QMB Exam 3
Collaborative Study Guide
Exam 3 Formatting & Question Breakdown
Biggest changes
● We can go back to previous questions.
● 1 multiple choice question will be after each excel problem asking what type of
problem we just completed
● Excel intensive exam 70 points come from the excel portion. 80 from the
remaining short answer / multiple choice.
Topics to know
● Objective Functions
● Modules 8 & 9 Videos about graphing
● Different constraints for each type of linear programming problem
○ Resource Allocation is less than or equal to (<=)
○ Cost benefit trade off is greater than or equal to (>=)
○ Mixed problems are less than or equal to, greater than or equal to, or
equal to. It could be any combination of the two or three aforementioned
constraints (<=,>=, or =)
○ Transportation and assignment problems are equals to (=)
● Story about a convenience store (Get ready to think outside the box)
○ Questions about the constraints the store would you use
○ What the objective function is
○ These will be multiple choice, but be prepared to figure out what relevant
information you will need for both of those situations
● A couple of questions on constraints
● Sensitivity Analysis (if such and such value changed by this amount, how would
this other value change)
○ This is from module 10
Module 8 — Linear Programming Basic Concepts
Learning Objectives
1. Explain what Linear Programming is
a. Uses a mathematical model to represent the problem being studied.
Linear in the name refers to the form of the mathematical expressions in
the model. Programming does not refer to computer programming, rather
another word for planning. Planning of Activities = Linear Programming
2. Identify the three key questions to be addressed in formulating any spreadsheet
model
a. What are the decisions to be made?
b. What are the constraints on these decisions?
c. What is the overall measure of performance for these decisions?
A. The decisions to be made are the production rates (number of units
produced per week) for the two new products.
B. The constraints on these decisions are that the number of hours of
production time used per week by the two products in the respective
plants cannot exceed the number of hours available
C. The overall measure of performance for these decisions is the total profit
per week from the two products.
3. Name and identify the purpose of the four kinds of cells used in linear
programming spreadsheet models
a. Data cells (Shaded light blue)
Cells in the spreadsheet that show the data of the problem
b. Changing cells (Shaded bright yellow w/ a light border)
The cells in the spreadsheet that show the values of the decision variables
c. Output cells (no shading)
Cells that provide output that depends on the changing cells. These cells
are frequently used to help specify constraints
d. Objective cell (shaded orange w/ a heavy border)
The cell that shows the overall measure of performance decisions
4. Formulate a basic linear programming model in a spreadsheet from a description
of the problem
Basic product mix excel format for 3 factories with 3 products.
X,Y,Z are the types of products (windows, doors, etc)
Remember to match signs for constraints with the constraints in solver.
5. Present the algebraic form of a linear programming model from its formulation on
a spreadsheet
Taking the above spreadsheet example our algebra would will be simplified as
the following three expressions
1X<=4
2Y<=12
3X+2Y<=18
The third equation has two variables so substitute 0 for y when solving for
x and vice versa. Ultimately you’ll wind up with X=6 and Y=9 for the third
expression above. This means that at its maximum we can make no more
than 6 Xs (doors) in the third plant, and no more than 9 Ys (Windows) if
we were to focus all of our resources on one or the other. These two
numbers are the intercepts for your X and Y axis that creates a line for the
Feasible region.
6. Apply the graphical method to solve a two-variable linear programming problem
The graphical method is when we take the formulas mentioned about and
graph them on a coordinate plane. Because we can’t have negative
products created this will always be in the quadrant # 1 (upper right
quadrant). We then graph the points on the plot and draw lines connecting
them as pictured here.
7. Use Excel to solve a linear programming spreadsheet model
8.4: Graphical method for solving linear programming
● This method can be used to solve problems with two variables
● To solve using this method you place the two rates of production on the x and y
axis and plot the rate that they are produced.
● When solving for multiple variables you can create a region that the solution must
fall into. The solution permitted by all the constraints are the feasible solutions
and the portion of the graph where the feasible solutions lie is referred to as the
Feasible region.
● In order to solve for this we plot all of the constraints on a graph and shade in the
region that is allowed by the constraints.
●
Module 9 — Linear Prog. Formulation & Application
Learning Objectives
1. Recognize various kinds of managerial problems to which linear programming
can be applied.
2. Describe the five major categories of linear programming problems, including
their identifying features.
