Problem Solving

Analytic And Creative Problem Solving

• In analytic problem solving there is one correct answer.

• In creative problem solving there is no single right answer.

Engineers approach problems using the Creative approach called Design Process following these 10 steps:

1. Identify the problem

2. Define the working criteria/goals

3. Research and gather data

4. Brainstorm creative ideas

5. Analyze (HERE IS WERE THE ANALYTIC APPROACH IS USED)

6. Develop models and tests

7. Make the decision

8. Communicate and specify

9. Implement and commercialize

10. Post-implementation review and assessment

Some Problem solving strategies:

• look for a pattern

• construct a table

• consider possibilities systematically

• act it out

• Make a model

• Make a figure, graph or drawing

• work backwards

• Select appropriate notation

• Restate the problem in your own words

• Identify, necessary, desired and given information

• Write an open ended sentence

• Identify a sub-goal

• First solve a simple problem

• Change your point of view

• Check  for hidden assumptions

• Use a resource

• Generalize

• Check the solution, Validate it

• Find another way to solve the problem

• Find another solution

• Study the solution process

• Get a bigger hammer

• Brainstorm

• Involve others

Analytic Problem Solving

The most important Analytic problem solving method is the Scientific Method:

• Define the problem

• Gather the facts (Identify the variables)

• Develop hypothesis (educated guess, If...Then...)

• Perform a test (test one variable at a time, perform the test at least 3 times maintaining the same condition, use a control)

• Evaluate the results

Applied to Engineering these are the steps:

Step 1:  Define the problem and make a problem statement

Restate the problem in your own words, to better understand which part of the problem to focus on

Step 2: Diagram and describe

List the information given and what needs to be found (What do I know?Given, What do I need to know?Needs). Make a diagram or a sketch, label clearly, try to maintain the scale, depict the connections of carious parts and their functions!!! "A picture is worth a thousand words!"

Step 3: Apply theory and equations

State Explicitly the theory or equations you need to solve the problem. Understand each component of equations. "often some parts of the equations can be neglected!" Start with a full equation and then simplify it as needed.

Step 4: Simplify the assumptions

To solve a problem in a timely and cost-effective manner simplifying assumption is required. While estimation and approximation are useful tools, engineers also are concerned with the accuracy and reliability of their results. Approximations are often possible if assumptions are made to simplify the problem at hand. An important concept for engineers to understand in such situations is the Conservative Assumption. 

• Example: An example of conservatism can be seen in the design of a swing set. In most sets, there is a horizontal piece from which the swings hang, and an inverted V-shaped support on each end. If you were the design engineer, you might have to size One of the first questions to ask is, For what weight do we size the swing set? One way to answer this question is to do a research project on the weight distribution of children followed by doing research into the use of swings by children at different ages, and then analyzing those data to determine typical weights of children that would use such swings. You might even need to observe playground activity to see if several children pile on a swing om load the set in different ways-say, by climbing on it. This might take weeks to do, but you would have excellent data.  

• On the other hand, you could lust assume a heavy load that would exceed anything the children would produce, For this case say 500 pounds per swing. That would assume the equivalent of two large adults on each swing make the calculation to determine the needed supports, and then ask if it makes sense to be more detailed. To answer this, one has to answer the question "What problem am I solving? Am I after the most precise answer I can get? Am I after a safe and reliable answer regardless of other concerns?

• In engineering the other concerns include such things as cost and availability of materials. In the current example, the supports would most likely be made of common materials. Swing sets are typically made of wood or steel tubing. So one way to answer the above questions is to quickly check and see it making a more detailed analysis would be justified. Check the prices at the materials needed for your conservative assumption against potential materials based on a more detailed analysis. Does the price difference justify a more detailed analysis? Another way to ask this is Does the price difference justify spending time to do the analysis? Remember as an engineer, your time costs money. The answer may be, it depends." It would depend on how much the difference is and how many you are going to produce. It wouldn't make sense to spend a week analyzing or researching the answer if it saves you or your company only $500. If your company was producing a million sets and you could save $5 per set, it would justify that week's work. 

• Safety of the public is of paramount concern in the engineering profession. As an Engineer, you will need to develop the ability to answer: "What problem am I really solving?" and "How do I get the solution I need most efficiently?"

Step 5: Solve the necessary problems

Now its time to perform the calculations. Document what you have done to derive the solution step by step, with clear explanations. This allows to find errors faster and to communicate to others what you have done.

Step 6: Verify accuracy to desired level

Engineers work on solution that can effect the safety of people.  It is of paramount importance that the solution an engineer develops is accurate. 

Some ways to verify the results:

• Estimate the answer

• Simplify the problem and solve the simpler problem. Are the answers consistent?

• Compare with similar solutions. In many cases, other problems were solved similarly.

• Compare to previous work

• Ask a more experience engineer to review the results

• Compare to published literature on similar problems

• Ask yourself if it make sense

• Compare to your own experience

• Repeat the calculations

• Run a computer simulation or model

• Redo the calculations backward