Solving Problems

—Creating solutions

Life consists primarily of solving problems; they are a normal part of life. Learn to expect them and enjoy solving them. Often “a problem is nothing more than an opportunity in work clothes.”^[1] Life would be boring if there were no problems to solve. Treat them as expected rather than as anomalies.^[2]

This course describes various approaches, processes, and thinking tools useful for solving problems. Although the title of this course is solving problems, the materials apply equally well to both solving problems and seizing opportunities. A problem describes the gap between the way things are now and the way we would like them to be. Solving a problem often requires taking some action to remove some troublesome deficit or deficiency. Opportunities arise when we notice that conditions have changed. Amazon, Google, Facebook, and eBay all seized opportunities when the emergence of the internet created new ways to provide new conveniences and services to customers. Whenever the word problem appears in the text, it also refers to opportunities.

A list of example problem topics is available to use throughout this course, in case you do not have enough problems of your own! A list of Thinking tools useful for solving problems is also provided.

Completion status: this resource is considered to be complete.

Attribution: User lbeaumont created this resource and is actively using it. Please coordinate future development with this user if possible.

The objectives of this course are to help students identify problems, solve problems, and assess the success of the solution.

This course uses many useful thinking tools, and many others exist. Please browse this inventory of problem solving thinking tools and this list of additional thinking tools to continue to improve your ability to solve problems and think creatively.

This is a course in the possibilities curriculum, currently being developed as part of the Applied Wisdom Curriculum.

If you wish to contact the instructor, please click here to send me an email or leave a comment or question on the discussion page.

The work of solving problems often proceeds through a series of stages. The nature of the tasks changes as the work proceeds from what we know today to understanding how it can be in the future. Solving problems requires several disciplined shifts between divergent thinking, which expands the number, character, and scope of ideas that are considered to convergent thinking which narrows the number of alternatives being considered and increases focus. These shifts occur within some stages, between certain stages, and across the entire problem-solving process.

In each stage there is some transformation from the unknown to known, vague to specific, concepts to actions, general to detailed, expansion and divergence to convergence, and past to future. Problems are often solved through some process of stepwise refinement. The path toward solutions requires investigation, analysis, conception, elaboration, clarification, experimentation, evaluation, iteration, refinement, verification, and sometimes breakthroughs.

Although this text is presented serially, the path forward is rarely straightforward. Solving problems requires iteration, recursion, feedback loops, retracing steps, non-linear imagination, and often more.

Several organizations and authors, including ASC^[3], Xerox ^[4],[5], Crestcom ^[6], AT&T ^[7], McKinsey & Company ^[8], The Ideal Problem Solver ^[9], Phase-gate processes, and others describe general problem solving systems, presented as a series of stages. The number of stages and description of each stage varies across these various systems. This course uses a blend of these recommendations to identify and describe problem solving stages. These stages establish the next nine high-level headings in this course.

Adjust the level of rigor to fit the problem at hand. When deciding what to eat for lunch you are likely to speed through these stages almost instantly. Solving engineering, medical, environmental, behavioral, family, social, economic, or political problems requires more depth, more expertise, and more effort at each stage.

Persevere and a solution will appear.

The goal of this first stage is to write, refine, and agree on a problem statement that clearly defines the real problem to be solved.

Begin by considering the question, what do we want to change? Consider: What do we want to have happen? What is true? and What are we going to do about it? Because problems are often accompanied by many symptoms and may arise from many causes, it is often difficult to identify the real problem. Persevere to ask: What is the problem? What is the real problem, and what is the problem really? Iterate these questions until you are confident you have identified the real problem.

The figure on the right illustrates the many sources of problems and opportunities that are likely to exist at any time. These stimuli may include considerations of: adding value, aesthetics, benchmarking, bigger picture, business as usual, competitor analysis, complaints, context, contributing causes, cost, creative destruction, critics, cultural trends, dangers, delay, discomfort, discontent, disruptions, emerging technologies, errors, errors, expanding scope, externalities, fads, failures, false starts, inconveniences, insights, interactions, irrelevancies, market research, misfits, needs, new viewpoints, opportunities, performance, pollution, possibilities, reality, reliability, scrap, symptoms, rework, voice of the customer, and many more.

