The Problem-Solving Cycle

The problem-solving cycle is an iterative approach that involves brainstorming, constructing matrices, analyzing and testing until the optimal solution is reached. It is important that all steps be done in order.

1. State the Problem

Enter the creative problem-solving cycle with a statement of a problem that pertains to a specific topic. It may take any of these forms:

  • an open-ended question
  • an existing condition in need of change
  • a kit of materials provided to design and build something
  • a research proposal for a student project

Teachers are encouraged to select age-appropriate topics for their students, keeping in mind their particular enthusiasms and environments. Think of yourself, the teacher, as a customer with a problem in need of a solution. Small groups of students become team problem solvers.

Example: A self-described "ecologically concerned" client wants to change her home heating system from electricity to gas in order to dramatically reduce her heating costs.

2. Redefine the Problem

The problem solvers should assume that the initial problem comes to them reflecting the bias of their customer and also his/her preconceived notion(s) of a desired solution. Therefore, the problem solvers must question the customer and redefine the problem in a "cleaner" form.

The new problem statement is less ambiguous; it is open-ended and not constrained by the customer's preconceived solution.

Example: The customer's perceived problem is two-fold:

  1. The cost of heating her house is too high.
  2. She heats with electricity, which is expensive.

Her implied solution is that a change from electricity to gas is going to reduce her heating cost and is the best way to lower her cost. The biases are:

  1. That gas is cheaper than electricity, not counting the cost to change over.
  2. That reducing her cost by changing from electricity to gas is "ecologically sound," i.e., that reduced cost = reduced energy usage. (Is electricity less efficient, as opposed to less expensive, than gas?)

The redefined problem might be:

  • What is the most cost-effective change the woman can make to reduce her energy costs?

3. Identify Constraints and Set General Specifications

Once the problem solvers have a clear understanding of the customer and his/her needs, brainstorming will help generate a list of specifications that will establish the constraints the solution must meet. Some constraints (moral, legal, ethical) may apply to any problem, not just this one.

Example: The customer (now a client) is an engineer who lives alone in a mid-Atlantic state. Her sprawling brick ranch home is heated by an electric baseboard system. She has single-pane crank-out casement windows with aluminum frames. Although she has installed some energy-saving devices, her energy costs are significantly higher than those of others in her area with comparable homes. She likes to think of herself as environmentally concerned, a factor which should figure in any list of specifications.

The first time through the cycle, the specifications will be general in nature. For optimal effectiveness, each should be defined, quantified, and justified.

Example: Any solution for this client must be:

feasible safe legal
ethical aesthetically pleasing reliable
environmentally sound moral economical in terms of capital cost, operating cost, and savings
practical timely

We will take one specification as an example to be defined, quantified and justified.

Example: The specification "economical"...

  • defined as the greatest savings, considering both capital cost and operating costs, when compared with current costs.
  • quantified in terms of capital cost, operating costs, and savings.
  • ... is justified in terms of reducing costs as quickly and efficiently as possible.

4. Identify Alternative Solutions

Brainstorm possible solutions to the problem using established specifications and constraints. Brainstorming is a free flow of ideas without criticism, since this would hinder tapping into the group's innate creativity. A long list assures the problem solvers that another solution can be found should a first or second choice fail.

Example: A sample list of alternative solutions for this client might include:

switch from electricity to gas add insulation add shutters
bury the house in an earth berm put a dome over the house burn coal
fit windows with new drapes purchase programmable thermostat brick-in existing windows
install high-efficiency heat pump replace oil burner with gas burner plant trees to block wind

5. Select the Most Viable Alternative

In order to identify those advantages which will have the most favorable impact on this client's energy costs, we must weigh the advantages and disadvantages of each alternative. To do this, we create a matrix by examining the brainstormed list of alternatives, categorizing them according to broad similarities. (In this case, all alternatives are either new energy sources, changes in efficiency, or lowering of energy losses.) A qualitative or quantitative scale should be established to judge the merits of each alternative against each specification. The matrix analysis yields a pool of alternative solutions that may be ranked from most to least desirable. The best alternative is selected based on the results of this analysis.

In constructing and analyzing the matrix, problem solvers may have to engage in some experimentation. They certainly will have to do market and technical research, either in the library or by telephoning outside sources such as companies and trade associations.

6. Redefine the Problem

The highest-ranking alternative is re-evaluated by redefining the problem as necessary.

Example: The redefined problem is to determine where in the home additional insulation would be most effective. To determine this, another matrix must be employed to compare different techniques.

7. Refine and Add Specifications

Brainstorm to develop refined specifications for the alternative selected. In this second iteration, the specifications should be more specifically defined, quantified, and justified relative to the alternative solution which has been chosen.


  • must be non-toxic, non-carcinogenic
  • must not detract from the home's appearance
  • must have a reasonable installation cost
  • must reduce heat loss

8. Brainstorm Alternatives

Using the refined and more-focused specifications, additional appropriate alternatives should be generated.

Example: Refined alternatives for insulation location include:

  • windows
  • walls
  • attic
  • doors
  • floors

9. Reiterate Until the Problem Is Solved

The redefined problem now is to determine the best method to insulate the attic and the windows. So, a new set of specifications is developed.


  • capital cost
  • operating costs
  • potential savings
  • non-toxic, non-carcinogenic
  • must not detract from home's appearance
  • longevity (7- to 10-year)
  • requires or does not require homeowner's participation

10. Select the Most Viable Alternative

Establish a new matrix based on the new specifications and alternatives. Analyze the alternatives and re-rank from the best to the least desirable.

Example: To determine the best location for insulation, a heat-loss analysis was done using infra-red photography. It was determined that most of the heat was being lost through the windows, with attic losses secondary. Let's assume concentration on the heat loss through the windows.

The alternatives are ranked as:

  • plastic film over the windows
  • install storm windows
  • shutters on outside of windows
  • fiberglass on outside of windows
  • replacement Thermopane windows

The conclusion is that the homeowner should retrofit her house with Thermopane windows even though the capital cost is higher than for the other alternatives. The reasoning included:

  • Plastic film is ugly, lasts only one year, and requires annual installation.
  • Storm windows are also ugly and require opening/closing.
  • Shutters are efficient but also require opening/closing.
  • Fiberglass on outside of windows is ugly.
  • Thermopane windows are the most expensive, but are long-lasting, invisible, and require no owner participation. They are the most viable solution.

"The woman wanted gas but got glass!"