ${\bigcup }_{1\le i\le k}{E(RL}_{i})$ = E(G) and $\underset{1\le i\le k}{\mathit{max}}(L(RLi))$ minimize. where V is the set of vertices, E is the set of edges, RL is the loop, and L(RL) is the path length of the loop.

The loop RL is defined as follows: given a sequence of vertices v 1 , v 2 , …, v n , such that ( v i , v i +1 ) ∈ E (1 ≤ i < n ), then the vertex sequence v 1 , v 2 , …, v n denotes a path from point v 1 to point v n . A path is said to be a loop, denoted RL, if v 1 = v n .

Mathematical modeling

The set of all possible solutions that satisfy the constraints is denoted as M , each S consists of k loops:

Objective function: find the set of loops whose longest path length is minimized: ${S}_{opt}$

The length of the longest loop path in the S :

Optimal solution ${S}_{opt}\epsilon M, {L}_{max}({S}_{opt})$ satisfies:

where $\omega \left(e\right)$ is the weight of the edge $e$ , and ${x}_{e}$ is the number of times the edge $e$ passes through the loop RL.

Constraint 1: Each edge is passed through S at least 1 time.

Constraint 2: The target paths are all loops.

where $\delta \left(v\right)$ is the number of sides passing through the point $v$ , and $V(RL)$ is the set of points in the loop RL.

Constraint 3: The number of traversals per edge should be an integer.

Constraint 4: Number of target loops.

CTA-kroutes algorithmic framework

Cta-kroutes algorithm flow.

The basic idea of the CTA-kroutes algorithm is to improve the initial solution by means of a tabu search algorithm, which continuously searches for the optimal solution. The main contribution of this paper is to introduce the idea of critical edges in the construction process of the neighborhood and to propose the corresponding solution optimization method. The CTA-kroutes algorithm has three parts, which include: the construction of the initial solution, the construction of the neighborhood using critical edges and tabu search, and the solution optimization method. The algorithm flow is as follows:

The initial solution S1, which is the current solution S, is found using the improved K-POSTMEN algorithm;

Compute the set of critical edges KE in the graph G and compute the set of critical edges Sk contained in each loop RL in the initial solution S1;

Construct a neighborhood by moving critical edges and search for the optimal solution using a tabu search algorithm, select the next current solution S in the neighborhood according to the tabu table, and record if S is better than the current optimal solution opt;

Perform a solve-optimize operation on the current solution S;

If the number of iterations without improvement of the optimal solution exceeds the upper limit or the next current solution S cannot be selected in the neighborhood, the algorithm ends; otherwise, jump to 3) to continue the iterative search;

Output the optimal solution OPT during the iterative search.

In Section " Initial solution construction " the method of constructing the initial solution will be introduced first. After that, in Section" Tabu search algorithm based on critical edges " the computation of critical edges and how to use critical edges for neighborhood construction and search to improve the initial solution will be introduced respectively. Finally, in Section " Solving the optimization process " how to optimize the search solution will be presented.

Initial solution construction

The basic idea of CTA-kroutes algorithm is the improvement of the initial solution, and the merit of the initial solution will affect the convergence time of the subsequent tabu search and the reliability of the search results. Therefore, in this paper, we improve on the K-POSTMEN algorithm to construct the initial solution with more balanced length of each loop. The algorithm is procedure 1, where ER = {v 1 ,v 2 ,…,v 1 } is the Eulerian loop on the undirected graph G with starting point v 1 . This algorithm performs a balanced decomposition of the Eulerian loops, improves the calculation method of each len, and enlarges the value of each midlen appropriately when finding each path, which makes the lengths of the k loops in the initial solution S1 more balanced. the relevant schematic diagram for k = 3 is shown in Fig. 1 .

Schematic diagram of the initial solution for k = 3.