During the expansive phase of this stage, work to expand the list of problems that may be considered. This can be done using tools that assist in generating ideas. Use the ideation tools described in the thinking tools course, other thinking tools, or other approaches you find useful.

A creative environment is especially important during this problem-solving phase.

1. Complete the course on unleashing creativity.
2. Find an environment that will help you unleash creativity.

During the convergence phase, work to clarify the problem statement. Use the clarifying tools described in the thinking tools course, other thinking tools, or other approaches you find useful.

This stage is complete when there is a written and agreed to problem statement that clearly defines the real problem to be solved. The desired state to be achieved when this problem is solved should be clearly specified.

1. Complete the Wikiversity course on Problem Finding.
2. Find the real problem.
3. Write a well-chosen and well-written problem statement, as described here.
4. Assess the problem statement by sharing it with various stakeholders and encouraging their candid feedback, comments, or suggestions. This may include customers, suppliers, others in your organization, and especially those people who are now most affected by the existing problems and may be the most to benefit from any solution.
5. Revise the problem statement based on what is learned.
6. Repeat steps 1-5 as often as necessary until the problem really is found.

It is often helpful to deconstruct a problem into component parts to assist in the analysis.^[10] This can often be done by cleaving (subdividing, disaggregating) the problem into complementary factors or subcomponents. For example, if the problem is “lose weight” then eating healthier and exercising more can both contribute to the solution. Each factor can be considered largely independently of the other.

Here are some suggested “cleaving frames”:^[11]

1. For resource problems, consider input/outputs, supply/demand, sources/sinks, producer/consumer, create/conserve, generation/consumption, or MacGyver (improvising) a solution. For example, if the problem is to reduce disease rates, decompose the problem in to “New infections” and “Recoveries”.
2. For general problems consider local/global, temporary/permanent, short term/long term, common causes/special causes, internal/external, assistors/resistors, power/reason, frame-up/drill down.
3. For disease, accidents, crime, or other mishaps, consider number of incidents/severity of incidents.
4. For revenue generation consider price/volume, diversify/focus, direct/distributer, direct/broker, increase value/reduce cost product/price/place/promotion, Porter's five forces, SWOT.
5. For product or services consider increasing quality/quantity.
6. For process design, consider throughput/delay, serial/parallel.
7. For policy decisions, consider equality/liberty, regulate/incent, or public/private.
8. For reducing harm, consider prevention/repair, or mitigate/adapt.
9. For addressing regional shortages, consider generate/redistribute
10. For reducing pollution, consider reduce/reuse/recycle.
11. For obtaining resources consider make/buy/reuse.
12. For achieving a goal, consider work harder/work smarter, advance/retreat.
13. For modifying behavior consider rewards/punishments, training/assisting/constraining, passion/reason.
14. For communications issues consider advocacy/inquiry.
15. For reducing costs consider fixed costs/variable costs, purchase costs/life cycle costs, material costs/labor costs.

As the problem is deconstructed, strive to identify factors that are mutually exclusive and collectively exhaustive (MECE). Creating a cause-effect diagram can help.

The deconstruction can be represented in outline form, or graphically as a tree as shown on the right.

Here is an outline showing a deconstruction of the problem “lose weight”

Problem: Lose Weight

1. Eat healthier
   1. Eat food, not too much, mostly plants^[12]
      1. Three healthy meals each day.
      2. Whole grains
      3. Fruits and vegetables
      4. Avoid fast foods
   2. No snacks
2. Move more
   1. Walk every day
      1. Take the stairs.
      2. Walk rather than drive.
      3. Go for walks.
   2. Play pickleball
   3. Swim
   4. Go to the gym and work out

Create a deconstruction of your problem, represented as either an outline or a graphic. Use the cleaving frames listed above, other helpful cleaving frames, and any helpful thinking tools.

