Deck 14: Multicriteria Decisions

Question 1

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

Answer 1

B

Question 2

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.

Answer 2

C

Question 3

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.

Answer 3

B

Question 4

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 5

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 6

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

Question 7

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 8

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 9

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 10

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 11

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 12

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 13

Objectives in multicriteria problems seldom conflict.

Question 14

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

Question 15

There can only be one goal at each priority level.

Question 16

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 17

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 18

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 19

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 20

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 21

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

Question 22

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

Question 23

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 24

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 25

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 26

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

Question 27

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

Question 28

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 29

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 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.
Develop a goal programming model that would represent these goals and priorities.

Question 31

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 32

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

Question 33

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

Question 34

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
Give the goal programming model and solve it graphically.

Question 35

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

Question 36

Solve the following problem graphically:

Question 37

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 38

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

Question 39

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