In the initial solution construction, each_len is the segmentation length of each loop in the single Euler path segmentation after removing the length of the first and last ends. each_midlen is the total length of each loop in the single Euler path segmentation. As in Fig. 1 , each loop can be expressed as SP(v 1 ,v (1) ) + SP(v 1 ,v (2) ) + R(v (1) ,v (2) ). SP(v 1 ,v (1) ) and SP(v 1 ,v (2) ) are the paths of the first and last ends of the loop, and R(v (1) ,v (2) ) is the path of the loop split. each_len is a criterion for the segmentation length, which is computed by taking the mean of the k paths after subtracting the maximum length of the first and last ends from the total length of the single Euler path. each_midlen is the criterion of the split single loop, which is calculated as each_len plus the maximum length of the length of the first and last ends. The length of the first and last ends is expressed as 2 times SP max . SP max is the maximum value of the shortest path from each node in the set of path points to the start point.

Tabu search algorithm based on critical edges

After the initial solution is constructed, the CTA-kroutes algorithm will improve the initial solution by means of a tabu search algorithm. During the search process, in order to improve the search efficiency and the possibility of convergence of the results to the global optimal solution, the CTA-kroutes algorithm uses critical edges for the construction of the neighborhood. The set of critical edges is a subset of E in the graph G, which contains edges in the graph G that are far from the starting point and discrete. By moving the critical edges in the longest and shortest loops to construct the neighborhood, the effectiveness of each search can be improved and the result can be closer to the global optimal solution.

Key edge set computation

In the road network graph G, given the starting point v 1 , the shortest path between two vertices v i , v j is represented by SP( v i , v j ), and the shortest path can be found by dijkstra's algorithm and floyd's algorithm. For any e ∈ E, LOOP is used to represent the edge loop formed by it and the starting point v 1 , and L(LOOP) denotes the path length of LOOP. All LOOPs form the set LP, LP = {LOOP 1 , LOOP 2 , …, LOOP m }. Procedure 2 involves the selection of critical edges and the calculation of LOOP.

Through the above process, the set of critical edges KE = {ke 1 , ke 2 , …, ke kn } is formed, which contains the number of critical edges kn.

Critical edge selection process

The key edge points out that when the current undirected graph G solves the MMKCPP, the effective number of vehicles k is at most kn . At this point, there are three scenarios of the problem for the given number of vehicles k as follows:

When k = kn, the set LP consisting of LOOPs corresponding to each critical edge in KE is the optimal solution of the problem.

When k > kn, since kn points out the upper limit of k required for multiple vehicles on the current road network, the solution corresponding to kn remains optimal, and the extra vehicles will only increase the duplicated paths and will not decrease $\text{min}\left(\underset{1\le i\le k}{\text{max}}\left(L\left(R{v}_{i}\right)\right)\right)$ the size of the road network.

When k < kn, multiple critical edges are merged to form a new set of critical edges KE1 = {ken 1 , ken 2 , …, ken k }, where ken may be a set of multiple ke. At this time, the solution corresponding to KE1 obtained by merging is the final solution. The combination of the critical edges determines the final solution.

The CTA-kroutes algorithm is solved for the case k < kn, and after obtaining the set of critical edges of the undirected graph G, a tabu search algorithm is used for the computation of the near-optimal solution. During the tabu search, the construction of the neighborhood is performed by shifting the critical edges.

Neighborhood construction

The core of tabu search is the process of constructing a series of neighborhood solutions by making certain changes to the current solution, selecting the next current solution from them and repeating the process. The neighborhood construction rule determines how the current solution is changed, and also determines the search range and convergence speed of the algorithm. The CTA-kroutes algorithm is based on the critical edges, and moves the critical edges and their peripheral paths, rc, from the longest path, RL a , to the shortest path, RL b , i.e., removes rc from the longest path, RL a , and adds rc to the shortest path, RL b . This construction rule ensures the completeness of solution S, and improves the search speed compared with the scheme of moving each edge. S completeness while improving the search capability of the algorithm compared to the scheme of moving each edge, and accelerates the search efficiency of the algorithm and avoids many meaningless search processes.

