Engineering Problem Solving¶
Some problems are so complex that you have to be highly intelligent and well-informed just to be undecided about them.
—Laurence J. Peter
Steps in solving ‘real world’ engineering problems¶
The following are the steps as enumerated in your textbook:
Collaboratively define the problem
List possible solutions
Evaluate and rank the possible solutions
Develop a detailed plan for the most attractive solution(s)
Re-evaluate the plan to check desirability
Implement the plan
Check the results
A critical part of the analysis process is the ‘last’ step: checking and verifying the results.
Depending on the circumstances, errors in an analysis, procedure, or implementation can have significant, adverse consequences (NASA Mars orbiter crash, Bhopal chemical leak tragedy, Hubble telescope vision issue, Y2K fiasco, BP oil rig blowout, …).
In a practical sense, these checks must be part of a comprehensive risk management strategy.
My experience with problem solving in industry was pretty close to this, though encumbered by numerous business practices (e.g., ‘go/no-go’ tollgates, complex approval processes and procedures).
In addition, solving problems in the ‘real world’ requires a multidisciplinary effort, involving people with various expertise: engineering, manufacturing, supply chain, legal, marketing, product service and warranty, …
Exercise: Problem solving
Step 3 above refers to ranking of alternatives.
Think of an existing product of interest.
What do you think was ranked highest when the product was developed?
Consider what would have happened if a different ranking was used. What would have changed about the product?
Brainstorm ideas with the students around you.
Defining problems collaboratively¶
Especially in light of global engineering, we need to consider different perspectives as we define our problem. Let’s break the procedure down into steps:
Step 1¶
Identify each perspective that is involved in the decision you face. Remember that problems often mean different things in different perspectives. Relevant differences might include national expectations, organizational positions, disciplines, career trajectories, etc. Consider using the mnemonic device “Location, Knowledge, and Desire.”
Location: Who is defining the problem? Where are they located or how are they positioned? How do they get in their positions? Do you know anything about the history of their positions, and what led to the particular configuration of positions you have today on the job? Where are the key boundaries among different types of groups, and where are the alliances?
Knowledge: What forms of knowledge do the representatives of each perspective have? How do they understand the problem at hand? What are their assumptions? From what sources did they gain their knowledge? How did their knowledge evolve?
Desire: What do the proponents of each perspective want? What are their objectives? How do these desires develop? Where are they trying to go? Learn what you can about the history of the issue at hand. Who might have gained or lost ground in previous encounters? How does each perspective view itself at present in relation to those it envisions as relevant to its future?
Step 2¶
As formal problem definitions emerge, ask “Whose definition is this?” Remember that “defining the problem clearly” may very well assert one perspective at the expense of others. Once we think about problem solving in relation to people, we can begin to see that the very act of drawing a boundary around a problem has non-technical, or political dimensions, depending on who controls the definition, because someone gains a little power and someone loses a little power.
Step 3¶
Map what alternative problem definitions mean to different participants. More than likely you will best understand problem definitions that fit your perspective. But ask “Does it fit other perspectives as well?” Look at those who hold Perspective A. Does your definition fit their location, their knowledge, and their desires? Now turn to those who hold Perspective B. Does your definition fit their location, knowledge, and desires? Completing this step is difficult because it requires stepping outside of one’s own perspective and attempting to understand the problem in terms of different perspectives.
Step 4¶
To the extent you encounter disagreement or conclude that the achievement of it is insufficient, begin asking yourself the following: How might I adapt my problem definition to take account of other perspectives out there? Is there some way of accommodating myself to other perspectives rather than just demanding that the others simply recognize the inherent value and rationality of mine? Is there room for compromise among contrasting perspectives?
How ‘good’ a solution do you need¶
There is also an important aspect of real-world problem solving that is rarely articulated and that is the idea that the ‘quality’ of the analysis and the resources expended should be dependent on the context.
This is difficult to assess without some experience in the particular environment.
How ‘Good’ a Solution Do You Need?
Some rough examples:
10 second answer (answering a question at a meeting in front of your manager or vice president)
10 minute answer (answering a quick question from a colleague)
10 hour answer (answering a request from an important customer)
10 day answer (assembling information as part of a trouble-shooting team)
10 month answer (putting together a comprehensive portfolio of information as part of the design for a new $200,000,000 chemical plant)
Steps in solving well-defined engineering process problems, including textbook problems¶
Essential steps:
Carefully read the problem statement (perhaps repeatedly) until you understand exactly the scenario and what is being asked.
Translate elements of the word problem to symbols. Also, look for key words that may convey additional information, e.g., ‘steady state’, ‘constant density’, ‘isothermal’. Make note of this additional information on your work page.
Draw a diagram. This can generally be a simple block diagram showing all the input, output, and connecting streams.
Write all known quantities (flow rates, densities, etc.) from step 2 in the appropriate locations on, or near, the diagram. If symbols are used to designate known quantities, include those symbols.
Identify and assign symbols to all unknown quantities and write them in the appropriate locations on, or near, the diagram.
Construct the relevant equation(s). These could be material balances, energy balances, rate equations, etc.
Write down all equations in their general forms. Don’t simplify anything yet.
Discard terms that are equal to zero (or are assumed negligible) for your specific problem and write the simplified equations.
Replace remaining terms with more convenient forms (because of the given information or selected symbols).
Construct equations to express other known relationships between variables, e.g., relationships between stoichiometric coefficients, the sum of species mass fractions must be one.
Whenever possible, solve the equations for the unknown(s) algebraically.
Convert the units of your variables as needed to have a consistent set across your equations.
Substitute these values into the equation(s) from step 7 to get numerical results.
Check your answer.
Does it make sense?
Are the units of the answer correct?
Is the answer consistent with other information you have?
Exercise: Checking results
How do you know your answer is right and that your analysis is correct?
This may be relatively easy for a homework problem, but what about your analysis for an ill-defined ‘real-world’ problem?
Brainstorm ideas with the students around you.