Why Worry About Problem Solving?

        Problem solving is not something you may have thought about as a legitimate topic in a set of lessons on electrical topics. After all, doesn't everyone solve problems?

lFact 1: Most people believe that they are
    good problem solvers, but many individuals
    over-estimate their ability.

lFact 2: There are different levels of skill in
    problem solving, and many individuals never
    get beyond the lower skill levels.

lFact 3: With practice, and an understanding
    of where you want to get, you can improve
    your problem solving skills.


Lesson Objectives

        What do you hope to accomplish in this lesson?
 

lThis lesson is somewhat different. You have several goals,
lTo realize that your goal is to develop your problem
solving abilities,
lTo learn to think about problem definitions when
you begin to solve a problem,

Problem Definition

        How we define our goals and how we view the problem we face will affect greatly the way we approach our study and what we will achieve
 

l Any time that you have to solve a problem,
    the problem definition that you adopt will
    influence the solution you will find - and it
    may well completely determine your solution.
        Consider what this really means. If you have a problem that you must solve, you may kill your chances of solving the real problem if you define the problem in a way that prevents you from getting a solution to the real problem. When you get a problem to solve, it is probably going to be vaguely defined. Your first step is to get a problem definition for yourself that you can work with. If you don't do that carefully enough you may never get anywhere.

        The world is full of products put on the market to solve mis-perceived problems. Buried in the graveyard of bad problem definitions you will find the following.

l The car-bar, a system for delivering mixed drinks
    to automobile drivers.  (Clearly developed before
    the days of MADD, and still a bad idea)
Clearly, this is a case of solving the wrong problem.
l In the early days of automobiles drivers signalled
    turns by putting their hands out the window and
    pointing in the direction of the turn. The first automatic
    signalling device emulated that action with a
    mechanical arm that pointed in the direction of the
    turn. However, the problem was not emulating a
    human driver, the real problem was to signal
    the driver's intention to turn.  Using the new problem
    definition, designers began to focus on what evolved
    into the system of turn signals we use today.
We can conclude the following:
l The solution of a problem is very much influenced
    by the way the problem is defined.

l When a problem is first posed it is never completely
    clear how the problem should be defined.

To make this point clearer consider this story.

        Imagine that you are the manager of a multi-story building. You begin receiving complaints about the elevator service and they are severe enough that you feel that the issue must be addressed. The first thing you try to do is to define the problem as well as you can. Do not go to the next page until you have written down as many definitions of this problem as you can.

        The solutions to the problem depend upon how you define the problem. Let us examine a few problem definitions and the solutions that they lead to so that we can appreciate how the problem definition affects the solutions we generate.

lProblem Definition: There are not enough elevators.
lProblem Solution: If this is your problem definition, you
    may try to add more elevator shafts, and that is going to
    be very, very expensive. It will probably involve adding one
    or more elevators running in a cylinder attached to the
    building.Alternatively, you might come up with the (not-so)
    brilliant idea of running two elevators in one shaft. Whatever
    kind of solution you generate with this problem definition
    is going to be either expensive or absurd.


Let's try another definition.

lProblem Definition: The elevator service is lousy
    because the elevators are too slow.
lProblem Solution: If you think this way, then you will
    probably look into installing more powerful motors
    to move the elevators up and down more quickly.
... and another definition.
lProblem Definition: Schedules for people using
    the elevators cause peak loads that are too large.
lProblem Solution: If you think this is the problem, and
    you have an office building, you might go to some of the
    tenants and try to talk them into changing their hours
    so that everyone doesn't come in at 9am and leave
    at 5PM. (And don't forget to have them stagger lunch hours
    also!) If it is a residential building, then you want to go after
    tenants that work the night shift. (Give such tenants a break
    on the rent.)
... and another.
lProblem Definition: The elevator service algorithm is
    wrong.
lProblem Solution: If this is the problem, then you might
    want to go to a computer control system that monitors how
    many stops the elevator makes as it descends, guesses
    when it is full and then goes straight to the destination. You
    might even install sensors to measure when it has a full load,
    and use that information. You would need to define a new
    service algorithm that was more responsive to the
    conditions of the elevator system.
... and yet another definition.
lProblem Definition: Too many people are complaining
    about the elevator service.
lProblem Solution: This definition of the problem seems too
    trite. However, this was the actual problem definition arrived
    at by the building manager this story comes from. Before you
    read about what he did (and it was truly ingenious!) try to dream
    up a solution or two that uses this problem definition.
Here's that definition again.
lProblem Definition: Too many people are complaining
    about the elevator service.
lProblem Solution: What the building manager did was to
    have mirrors placed between the elevator openings. Then
    when people showed up at the elevators they looked at
    themselves in the mirrors, and they preened themselves.
    The complaints stopped, almost totally. The manager had
    solved the problem with a very ingenious problem definition
    and solution, and it was probably cheaper than the solution
    using any other definition.
Would you have thought of it?

        Now, consider what happened, and the moral you should draw from this.

lWhenever you have a problem to solve make sure
    that you have examined the problem definition
    critically.
lIf you have the opportunity to change the definition,
    do so in any way advantageous to you. If you don't
    have the opportunity to change the definition, then
    fight for the opportunity to do so. Your goal is to
    generate a problem definition that gets at the real
    problem.
        If you are using this material in a course you have a problem that you need to define. Here are some possible problem definitions for you.
lGet an A.
lLearn the material.
lSurvive the course with the least damage to GPA.


        You really should adopt the second goal - to learn the material - or you may have difficulty later. Often the material you try to learn will build on earlier material, and as you proceed through the later material you will come to appreciate that. Getting an A without really understanding the material, or just getting the highest grade may mean nothing in the long term if you don't build the foundation for later learning.