Question 1

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

Accepted Answer

A) True 
 B)False  False

Question 2

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.   ​   ​

Accepted Answer

a.Min d1minus, Z = 0
B.Min d2plus, Z = 0, the constraint d1minus = 0 was includeD.C.Min d3minus, Z = 0, the constraint d2plus = 0 was included.

Question 3

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.

Accepted Answer

Let
x₁ = the first coordinate of the ATM
x₂ = the second coordinate of the ATM
Min
Σ (d_i⁺ + d_i− )s.t.
x₁ + d₁− − d₁⁺ = 2
x₁ + d₂− − d₂⁺ = 2
x₁ + d₃− − d₃⁺ = 0
x₂ + d₄− − d₄⁺ = 6
x₂ + d₅− − d₅⁺ = 8
x₂ + d₆− − d₆⁺ = 0

Question 4

The variable d- measures

Accepted Answer

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. 
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 5

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

Accepted Answer

The hierarchy diagram used in the analyt

Question 6

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

Accepted Answer

A) True 
 B)False

Question 7

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

Accepted Answer

In the Analytic Hierarchy Process (AHP),

Question 8

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

Accepted Answer

A) True 
 B)False

Question 9

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

Accepted Answer

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. 
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 10

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?

Accepted Answer

The spread

Question 11

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

Accepted Answer

A) True 
 B)False

Question 12

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

Accepted Answer

A) True 
 B)False

Question 13

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?

Accepted Answer

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 
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 14

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.

Accepted Answer

Min P₁ d₁⁺ , P₂ d₃− , P₃ d₂⁺ s.t. 2x₁ + x₂ + d₁−

Question 15

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

Accepted Answer

Multicriteria problems are of special in

Question 16

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

Accepted Answer

A) True 
 B)False

Question 17

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

Accepted Answer

A) True 
 B)False

Question 18

Objectives in multicriteria problems seldom conflict.

Accepted Answer

A) True 
 B)False

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?

Accepted Answer

A)  d1+ = 0 
B)  d1+ + d2− = 0 
C)  −d1+ + d2− = 0 
D)  d1+ ≤ 0 
A)  d1+ = 0 
B)  d1+ + d2− = 0 
C)  −d1+ + d2− = 0 
D)  d1+ ≤ 0

Question 20

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

Accepted Answer

The Analytic Hierarchy Process (AHP) is

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

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.

The variable d^- measures

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

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

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

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

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

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

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

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?

Why are multicriteria problems of special interest to quantitative analysts?

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

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

Objectives in multicriteria problems seldom conflict.

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?

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

Introduction

An Introduction to Linear Programming

Linear Programming: Sensitivity Analysis and Interpretation of Solution

Linear Programming Applications in Marketing, Finance, and Operations Management

Advanced Linear Programming Applications

Distribution and Network Models

Integer Linear Programming

Nonlinear Optimization Models

Project Scheduling: Pertcpm

Inventory Models

Waiting Line Models

Simulation

Decision Analysis

Time Series Analysis and Forecasting

Markov Processes

Linear Programming: Simplex Method

Simplex-Based Sensitivity Analysis and Duality

Solution Procedures for Transportation and Assignment Problems

Minimal Spanning Tree

Dynamic Programming

Filters

Exam 14: Multicriteria Decisions

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

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.

The variable d- measures

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

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

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

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

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

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

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

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?

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

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

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

Objectives in multicriteria problems seldom conflict.

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?

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

Introduction

An Introduction to Linear Programming

Linear Programming: Sensitivity Analysis and Interpretation of Solution

Linear Programming Applications in Marketing, Finance, and Operations Management

Advanced Linear Programming Applications

Distribution and Network Models

Integer Linear Programming

Nonlinear Optimization Models

Project Scheduling: Pertcpm

Inventory Models

Waiting Line Models

Simulation

Decision Analysis

Time Series Analysis and Forecasting

Markov Processes

Linear Programming: Simplex Method

Simplex-Based Sensitivity Analysis and Duality

Solution Procedures for Transportation and Assignment Problems

Minimal Spanning Tree

Dynamic Programming

Filters

The variable d^- measures

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

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

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?

Why are multicriteria problems of special interest to quantitative analysts?

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?

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