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

	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.

[Top] 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:

a. The cost of heating her house is too high.
b. 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

a. that gas is cheaper than electricity, not counting the cost to change over
b. 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?

[Top] 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
economical in terms of capital cost, operating cost, and savings	environmentally sound	moral
	practical	timely

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

Example: The specification"economical"...

...is defined as the greatest savings, considering both capital cost
and operating costs, when compared with current costs.

...is quantified in terms of capital cost, operating costs, and savings.

... is justified in terms of reducing costs as quickly and efficiently as possible.

[Top] 4. Identify Alternative Solutions

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

[Top] 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.

[Top] 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.

[Top] 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

[Top] 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

[Top] 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

[Top] 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!"

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