The tabu unit ‘cone’ is formed by rc, denoted as (left, seq, right), where seq is the number of the critical edge, left is the connected node that is closest to the critical edge to the left of seq under the sequence along the current path RL, and similarly, right is the connected node that is closest to the critical edge to the right of seq under the sequence along the current path RL. As in Fig. 2 , the graph has rc = {v i+1 , …, v j , v j+1 , …, v x } and cone = {v i+1 , (v j , v j+1 ), v x }.

Example of rc and cone.

The process of rc deletion: in order to ensure connectivity, uses SP(v i+1 , v x ) in RL a to replace the relevant path of rc and completes the deletion of rc and generates a new RL a 2. The process is shown in the Fig. 3 :

Deletion process of rc.

The process of adding rc: to ensure that the change of L(RL b ) is minimized, it is necessary to find the node v b in V(RL b ) that is closest to the distance between the two endpoints of rc, i.e. ${v}_{b}=\text{min}\left(SP\left({v}_{m},{v}_{i+1}\right)+SP\left({v}_{m},{v}_{x}\right)\right) \left({v}_{m}\in V\left({RL}_{b}\right)\right)$ . The flowchart is shown in Fig. 4 .

Flow of adding rc.

Tabu search process

After using the critical edges for neighborhood construction, the tabu search algorithm will select the current optimal solution as the input for the next search according to the tabu table and the generation value of the neighborhood solution, and keep repeating the process of neighborhood construction and the selection of the current optimal solution until the improvement of the optimal solution is not achieved within a certain number of iterations or there is no feasible solution in the neighborhood, the tabu search algorithm ends, and the optimal solution in the search process is the algorithm output. The tabu search process is as follows, where rlc represents the set of critical edges contained in each loop RL in S, the generation value of the neighborhood solution is the amount of change with respect to the current max(S), and ‘cone’ is the unit of the tabu table. opt represents the optimal solution, and max(opt) represents the maximum length in the optimal solution. The algorithm process is procedure 3.

Solving the optimization process

Local solutions for each search in tabu search are generated by moving critical edges, and each key edge move causes a change in the allocation of non-critical edges. At the same time, the construction goal of the neighborhood solution is to run fast and represent the surrogate values as accurately as possible. The above reasons lead to the presence of more duplicate edges in the local solution, where the length of each loop path can still be shortened. Therefore, after obtaining the local solution for each search, solution optimization is required to reduce the number of duplicate edges and also to optimize the structure of the solution using the yq_RPP algorithm to generate new loops. The process of solution optimization is as shown in procedure 4.

The main role of the solution optimization is to remove the duplicate edges of each loop and calculate the new loop after removing the duplicate edges. The solution optimization algorithm can effectively reduce the length of each path, improve the effectiveness of the subsequent search, and more conducive to the convergence of the search to the optimal solution.

Experimental results and analysis

In this paper, experiments are conducted in Win10 platform and Visual Studio 2019 environment. The inputs are undirected connected road network graphs of different sizes, in which the path lengths between nodes are randomly generated. This is done in order to simulate the randomness between different path lengths in the real road network environment, so as to exclude the error caused by the specificity of the data on the experimental results. The outputs are the K-POSTMEN algorithm, the tabu algorithm and CTA-kroutes algorithms to calculate the maximum path length in k loops.

The percentage of difference between the longest path length and the ideal optimal solution as well as the approximation ratio are used as evaluation metrics in the experiments. For the comparison object, K-POSTMEN algorithm is used for the traditional algorithm and tabu algorithm is used for the heuristic algorithm. The rest of the proposed algorithms include deterministic algorithms as well as approximation algorithms. For deterministic algorithms, the comparison is not relevant due to the unacceptable computation time at larger scale. For approximate algorithms, the approximation ratio in certain cases is provided as a reference due to the variation in the solution of the heuristic algorithm. The study mainly aims at improving the feasible solution, expecting to obtain a more superior feasible solution in an acceptable time. Therefore, the computational time of the algorithm has not been improved and the computational time remains flat compared to the tabu algorithm and longer than the K-POSTMEN algorithm. The computational time of the algorithm is not the direction of improvement or innovation in this paper, so subsequent experiments will focus on the comparison of results.