3. Formulate a linear programming model from a description of a problem in any of
these categories
4. Describe the difference between resource constraints and benefit constraints
including the difference in how they arise
5. Describe fixed-requirement constraints and where they arise
6. Identify the kinds of Excel functions that linear programming spreadsheet models
use for the output cells, including the objective cell
7. Identify the four components of any linear programming model and the kind of
spreadsheet cells used for each component- ASKING FOR DATA, DECISIONS,
CONSTRAINTS, MEASURE OF PERFORMANCE
8. Recognize managerial problems that can be formulated and analyzed as linear
programming problems
9. Understand that flexibility
1. Recognize various kinds of managerial problems to which linear programming can be
applied. = advertising-mix problem, product-mix problem, equipment acquirement mix problem,
budget problem, personnel scheduling problem, transportation problem, assignment problem.
2.Describe the five major categories of linear programming problems, including their
identifying features.
2a)Resource allocation problems our linear programming problems involving the
allocation of resources to activities. The identifying feature for such a problem is that
each functional constraint in the linear programming model is a resource constraint.
An initial step in formulating any resource allocation problem is to identify the activities
and the resources.
These three kinds of data are needed for any resource allocation problem.
1.
the amount available of each resource
2.
the amount of each resource needed by each activity. Specifically, for
each combination of resources an activity, the amount of the resource used per
unit of the activity must be estimated.
3.
The contribution per unit of each activity to the overall measure of the
performance.
2b)Cost benefit tradeoff problems are linear programming problems where the mix of
levels of various activities is chosen to achieve minimum acceptable levels for various
benefits at a minimum cost. The identifying feature is that each functional constraint is a
benefit constraint, which has the form for one of the benefits.
Cost benefit tradeoff formulation enables management to specify minimum goals for the
benefits that need to be achieved by the activities.
these three kinds of data are needed for any cost benefit tradeoff problem
1.
the minimum acceptable level for each benefit (a managerial policy
decision)
2.
for each benefit, the contribution of each activity to that benefit (per unit of
the activity).
3.
the cost per unit of each activity
2c)Mixed problems Each describe a broad category of linear programming problems
like resource allocation in cost benefit tradeoff problems.
2d)Transportation problem is optimizing a shipping plan for transporting goods. It
answers the question on how much should each plant ship to each customer in order to
minimize the total cost.
2e)Assignment problems are our kinds of problems that involve making assignments.
Frequently, these are assignments of people to jobs. Thus many applications of the
assignment problems involve 80 managers in matching up their personnel with tasks to
be performed. Other applications might instead involve assessing machines, vehicles or
plants to task.
3.Formulate a linear programming model from a description of a problem in any of these
categories.
● This is her videos in chapter 9 that shows how to do the model for each type of
the 5.
4.Describe the difference between resource constraints and benefit constraints
including the difference in how they arise.
● Different constraints for each type of linear programming problem
○ Resource Allocation is less than or equal to (<=)
○ Cost benefit trade off is greater than or equal to (>=)
○ Mixed problems are less than or equal to, greater than or equal to, or
equal to. It could be any combination of the two or three aforementioned
constraints (<=,>=, or =)
○ Transportation and assignment problems are equals to (=)
5. Describe fixed-requirement constraints and where they arise.
●
●
●
●
Fixed requirement constraint
LHS = RHS
For some quantity, amount provided = Required amount
Fixed required constraints require that the left-hand side of each such constraint
must exactly equal some fixed amount. Thus, since the left-hand side represents
the amount provided of some quantity the form of a fixed requirement constraint
is amount provided = required amount.
● The identifying feature of a pure fix requirement problem is that it is a linear
programming problem where all its functional constraints are fixed requirements
constraints. The next two sections will describe two particularly parliamentary
types of fixed requirement problems called transportation problems and
assignment problems.
Module 10 — What-If Analysis
Learning Objectives
1. Explain what is meant by “What-if analysis”
It involves addressing some questions about what would happen to the optimal
solution if different assumptions were made about future conditions.
2. Summarize the benefits of what-if analysis
What-if analysis reveals how close each estimate needs to be (in quantities/units)
to avoid obtaining an erroneous optimal solution and therefore pinpoints
sensitive parameters
If conditions change after the study has been completed (very common) what-if
analysis leaves signposts that indicate whether a resulting change in a parameter
of the model changes the optimal solution.
3. Enumerate the different kinds of changes in the model that can be considered by
what-if analysis
4. Describe how the spreadsheet formulation of the problem can be used to perform
any of these kinds of what-if analysis.
5. Use Parameters with Risk Solver platform for Education to systematically
investigate the effect of changing either one or two data cells to various other trial
values
6. Find how much any single coefficient in the objective function can change without
changing the optimal solution
7. Evaluate simultaneous changes in objective function coefficients to determine
whether the changes are small enough that the original optimal solution must still
be optimal.
8. Predict how the value in the objective cell would change if a small change were
to be made in the right-hand side of one of more of the functional constraints
9. Find how much the right hand side of a single functional constraint can change
before this prediction becomes no longer valid.