If not already in place, it is likely that a team leader will have to be identified and recognized at this stage.

The goal of this stage is to identify and briefly describe several approaches that may provide a useful solution to the identified problem.

A solution approach is some high-level description of an architecture, technology, or plan for solving a problem. For example, if the problem to be solved is “what to eat for lunch”, several solution approaches are available. You can sit down at a restaurant, go to the drive through, order out, have lunch delivered, eat a sandwich at home, or eat a power bar on the go. As another example, the variety of bridge designs represent a wide variety of solution approaches to the problem of crossing a river.

During the expansive phase of this stage, work to expand the list of solution approaches that may be considered. This can be done using tools that assist in generating ideas. Use the ideation tools described in the thinking tools course, other thinking tools, or other approaches you find useful. The SCAMPER tool can provide a good starting point for this enumeration.

This stage is complete when several feasible solution approaches are identified and described in enough detail to communicate each approach to others on the team.

This stage has no convergence phase, the next stage provides convergence by evaluating the candidate solution approaches.

The goal of this stage is to choose the most suitable solution approach from several approaches described above.

Begin by establishing the most important criteria for selecting the most suitable approach. These criteria might include a few chosen from this list: accessibility, aesthetics, availability, bandwidth, benefits, competitive advantage, cost, durability, efficiency, elegance, ergonomics, externalities, feasibility, features, flexibility, leverage, lifespan, novelty, performance, profitability, reliability, risk, robustness, ruggedness, safety, scalability, security, serviceability, signal to noise ratio, size, standards, strategic fit, usability, weight, and others. Consider establishing relative weights (importance), or at least some ordering, of these criteria to identify the critical, more important, and less important criteria.

Use the tools described in the develop section of the thinking tools course to select the most suitable solution approach, based on the established criteria.

Other useful tools include focus groups, Pugh concept selection^[13], the Analytic Hierarchy process ^[14] and other thinking tools.

This stage is complete when one solution approach that can solve the problem has been selected. In some circumstances, when resources are abundant and time is short, it may be useful to select more than one approach to be developed in parallel. This was done during the 2010 Copiapó mining accident rescue where time was critical.

The goals of this stage are to plan the remaining work, and to complete the detailed design of the chosen solution. The outputs will include a project plan along with detailed designs and specifications. Prototype models, computer aided designs, or simulations may be used to better understand, analyze, and communicate the solution.

Difficult problems are likely to require a team of people providing the range of expertise required to solve the problem. As the team grows, ensure competencies, communications, decision making, governance, teamwork skills, and working conditions are suitable to the work being performed.

Two major project approaches are possible at this stage. These are the waterfall model and the spiral model. Many other approaches are also possible that seek to blend and gain the advantages of these two major approaches. Choose the approach that is most suitable to the work being performed.

Larger project will require appointing a project manager or a program manager at this stage, or earlier.

The goal of this stage is to execute the plans created in the previous stage. This results in solutions that are verified to solve the problem.

Specification documents guide the creation of working products or services. Resources are gathered, and tasks are accomplished according to the project plan. Obstacles are identified and overcome. Replanning occurs as needed to resolve emergent or otherwise unforeseen problems.

Use the tools described in the implement section of the thinking tools course during this stage, or any other helpful thinking tools.

Samples of the solution need to be suitably verified to ensure that design output meets design input requirements.

This stage is complete when it is verified that the solution solves the identified problem.

In this stage the solution is introduced to the users. The goal of the stage is to have some planned number of users make use of the solution. Previews, beta tests, soft launches, controlled introductions, early adopter programs, friendly users, clinical trials, and other approaches to introducing the solution to users are used.

For the solution to become effective, it must be used. Tell the story of the problem as it originally existed and how the problem has been solved. Emphasize the benefits and be candid about the shortcomings. This story may become part of a sales campaign, and education campaign, investment requests, policy advocacy work, or some other work to highlight the advantages provided by this solution.

