Deck 14: Multicriteria Decisions

Question 1

There can only be one goal at each priority level.

Answer 1

False

Question 2

Goal programming with preemptive priorities never permits trade-offs between

A)goals with the same priority level and the same weights.
B)goals with different priority levels.
C)goals with the same priority level and different weights.
D)any goals.

Answer 2

B

Question 3

Computing the consistency ratio for a criterion's pair-wise comparison matrix is the next step after

A)developing the criterion's pair-wise comparison matrix.
B)converting the criterion's pair-wise comparison matrix to a normalized matrix.
C)developing the criterion's priority vector.
D)developing the overall priority vector.

Answer 3

C

Question 4

When using a linear programming approach to solving a goal programming problem, a linear program must be solved for each

A)goal.
B)pair of deviation variables.
C)priority level.
D)pair-wise comparison.

Question 5

Inconsistency in the pair-wise judgments is indicated by a consistency ratio that is

A)less than zero
B)greater than 0.10
C)greater than 0.50
D)greater than 1.00

Question 6

A required step in the analytic hierarchy process is to determine

A)the goals to be satisfied.
B)the expected value of the criteria.
C)the relative importance of a set of features based on a criterion.
D)how many hierarchies to use.

Question 7

Target values will never be met precisely in a goal programming problem.

Question 8

The steps of the scoring model include all of the following EXCEPT:

A)list the decision-making criteria and assign a weight to each.
B)develop a pair-wise comparison matrix for each criterion.
C)rate how well each decision alternative satisfies each criterion.
D)compute the total score for each decision alternative.

Question 9

Pair-wise comparisons are used to

A)compare criteria in terms of the overall goal.
B)compare choices on each criterion.
C)both a and b are true.
D)neither a nor b is true.

Question 10

Goal equations consist of a function that defines goal achievement and deviation variables that measure the distance from the target.

Question 11

The variable d^- measures

A)the amount over the target and is similar to a slack.
B)the amount under the target and is similar to a slack.
C)the amount over the target and is similar to a surplus.
D)the amount under the target and is similar to a surplus.

Question 12

A decision with more than one objective

A)cannot have an optimal solution.
B)requires the decision maker to place the objectives in some order of importance.
C)depends on the probability of satisfying each objective.
D)should be decomposed into a separate model for each objective.

Question 13

The overall priorities for decision alternatives

A)are the sum of the products of the criterion priority times the priority of the decision alternative with respect to that criterion.
B)sum to 1.
C)indicate what choice is preferred, but do not force that choice to be made.
D)each of the above is true.

Question 14

To solve a goal programming problem with preemptive priorities, successive linear programming programs, with an adjustment to the objective function and an additional constraint, must be solved.

Question 15

The constraint 5x₁ + 3x₂ $\le$ 150 is modified to become a goal equation, and priority one is to avoid overutilization. Which of the following is appropriate?

A)Min P₁d₁^- ; 5x₁ + 3x₂ + d₁^--d₁⁺ = 150
B)Min P₁d₁⁺ ; 5x₁ + 3x₂ + d₁^- -d₁⁺ = 150
C)Min P₁d₁⁺ ; 5x₁ + 3x₂ + d₁⁺ = 150
D)Min P₁d₁⁺ ; 5x₁ + 3x₂ -d₁⁺ = 150

Question 16

Preemptive priorities in goal programming

A)show the target values for the problem.
B)prevent sacrifice of a goal to satisfy a lower level one.
C)force the problem to be a standard linear program.
D)limit deviations to d^- only.

Question 17

Deviation variables that occur in the objective function indicate

A)the targets.
B)the priorities.
C)only the areas that are of concern.
D)the difference between all actual and target values.

Question 18

Variables that indicate the distance a target is from the level achieved are called

A)goal variables.
B)target variables.
C)deviation variables.
D)preemptive variables.