10. Evaluate simultaneous changes in the right-hand to determine whether the
changes are small enough that this prediction must still be valid
Video Review Summary
● 2/5 module 9 videos, figure out what types they are by:
○ figure out what she's asking: FInd max profit/ exposures, minimum cost,
once max/min is figured out find constraints.
○ Something equal to something, transportation)shipping) problem or
assignment (assigning).
● What type of linear programming problem did you just complete?
● Fill in the blank based off 2nd excel problems
● Objective functions
● Graphing
● Different constraints
○ Resource allocation-less than or equal to
○ Cost of trade off- greater than or equal to
○ Mixed-less greater or equal to
○ Transportation and Assignment are equals
● Story about store and asks about constraints you would use and objective
functions
● What if analysis
○ Understand how to read sensitivity report, if right hand values change
what changes?
How to study: go through excel videos
https://youtu.be/fj8ZYfjcS4k
https://youtu.be/o5iTulrZ5i4
https://youtu.be/STTYxT6iFio
Chapter 10 Textbook Notes
o If the optimal solution will remain the same over a wide range of values for a
particular coefficient in the objective function, then management will be content
with a fairly rough estimate for this coefficient
o If even a small error would change the optimal solution, then management will
want to take special care to refine this estimate
Benefits of What-If Analysis:
1.
Reveals how close each of the estimates need to be to avoid an
erroneous solution and pinpoints the “sensitive parameters” (when a small
change in value changes optimal solution)
2.
If conditions change after the study has been completed, what if analysis
leaves signposts that indicate (without having to solve the model again) whether
a resulting change in a parameter of the model changes the optimal solution.
Sensitivity analysis – focuses on individual parameters of the model. It involves
checking how sensitive the optimal solution is to the value of each parameter.
o An analysis can be made proactively about managerial actions that would
result in changes to the model.
o An example: when certain parameters of the model represent
“managerial policy decisions” rather than quantities that are largely outside
of the control of management. (Product Mix Problem – management can
change resource amounts by altering the production levels for old
products. If management can figure out how to make the new products
profit increase and the old products increase while incorporating all of the
plants, they will want to make this change)
3.
When certain parameters of the model represent managerial policy
decisions, what if analysis provides valuable guidance to management regarding
the impact of altering these policy decisions.
o When there is considerable uncertainty about what the actual values of
the model parameters will turn out to be, management might want to
identify a solution that is virtually guaranteed to be both feasible and
nearly optimal for all plausible combinations of the actual values of these
parameters.
Allowable Range for a unit profit indicates how far its estimate can be off without
affecting the optimal product mix
Q1: What happens if the estimate of the unit profit of one of Wyndor’s new products is
inaccurate?
Make the change and run the solver again. If the optimal solution (units produced) does
not change, it is not known to be sensitive.
Parameter Cell – a data cell containing a parameter that will be systematically varied
when generating a parameter analysis report (used to show the results in the changing
cells and/or objective cell for various trial values in the parameter cell).
The Effect of Simultaneous changes
o What would happen if the Wyndor doors estimate was too low and the
window estimate was too high?
o The 100% Rule – if simultaneous changes are made in the coefficients
of the objective function, calculate for each change the percentage of the
allowable change (increase or decrease) for that coefficient to remain
within its allowable range. If the sum of the percentage changes does not
exceed 100%, the original optimal solution will still be optimal. If it does
exceed 100% then we cannot be sure.
§ Can be used to determine just how large the changes in the
objective function coefficients need to be before the original optimal
solution may no longer be optimal
§ When model has large # of decision variables, it may be
impractical to use the spreadsheet approach to systematically try
out a variety of simultaneous changes in many or all coefficients b/c
of the huge number of representative possibilities. Parameter
analysis can only be used for at most 2 changes. 100% rule
immediately indicates how much each coefficient can safely be
changed without invalidating the current optimal solution
§ After the study, if conditions change in the future that cause
some or all the objective functions to change, the 100% rule quickly
indicates whether the original optimal solution must remain optimal.
Ch 10 video notes
❖ SENSITIVE PARAMETERS- Parameters where extra care is needed to refine
their estimates because even small changes in their values can change the
optimal solution
❖ SENSITIVITY ANALYSIS- Checking how sensitive the optimal solution is to the
value of each parameter. How sensitive blue cells are to see how they’d change
yellow cells
What if analysis
❖ 3 benefits of what if analysis
➢ Pinpoints the sensitive parameters
➢ Leaves sign posts to indicate if changing a parameter will change
the optimal solution
➢ When parameters represent managerial decisions what if analysis
offers guidance regarding the impact of altering the decisions
Allowable range- the range a parameter can be within without changing the optimal
solution. (how much blue cells can change for yellow to change)
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