Use the skills taught in this course to solve the problem of using the solution to solve problems.

Use the tools described in the implement section of the thinking tools course, or any other useful thinking tools as you launch the solution.

Often systems are put in place to gather feedback from these first users to be used to improve the product.

This stage is complete when the planned number of users are making use of the solution and the planned feedback is gathered and acted on.

In this stage the effectiveness of the solution, as assessed by users, is evaluated. The rate of adoption, user reactions, focus group findings, unexpected problems and benefits, and other assessments of the solution effectiveness are collected and analyzed.

Is the problem solved? How do you know?

Deployment of the solution continues until each of the users who can benefit from this solution are reached.

On-going work to improve results is known as continuous improvement. The existing solution can be evaluated and improved based on the answers to these questions:

1. How well are existing problems being solved?
   1. What are the results?
   2. Are the results adequate?
   3. How do we know?
2. What problems remain to be addressed?
3. What opportunities are now available to address?
4. How can we act on this information?

1. Study the Grand Challenges course.
2. Choose one grand challenge to address.
3. Use problem solving skills to solve the grand challenge.

Students who are interested in learning more about solving problems may wish to read these books:

Overviews

• Corpeño, E (October 6, 2021). The Top-Down Approach to Problem Solving: How to Stop Struggling in Class and Start Learning. ISBN 979-8464073296.
• Bransford, John D. (February 15, 1993). The Ideal Problem Solver: A Guide to Improving Thinking, Learning, and Creativity. Worth Publishers. ISBN 978-0716722052. 
• Conn, Charles; McLean, Robert (March 6, 2019). Bulletproof Problem Solving: The One Skill That Changes Everything. Wiley. ISBN 978-1119553021. 
• Rosenau, Milton D. (1996-09-27). The PDMA Handbook of New Product Development. Wiley. pp. 636. ISBN 0-471-14189-5. 
• Glegg, Gordon Lindsay (January 1, 1969). Design of Design Hardcover. Cambridge University Press. pp. 93. 
• Pugh, Stuart (February 1, 1991). Total Design: Integrated Methods for Successful Product Engineering. Addison-Wesley. pp. 278. ISBN 978-0201416398. 
• Deming, W. Edwards (January 1, 1986). Out of the Crisis. Massachusetts Inst Technology. pp. 448. ISBN 9780262350037. 
• Juran, J. M. (January 1, 1987). Juran on Planning for Quality. The Free Press. ISBN 978-0029166819. 
• Process Quality Management and Improvement Guidelines, Roger B. Ackerman
• Clausing, Don (April 1, 1994). Total Quality Development: A Step-By-Step Guide to World-Class Concurrent Engineering. Amer Society of Mechanical. pp. 506. ISBN 978-0791800355. 
• Kidder, Tracy (January 1, 1982). The Soul of a New Machine by Tracy Kidder. ISBN 0140062491. 
• Ackroff, Russell L. (June 1, 1978). The Art of Problem Solving: Accompanied by Ackoff's Fables. John Wiley & Sons Inc. pp. 214. ISBN 978-0471042891. 
• Williams, Christopher G (January 1, 1974). Craftsmen of necessity. Random House. pp. 182. ISBN 978-0394489834. 
• Stone Zander, Rosamund; Zander, Benjamin (224). The Art of Possibility: Transforming Professional and Personal Life. Penguin. pp. 224. ISBN 978-0142001103. 
• Nierenberg, Gerard (1996). The Art of Creative Thinking. Barnes Noble Books. pp. 240. ISBN 978-0760701249. 
• Maeda, John (August 21, 2006). The Laws of Simplicity. The MIT Press. ISBN 978-0262134729. 