Question 19

The goal programming problem with the objective function min P₁(d₁⁺) +P₂(d₂^-) is initially solved by the computer and the objective function value is 0. What constraint should be added for the second problem?

A)d₁⁺ = 0
B)d₁⁺ + d₂^- = 0
C)-d₁⁺ + d₂^- = 0
D)d₁⁺ $\le$ 0

Question 20

Objectives in multicriteria problems seldom conflict.

Question 21

A problem involving only one priority level is not considered a goal programming problem.

Question 22

Explain the difference between hard and soft constraints in a goal programming problem.

Question 23

Explain why goal programming could be a good approach to use after a linear programming problem is found to be infeasible.

Question 24

The goal programming approach can be used when an analyst is confronted with an infeasible solution to an ordinary linear program.

Question 25

How can you be sure your rankings in AHP are consistent?

Question 26

The goal programming problem below was solved with the Management Scientist.
Min
P₁(d₁^-) + P₂(d₂⁺) + P₃(d₃^-)
s.t.
72x₁ + 38x₂ + 23x₃ - 20,000
.72x₁ -.76x₂ - .23x₃ + d₁^- - d₁⁺ = 0
x₃ + d₂^- - d₂⁺ = 150
38x₂ + d₃^- -d₃⁺ = 2000
x₁, x₂, x₃, d₁^-, d ₁⁺, d₂^-, d₂⁺, d₃^-, d₃⁺ $\ge$ 0
Partial output from three successive linear programming problems is given. For each problem, give the original objective function expression and its value, and list any constraints needed beyond those that were in the original problem. $$\begin{array}{l}\text { a. Objective Function Value } = 0.000\\\begin{array} { l c c } \text { Variable } & \text { Value } & \text { Reduced Cost } \\\text { D1MINUS } & 0.000 & 1.000 \\\text { X1 } & 52.632 & 0.000 \\\text { X2 } & 0.000 & 0.000 \\\text { X3 } & 150.000 & 0.000 \\\text { D1PLUS } & 3.395 & 0.000 \\\text { D2MINUS } & 0.000 & 0.000 \\\text { D2PLUS } & 0.000 & 0.000 \\\text { D3MINUS } & 0.000 & 0.000 \\\text { D3PLUS } & 0.000 & 0.000\end{array}\end{array}$$ $$\begin{array}{l}\text { b. Objective Function Value } = 0.000\\\begin{array} { l c c } \text { Variable } & \text { Value } & \text { Reduced Cost } \\\text { D2PLUS } & 0.000 & 1.000 \\\text { X1 } & 52.632 & 0.000 \\\text { X2 } & 0.000 & 0.000 \\\text { X3 } & 150.000 & 0.000 \\\text { D1MINUS } & 0.000 & 0.000 \\\text { D1PLUS } & 3.395 & 0.000 \\\text { D2MINUS } & 0.000 & 0.000 \\\text { D3MINUS } & 0.000 & 0.000 \\\text { D3PLUS } & 0.000 & 0.000\end{array}\end{array}$$ $$\begin{array}{l}\text { c. Objective Function Value } = 0.000\\\begin{array} { l c c } \text { Variable } & \text { Value } & \text { Reduced Cost } \\\text { D3MINUS } & 0.000 & 1.000 \\\text { X1 } & 52.632 & 0.000 \\\text { X2 } & 0.000 & 0.000 \\\text { X3 } & 150.000 & 0.000 \\\text { D1MINUS } & 0.000 & 0.000 \\\text { D1PLUS } & 3.395 & 0.000 \\\text { D2MINUS } & 0.000 & 0.000 \\\text { D2PLUS } & 0.000 & 0.000 \\\text { D3PLUS } & 0.000 & 0.000\end{array}\end{array}$$

Question 27

The Lofton Company has developed the following linear programming problem but finds it is infeasible. In revision, Lofton drops the original objective and establishes the three goals
Goal 1:
Don't exceed 10 in constraint 1.
Goal 2:
Don't fall short of 36 in constraint 3.
Goal 3:
Don't exceed 24 in constraint 2.
Give the goal programming model and solve it graphically.