Comparison of algorithm results for different number of vehicles k

In the experiment, the mean score of the total path length under different scales for k is used as the ideal optimal solution ideal-opt for MMKCPP under the current scale road network, and this value is the upper bound and the true optimal solution true-opt must be greater than or equal to the ideal-opt. A total of three scales of road networks are set up in the experiment, whose node numbers and edge numbers are (20,190), (40,780), (60,1770), and the MMKCPP problem is solved using different algorithms for the above three sizes of road networks under k = 2, 5, 10, 15, and 20.

The solution results are as follows, where Ki, ti, Ci denote, respectively, the difference between the results of the K-POSTMEN algorithm, the tabu algorithm, and the CTA-kroutes algorithm and ideal-opt. Tabu algorithm do not use a solution optimization step and critical edge construction. Ideal denotes ideal-opt, K-P denotes K-POSTMEN. CTA denotes CTA-kroutes. path units are all m. The percentage of difference relative to the ideal optimal solution is calculated as in Eq. ( 2 ).

where Mi denotes the difference of algorithm M with respect to ideal-opt, M denotes the comparison algorithm, and ideal denotes the ideal optimal solution.

From the Figs. 5 , 6 and 7 , it can be seen that the CTA-kroutes algorithm improves compared to both K-POSTMEN and tabu algorithms under different sizes of road network and different number of vehicles k. Since the reference is IDEAL-OPT and not actual TRUE-OPT, the enhancement is not fixed in some cases.

(20.190) Difference from ideal value.

(40,780) Difference from ideal value.

(60,1770) Difference from ideal value.

The results of MMKCPP are related to the balance of the length of each edge in the road network diagram, the length of each edge and the number of vehicles. The more balanced and shorter the length of each edge in the road network graph, the easier it is to solve the feasible solution of MMKCPP. Additionally, the closer the feasible solution is to the ideal optimal solution. At this time, the gap between the algorithms is smaller. At the same time, the more the number of vehicles, the smaller the ideal optimal value, the more difficult to reflect the gap between different algorithms. Figure 5 reflects the improvement effect of tabu search compared with the traditional method. Figure 6 reflects the enhancement effect of the tabu search combined with key edges compared with the traditional tabu search. And the construction of the neighborhood combined with key edges further improves the quality of the feasible solution obtained by the tabu. search algorithm and improves the effectiveness of the feasible solution. Figure 7 simulates the case of balanced edge lengths and shorter edge lengths in the road network graph, when the solution obtained by the algorithm is still closer to the ideal solution.

Comparison of different algorithms for boosting

The lift of the algorithm is benchmarked against the K-POSTMEN algorithm and the tabu algorithm, and the lift is the difference between the algorithm and ideal-opt with respect to the benchmark algorithm. It is calculated as in Eq. ( 3 ):

where Mi denotes the difference of a particular algorithm with respect to ideal-opt, Ni denotes the benchmark algorithm, and improve denotes the magnitude of the improvement.

The lift results are as follows, Ci-Ki denotes the lift of the CTA-kroutes algorithm with respect to the K-POSTMEN algorithm, ti-Ki denotes the lift of the tabu algorithm with respect to the K-POSTMEN algorithm, and Ci-ti denotes the lift of the CTA-kroutes algorithm with respect to the tabu algorithm. The lift values are all percentages, and average indicates the average lift of the algorithm at the current scale (Table 1 ).

In all the experiments, the algorithms were boosted on average, as shown in Table 2 .