Creating Ideas

• von Oech, Roger (May 5, 2008). A Whack on the Side of the Head: How You Can Be More Creative. Grand Central Publishing. pp. 256. ISBN 978-0446404662. 
• Gause, Donald C.; Weinberg, Gerald M. (March 1, 1990). Are Your Lights On?: How to Figure Out What the Problem Really Is. Dorset House Publishing Company. pp. 176. ISBN 978-0932633163. 
• Gelb, Michael J. (February 8, 2000). How to Think Like Leonardo da Vinci: Seven Steps to Genius Every Day. Dell. pp. 336. ISBN 978-0440508274. 
• Christensen, Clayton M. (January 5, 2016). The Innovator's Dilemma: When New Technologies Cause Great Firms to Fail. Harvard Business Review Press. pp. 288. ISBN 978-1633691780. 
• Ridley, Matt. How Innovation Works: And Why It Flourishes in Freedom. Harper. pp. 416. ISBN 978-0062916594. 
• De Bono, Edward (August 18, 1999). Six Thinking Hats. pp. 192. ISBN 978-0316178310. 
• Jones, Morgan D. (June 30, 1998). The Thinker's Toolkit: 14 Powerful Techniques for Problem Solving. Crown Business. pp. 384. ISBN 978-0812928082. 
• Michalko, Michael (June 8, 2006). Thinkertoys: A Handbook of Creative-Thinking Techniques. Ten Speed Press. pp. 416. ISBN 978-1580087735. 
• Plucker, Jonathan (September 1, 2016). Creativity and Innovation: Theory, Research, and Practice. Prufrock Press. pp. 400. ISBN 978-1618215956. 
• De Bono, Edward (February 24, 2015). Lateral Thinking: Creativity Step by Step. Harper Colophon. pp. 300. ISBN 978-0060903251. 
• Lakoff, George; Johnson, Mark (April 15, 2003). Metaphors We Live By. pp. 242. ISBN 978-0226468013. 
• Camp, Robert C.. Benchmarking: The Search for Industry Best Practices that Lead to Superior Performance. Productivity Press. pp. 320. ISBN 978-1563273520. 
• Cameron, Julia (October 25, 2016). The Artist's Way. TarcherPerigee. pp. 272. ISBN 978-0143129257. 
• Stone Zander, Rosamund; Zander, Benjamin (224). The Art of Possibility: Transforming Professional and Personal Life. Penguin. pp. 224. ISBN 978-0142001103. 
• Edwards, Betty (April 6, 1987). Drawing on the Artist Within: An Inspirational and Practical Guide to Increasing Your Creative Powers. Touchstone. pp. 256. ISBN 978-0671635145. 
• Wilson, Paul F. (September 1, 1993). Root Cause Analysis : A Tool for Total Quality Management. American Society for Quality. pp. 216. ISBN 978-0873891639. 

Product Development

• Smith, Preston G. (October 10, 1997). Developing Products in Half the Time: New Rules, New Tools. Wiley. pp. 320. ISBN 978-0471292524. 
• Meyer, Christopher (June 1, 1993). Fast Cycle Time: How to Align Purpose, Strategy, and Structure for Speed. Free Press. pp. 290. ISBN 978-0029211816. 
• Rosenau, Milton D. (April 12, 1990). Faster New Product Development: Getting the Right Product to Market Quickly. AMACOM. pp. 432. ISBN 978-0814459423. 
• Rosenau, Milton D. (January 1, 1993). Managing the Development of New Products: Achieving Speed and Quality Simultaneously Through Multifunctional Teamwork. John Wiley & Sons Inc. ISBN 978-0442013950. 
• Wheelwright, Steven C.; Clark, Kim B.. Revolutionizing Product Development: Quantum Leaps in Speed, Efficiency, and Quality. Free Press. pp. 364. ISBN 978-0029055151. 
• Cooper, Robert G. (May 24, 2001). Winning at New Products: Accelerating the Process from Idea to Launch. Basic Books. pp. 416. ISBN 978-0738204635. 
• Cooper, Robert G. (October 19, 1998). Product Leadership: Creating And Launching Superior New Products. Basic Books. pp. 336. ISBN 978-0738200101. 
• Phadke, Madhav S. (January 1, 1989). Quality Engineering Using Robust Design. Prentice Hall PTR. pp. 334. 