Question 28

If airline A is moderately preferred to airline B, at a value of 3, then airline B is compared to airline A at a value of -3.

Question 29

One limitation of a scoring model is that it uses arbitrary weights that do not necessarily reflect the preferences of the individual decision maker.

Question 30

As treasurer of the school PTA, you chair the committee to decide how the $20,000 raised by candy sales will be spent. Four kinds of projects have been proposed, and facts on each are shown below. $$\begin{array} { l c c c } { \text { Froject } } & \begin{array} { c } \text { Number } \\\text { Requested }\end{array} & \text { Unit Cost } & \begin{array} { c } \text { Volunteers Needed } \\\text { (Person-days, each) }\end{array} \\\hline \text { Basketball goals } & 12 & \$ 400 & 2 \\\text { Encyclopedia sets } & 5 & 750 & 0 \\\text { Field trips } & 6 & 300 & 3 \\\text { Computer Stations } & 20 & 800 & .5\end{array}$$ Develop a goal programming model that would represent these goals and priorities. $\begin{array} { lll } \text {Friority 1 }\\ \text {Goal 1 }& \text {Spend the entire \( \$ 20,000 \). }\\ \text {Goal 2 }& \text {Do not use more than 50 person-days of volunteer time }\\ \text { Friority 2}\\ \text {Goal 3 }& \text { Frovide at least as many encyclopedias and computers as requested.}\\ \text {Goal 4 }& \text { Frovide at least as many field trips as requested.}\\ \text {Goal 5 }& \text {Do not provide any more basketball goals than }\\\end{array}$

Question 31

Why are multicriteria problems of special interest to quantitative analysts?

Question 32

An ATM is to be located in a campus union building so that it minimizes the distance from the food court, the gift shop, and the theater. They are located at coordinates (2,2), (0,6) and (8,0). Develop a goal programming model to use to locate the best place for the ATM.

Question 33

Solve the following problem graphically:

Question 34

For a scoring model, the decision maker evaluates each decision alternative using equally weighted criteria.

Question 35

A consistency ratio greater than 0.10 indicates inconsistency in the pair-wise comparisons.

Question 36

If a problem has multiple goals at different priority levels, then usually they can all be achieved.

Question 37

The priority matrix shows the priority for each item on each criterion.

Question 38

Should the decision maker always accept the alternatives with the highest AHP rating? Explain.

Question 39

An item's priority reveals how it compares to its competitors on a specific criterion.

Question 40

Calculating the priority of each criterion in terms of its contribution to the overall goal is known as developing the hierarchy.

Question 41

A consumer group is using AHP to compare four used car models. Part of the pair-wise comparison matrix for "repair frequency" is shown below.
a.Complete the matrix.
b.Does it seem to be consistent?

Question 42

Rosie's Ribs is in need of an office management software package. After considerable research, Rosie has narrowed her choice to one of three packages: N-able, VersaSuite, and SoftTrack. She has determined her decision-making criteria, assigned a weight to each criterion, and rated how well each alternative satisfies each criterion. Using a scoring model, determine the recommended software package for Rosie's.

Question 43

Like many high school seniors, Anne has several universities to consider when making her final college choice. To assist in her decision, she has decided to use AHP to develop a ranking for school R, school P, and school M. The schools will be evaluated on five criteria, and Anne's pair-wise comparison matrix for the criteria is shown below. The universities' pair-wise comparisons on the criteria are shown below.
a.What is the overall ranking of the five criteria?
b.What is the overall ranking of the three universities?

Question 44

In an AHP problem, the priorities for three criteria are The priority matrix is Compute the overall priority for each choice.

Question 45

A computer company looking for a new location for a plant has determined three criteria to use to rate cities. Pair-wise comparisons are given. Determine priorities for the three relative to the overall location goal.