From the Table 1 , it can be seen that the initial solution construction, tabu search, and solution optimization methods adopted by CTA-kroutes can effectively reduce the length of the longest loop of the optimal solution and make it closer to the ideal optimal solution.

Algorithm Approximation Ratio Analysis

Since the CTA-kroutes algorithm takes the K-POSTMEN algorithm as the initial solution and improves upon it, the worst case of the solution obtained by the CTA-kroutes algorithm in general is shown in Eq. ( 4 ). Therefore, the CTA-kroutes algorithm is a 4-approximation algorithm, i.e., the worst case of the solution obtained by it is four times the ideal-opt. In the current optimal case, the solution obtained by the CTA-kroutes algorithm is 1.01 times the ideal-opt.

where $\text{max}\left(CTA-kroutes\right)$ is the longest path length in the CTA-kroutes result, x is the total path length of the original road network, k is the number of postmans, and x/k is the ideal-opt.

The main body of the CTA-kroutes algorithm is divided into two steps: construction of the initial solution and optimization of the k loops. The construction of the initial solution includes the construction of the Euler loop and the construction of the k initial loops. The simplest Euler loop construction method is to add a duplicate edge to all edges of the original road network. This method is the worst case of Euler graph construction, the length of the Euler loop is 2x. From the construction method of each_len in the initial structure, the worst case of each_len is $2x/k$ . At this time, in the process of each_midlen, when ${SP}_{max}\le x/k$ he worst case of the CTA-kroutes is $4x/k$ . when ${SP}_{max}>x/k$ , the worst case of ${SP}_{max}$ is x, i.e., all the edges are on a straight line, and the worst case is $(\left(2+2k\right)x)/k$ . However, in general, the ${SP}_{max}$ in the road network graph won't be more than $x/k$ , so we take $4x/k$ as the approximation of the worst case of CTA-kroutes here.

In this paper, a heuristic algorithm CTA-kroutes for solving the min–max multi-vehicle Chinese letter carrier problem is proposed by combining the tabu search algorithm and the key edge idea. The method searches for the optimal allocation scheme of the key edges in the initial solution within the iteration number through the tabu search algorithm, and proposes the yq_RPP algorithm for solving the RPP formed after the allocation of key edges. The neighborhood construction scheme and tabu table update scheme proposed in this paper effectively reduce the occurrence of invalid iterations. This enables the method to find the feasible solution faster within the specified number of iterations, even for large-scale road networks. As a result, the availability of results is ensured.

In the experimental results, the usability of the solutions obtained by the CTA-kroutes algorithm is improved for different sizes of road networks. Thus, it shows that the algorithm is optimized in the computation of the solution as well as in the construction of the neighborhood compared to the traditional algorithm K-POSTMEN and the heuristic algorithm tabu. Since the evaluation criterion of MMKCPP is the proximity to the ideal optimal solution, it is easier to see in the performance comparison among the algorithms that the CTA-kroutes algorithm has improvement in the effectiveness of the solution. Finally, the approximation ratio of the algorithm in the case of ${SP}_{max}\le \frac{x}{k}$ also represents the upper limit of the solution of CTA-kroutes algorithm in the worst case, which ensures the applicability of the algorithm. The large scale of the road network for all the experiments in this paper ensures the usability of the algorithm on large-scale road networks.

Data availability

The datasets analysed during the current study are available from the corresponding author on reasonable request.

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Acknowledgements

This work was supported by the National Key Research and Development Program of China (2022YFF06069003-02)

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H.L.L., B.H.T., C.Y.H, T.J.Z. conceived the experiment. T.J.Z .conducted the experiment and performed statistical analysis and figure generation. H.L.L. and B.H.T. provided improvement methods. All authors reviewed the manuscript.

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Tang, J., He, L., Cao, Y. et al. Critical-edge based tabu search algorithm for solving large-scale multi-vehicle Chinese postman problem. Sci Rep 14 , 12437 (2024). https://doi.org/10.1038/s41598-024-62992-2

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