Principles of Problem Solving

PPS-13: Define the Stated Problem

(Adapted from MPS 8, Don Woods 2003)

Pre-class assignment

1. Read sections What is It?, Why Do It?, New Concepts, How to  Do It, and Learning Objectives
2. Take the Define the Stated Problem Pretest
3. Be able to describe the step Define the Stated Problem and how it fits into the Six Step Problem Solving Method

What is It?

As stated in PPS-11, this is the step when you dissect the words of the problem description to extract the important information – the problem, what is known, and the constraints before you can begin.

It is the second step in the Six Step Method of Engage, Define, Explore, Plan, Do It, and Look Back.

Note that the problem that you extract from the problem statement may not be the “Real Problem”.  For example, you may be facing the problem of getting a production line back up and running after a machine breakdown.  The “Real Problem” may be a lack of preventive maintenance, but you need to first address the stated problem of resuming production.

New Concepts

Given, Known, Constraint, Problem Ownership, Real Problem

Why Do It

Again, we are learning the techniques used by expert problem solvers.  Defining the problem is like setting a clear measurable goal.  We’ll be able to tell if we have solved the problem if it is clearly defined.

How to Do It

Two tasks in problem definition are determining Problem Ownership and Dissection of the problem statement.

Problem Ownership

Before diving into a problem, you should check to see if you have ownership.  The problem owner has the authority, resources, and power to define the goal and implement the solution.  People affected by the problem and/or its solution are called stakeholders.  In engineering practice, you will often face problems for which you do not have ownership, but may be given some responsibility.  In that case, you are faced with developing cooperative problem definitions and solutions.

In this unit, we will be mostly concerned with the sort of technical problems you will see in engineering problems courses.  Since you are assigned the problem by the instructor through a textbook, you probably don’t have complete ownership.  You interpret the problem statement, rather than define the problem, but you are responsible for the solution.

Problem Dissection

In PPS-10 it says that in this stage you will:

• Systematically classify information
• Organize the information in a way that will be useful
• Extract the words relevant to the problem
• Be thorough in reviewing the problem statement
• Begin to translate the words into pictures
• Recognize that some information may be inferred rather than explicit

We will take care of the first five of those by dissecting the words and pictures of the problem statement into components, and placing those individual organs into appropriate bins.  As we place those parts in the bins, we remove those words from the original problem statement.

The Bins are –

Goal/Unknown          Given/Known                        Constraints                Situation

You will notice that these bins are typical categories seen in the standard format for solutions used in many courses.

Consider an example problem from Callister

A piece of copper originally 305 mm (12in.) long is pulled in tension with a stress of 276 MPa (40,000 psi).  If the deformation is entirely elastic, what will be the resultant elongation?

Let’s put this information into our bins and cross out the information as we use it.

A piece of copper originally 305 mm (12in.) long is pulled in tension with a stress of 276 MPa (40,000 psi).  If the deformation is entirely elastic, what will be the resultant elongation?

 Goal/Unknown Given/Known Constraints Situation What will be the resultant elongation? ·       Material is copper ·       Stress is 276 MPa ·       Original length is 305 mm ·         Deformation is entirely elastic Pulled in Tension

We

• tried to use the wording of the problem statement as much as possible
• used up all of the problem statement
• started to picture the situation.

We did not

• start or even discuss a solution
• translate the information into engineering symbols and pictures
• try to make the stated problem “just like” an example problem in the text.

You may not bin this information exactly the same as I did.  You may think that “Deformation is entirely elastic” could also be a Given/Known.  It probably could, but looked more like a constraint to me.

What about implied information?  In this case the instructor probably wants the numerical answer in decimal form with no more that 3 significant figures, wants you to do it yourself rather than copy it our of the solution manual, wants no round off error in the first two decimal places, and wants to see a step by step solution rather than a single number.  The stress is probably the normal rather than shear stress and elastic means linear elastic.

Important inferred statements should be listed in their own bin as Assumptions.

Learning Objectives

Given a problem statement, you should be able to:

1. Identify the Goal/Unknowns
2. Identify Given/Knowns
3. Identify the Constraints
4. Identify Inferred Knowns and Constraints

Pretest

Awareness:

How aware are you of what you do when you define the stated problem?    _________

On a scale of 1-10, where

1   is Unaware, I just do it,

5   is Aware of some

10 is Very aware: I can describe the details of how I do it

Skill:

How skilled are you in doing this activity?                               _________

On a scale of 1-10, where

1 is poor, 3 is fair, 5 is good, 7 is very good, and 10 is excellent?

In-Class

Exercise 1 (5 min.): (instructor hands out problem statement with bins shown.)

1. Individually sort the information in a problem statement by the instructor into the defined bins.
2. Compare your list with one or two people near you, note differences, and try to resolve those differences.

PPS-13  Define the Stated Problem

Assignment 1  Individual

For the problem statement assigned,

1. Sort all the information into bins of Goal/Unknown, Given/Known, Constraints, Situation
2. List Inferred Knowns and Constraints as Assumptions

 Goal/Unknown Given/Known Constraints Situation

Assumptions

Evaluation:

1. Considered All information

Excellent (10)  - all of information in problem statement was binned

Mediocre (5)    - some of information in problem statement was not binned

Weak (0)         -  significant information was not binned

2. Appropriate Binning

Excellent (10)  – all information was in appropriate (or reasonable) categories

Mediocre (5)    - some information was not in appropriate categories

Weak (0)         – most information was incorrectly binned