Deck 14: Multicriteria Decisions

Question 1

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.

Answer 1

B

Question 2

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

Answer 2

False

Question 3

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.

Answer 3

C

Question 4

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 5

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

Question 6

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

Question 7

AHP allows a decision maker to express personal preferences about the various aspects of a multicriteria problem.

Question 8

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

Question 9

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

Question 10

Objectives in multicriteria problems seldom conflict.

Question 11

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 12

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

Question 13

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

Question 14

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

Question 15

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

Question 16

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 17

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 18

There can only be one goal at each priority level.

Question 19

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 20

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

Question 21

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.

Question 22

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 23

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 24

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.

Question 25

Solve the following problem graphically:
Min
P₁(d₁⁺) + P₂(d₂−)
s.t.
3x₁ + 5x₂ ≤ 45
3x₁ + 2x₂ − d₁⁺ + d₁− = 24
x₁ + x₂ − d₂⁺ + d₂− = 10
x₁, x₂, d₁−, d₁⁺, d₂−, d₂⁺ ≥ 0

Question 26

The constraint 5x₁ + 3x₂ ≤ 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 27

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 28

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⁺ ≤ 0

Question 29

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 30

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.

Question 31

Durham Designs manufactures home furnishings for department stores. Planning is underway for the production of items in the "Wildflower" fabric pattern during the next production period. ​
Inventory of the Wildflower fabric is 3000 yards. Five hundred hours of production time have been scheduled. Four hundred units of packaging material are available. Each of these values can be adjusted through overtime or extra purchases.
Durham would like to achieve a profit of $3200, avoid purchasing more fabric or packaging material, and use all of the hours scheduled. Give the goal programming model.

Question 32

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. ​
Develop a goal programming model that would represent these goals and priorities.
Priority 1
Goal 1
Spend the entire $20,000.
Goal 2
Do not use more than 50 person-days of volunteer time
Priority 2
Goal 3
Provide at least as many encyclopedias and computers as requested.
Goal 4
Provide at least as many field trips as requested.
Goal 5
Do not provide any more basketball goals than requested.

Question 33

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 34

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 35

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 36

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 37

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 38

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⁺ ≥ 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. ​ ​

Question 39

The Lofton Company has developed the following linear programming problem
Max
x₁ + x₂
s.t.
2x₁ + x₂ ≤ 10
2x₁ + 3x₂ ≤ 24
3x₁ + 4x₂ ≥ 36
​
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 40

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 41

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

Question 42

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

Question 43

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

Question 44

In an AHP problem, the priorities for three criteria are
Criterion 1
.1722
Criterion 2
.1901
Criterion 3
.6377
​
The priority matrix is ​
Compute the overall priority for each choice.

Question 45

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 46

John Harris is interested in purchasing a new Harley-Davidson motorcycle. He has narrowed his choice to one of three models: Sportster Classic, Heritage Softtail, and Electra Glide. After much consideration, John has determined his decision-making criteria, assigned a weight to each criterion, and rated how well each decision alternative satisfies each criterion. Using a scoring model, determine the recommended motorcycle model for John.

Question 47

​Why are multicriteria problems of special interest to quantitative analysts?

Question 48

The campaign headquarters of Jerry Black, a candidate for the Board of Supervisors, has 100 volunteers. With one week to go in the election, there are three major strategies remaining: media advertising, door-to-door canvassing, and telephone campaigning. It is estimated that each phone call will take approximately four minutes and each door-to-door personal contact will average seven minutes. These times include time between contacts for breaks, transportation, dialing, etc. Volunteers who work on advertising will not be able to handle any other duties. Each ad will utilize the talents of three workers for the entire week.
Volunteers are expected to work 12 hours per day during the final seven days of the campaign. At a minimum, Jerry Black feels he needs 30,000 phone contacts, 20,000 personal contacts, and three advertisements during the last week. However, he would like to see 50,000 phone contacts and 50,000 personal contacts made and five advertisements developed. It is felt that advertising is 50 times as important as personal contacts, which in turn is twice as important as phone contacts.
Formulate this goal programming problem with a single weighted priority to determine how the work should be distributed during the final week of the campaign.

Question 49

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

Question 50

​Explain the structure of a hierarchy diagram used in the analytic hierarchy process as a graphical representation of
the problem.