Decision Making

• Fisher, Roger; Ury, William L.; Patton, Bruce (May 3, 2011). Getting to Yes: Negotiating Agreement Without Giving In. enguin Books. pp. 240. ISBN 978-0143118756. 
• Saaty, Thomas L. (October 1, 1990). Multicriteria Decision Making: The Analytic Hierarchy Process: Planning, Priority Setting, Resource Allocation. RWS Pubns. ISBN 978-0962031724. 
• Saaty, Thomas L. (September 3, 2012). Decision Making for Leaders: The Analytic Hierarchy Process for Decisions in a Complex World. RWS Publications. pp. 323. ISBN 978-0962031786. 
• King, Bob (December 1, 1989). Better Designs in Half the Time: Implementing Qfd Quality Function Deployment in America. Goal Q P C Inc. pp. 315. ISBN 978-1879364011. 

I have not yet read the following books, but they seem interesting and relevant. They are listed here to invite further research.

• Strategies for Creative Problem-Solving, H. Scott Fogler
• Problem Solving 101: A simple Book for smart people, Ken Watanabe
• 101 Creative Problem Solving Techniques, James M. Higgins
• Solving Tough Problems: An open way of talking, listening, and creating, Adam Kahane
• Eating Problems for Breakfast, Tim Hansel
• The art and craft of problem solving, Paul Zeitz
• How to solve problems, Wayne A. Wickelgren
• Its not about the shark, David Niven
• The complete problem solver, John D. Arnold
• The art of systems thinking, Joseph O’Conner, Ian McDermott
• What’s your problem, Thomas Wedell-Wedellsborg
• Patterns of Problem Solving, Moshe F. Rubinstein
• Creative problem solver’s toolbox, Richard Fobes
• The Wright Way, Mark Eppler
• Creative Problem Solving, Donald J. Noone
• Techniques of Structured Problem Solving
• Techniques of Problem Solving, Steven G. Krants
• The 3rd Alternative, Stephen Covey

1. ↑ Michalko, Michael (June 8, 2006). Thinkertoys: A Handbook of Creative-Thinking Techniques. Ten Speed Press. pp. 416. ISBN 978-1580087735. Page 22.
2. ↑ Sam Harris, The Waking Up Course, Solving Problems lesson.
3. ↑ What is problem solving?, ASQ
4. ↑ 5 simple steps to problem solving, xerox website.
5. ↑ Building a Learning Organization, by David A. Garvin, Harvard Business Review July-August 1993.
6. ↑ 7 Steps to Effective Problem Solving, Crestcom, September 1, 2016.
7. ↑ Process Quality Management and Improvement Guidelines, Roger B. Ackerman
8. ↑ Conn, Charles; McLean, Robert (March 6, 2019). Bulletproof Problem Solving: The One Skill That Changes Everything. Wiley. ISBN 978-1119553021. 
9. ↑ Bransford, John D. (February 15, 1993). The Ideal Problem Solver: A Guide to Improving Thinking, Learning, and Creativity. Worth Publishers. ISBN 978-0716722052. 
10. ↑ Conn, Charles; McLean, Robert (March 6, 2019). Bulletproof Problem Solving: The One Skill That Changes Everything. Wiley. ISBN 978-1119553021. 
11. ↑ Cleaving frames, Bill Synnot and Associates, Technique 2.93
12. ↑ Food Rules: An Eater’s Manual, Michael Pollan
13. ↑ Pugh, Stuart (February 1, 1991). Total Design: Integrated Methods for Successful Product Engineering. Addison-Wesley. pp. 278. ISBN 978-0201416398. 
14. ↑ Saaty, Thomas L. (September 3, 2012). Decision Making for Leaders: The Analytic Hierarchy Process for Decisions in a Complex World. RWS Publications. pp. 323. ISBN 978-0962031786.