Question 1

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

Accepted Answer

A) True 
 B)False  True

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+ $\ge$ 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. $$\begin{array}{l}
\text { a. Objective Function Value } = 0.000\
\begin{array} { l c c } 
\text { Variable } & \text { Value } & \text { Reduced Cost } \
\text { D1MINUS } & 0.000 & 1.000 \
\text { X1 } & 52.632 & 0.000 \
\text { X2 } & 0.000 & 0.000 \
\text { X3 } & 150.000 & 0.000 \
\text { D1PLUS } & 3.395 & 0.000 \
\text { D2MINUS } & 0.000 & 0.000 \
\text { D2PLUS } & 0.000 & 0.000 \
\text { D3MINUS } & 0.000 & 0.000 \
\text { D3PLUS } & 0.000 & 0.000
\end{array}
\end{array}$$ $$\begin{array}{l}
\text { b. Objective Function Value } = 0.000\
\begin{array} { l c c } 
\text { Variable } & \text { Value } & \text { Reduced Cost } \
\text { D2PLUS } & 0.000 & 1.000 \
\text { X1 } & 52.632 & 0.000 \
\text { X2 } & 0.000 & 0.000 \
\text { X3 } & 150.000 & 0.000 \
\text { D1MINUS } & 0.000 & 0.000 \
\text { D1PLUS } & 3.395 & 0.000 \
\text { D2MINUS } & 0.000 & 0.000 \
\text { D3MINUS } & 0.000 & 0.000 \
\text { D3PLUS } & 0.000 & 0.000
\end{array}
\end{array}$$ $$\begin{array}{l}
\text { c. Objective Function Value } = 0.000\
\begin{array} { l c c } 
\text { Variable } & \text { Value } & \text { Reduced Cost } \
\text { D3MINUS } & 0.000 & 1.000 \
\text { X1 } & 52.632 & 0.000 \
\text { X2 } & 0.000 & 0.000 \
\text { X3 } & 150.000 & 0.000 \
\text { D1MINUS } & 0.000 & 0.000 \
\text { D1PLUS } & 3.395 & 0.000 \
\text { D2MINUS } & 0.000 & 0.000 \
\text { D2PLUS } & 0.000 & 0.000 \
\text { D3PLUS } & 0.000 & 0.000
\end{array}
\end{array}$$

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

Objectives in multicriteria problems seldom conflict.

Accepted Answer

A) True 
 B)False  False

Question 4

There can only be one goal at each priority level.

Accepted Answer

A) True 
 B)False

Question 5

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

Accepted Answer

A) True 
 B)False

Question 6

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

Accepted Answer

In the Analytic Hierarchy Process (AHP),

Question 7

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 8

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

Question 9

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 $. }\
 \text {Goal 2 }& \text {Do not use more than 50 person-days of volunteer time }\
 \text { Friority 2}\
 \text {Goal 3 }& \text { Frovide at least as many encyclopedias and computers as requested.}\
 \text {Goal 4 }& \text { Frovide at least as many field trips as requested.}\
 \text {Goal 5 }& \text {Do not provide any more basketball goals than }\
\end{array}$

Accepted Answer

Let
B = number of basketball goals
E = n

Question 10

Pair-wise comparisons are used to

Accepted Answer

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. 
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 11

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

Accepted Answer

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

Question 12

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. $$\begin{array} { l | c | c c c } 
 { \text { Criterion } } & & & { \text { Decision Alternatives } } \
& \text { Weight } & \text { N-Able } & \text { VersaSuite } & \text { Softrack } \
\hline \text { Ease of use } & 4 & 3 & 5 & 8 \
\text { Report generation } & 3 & 8 & 7 & 6 \
\text { Functional integration } & 5 & 5 & 8 & 6 \
\text { On-line help } & 3 & 8 & 6 & 4 \
\text { Entry error-checking } & 2 & 8 & 3 & 4 \
\text { Price } & 4 & 4 & 7 & 5 \
\text { Support cost } & 3 & 6 & 5 & 7
\end{array}$$ Using a scoring model, determine the recommended software package for Rosie's.

Accepted Answer

N-Able = 1

Question 13

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

Accepted Answer

A) True 
 B)False

Question 14

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

Question 15

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

Accepted Answer

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. 
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 16

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 17

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?
 $$\begin{array} { c | c c c c } 
\text { Repair Frequency } & \text { Model A } & \text { Model B } & \text { Model C } & \text { Model D } \
\hline \text { Model A } &1&5&&1/6\
\text { Model B } &1/5&1&&1/2 \
\text { Model C } & 1/4&1/3&1&\
\text { Model D } &&&1/4&1
\end{array}$$

Accepted Answer

The matrix is not co

Question 18

Preemptive priorities in goal programming

Accepted Answer

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. 
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 19

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

Accepted Answer

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

Question 20

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

Accepted Answer

A) True 
 B)False

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

Objectives in multicriteria problems seldom conflict.

There can only be one goal at each priority level.

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

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

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

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

Pair-wise comparisons are used to

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

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

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?

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

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

Preemptive priorities in goal programming

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

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

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 Problems

Integer Linear Programming

Nonlinear Optimization Models

Project Scheduling: Pertcpm

Inventory Models

Waiting Line Models

Simulation

Decision Analysis

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

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

Objectives in multicriteria problems seldom conflict.

There can only be one goal at each priority level.

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

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

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

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

Pair-wise comparisons are used to

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

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

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?

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

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

Preemptive priorities in goal programming

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

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

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 Problems

Integer Linear Programming

Nonlinear Optimization Models

Project Scheduling: Pertcpm

Inventory Models

Waiting Line Models

Simulation

Decision Analysis

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 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?