# Brs Mdm3 Tif Ch05

**Topics:**Flow network, Shortest path problem, Maximum flow problem

**Pages:**15 (1872 words)

**Published:**January 11, 2015

Managerial Decision Modeling w/ Spreadsheets, 3e (Balakrishnan/Render/Stair) Chapter 5 Transportation, Assignment, and Network Models

5.1 Chapter Questions

1) Which of the following is NOT a network flow model?

A) Transportation model

B) Assignment model

C) Product mix model

D) Shortest-path model

E) Minimal-spanning tree model

Answer: C

Page Ref: 162

Topic: Introduction

Difficulty: Easy

2) Which of the following models determines the path through the network that connects all the points? A) Transportation model

B) Assignment model

C) Product mix model

D) Shortest-path model

E) Minimal-spanning tree model

Answer: E

Page Ref: 163

Topic: Introduction

Difficulty: Easy

Use the information below to answer the following questions.

Consider the following maximal flow problem where node 1 is the source and node 6 is the destination.

3) Refer to the figure. What is the objective function?

A) Max X16

B) Min X16

C) Max X61

D) Min X61

E) Max X26 + X56

Answer: C

Page Ref: 209

Topic: Maximal Flow Problem

Difficulty: Easy

4) Refer to the figure. What is the constraint associated with node 6? A) X46 + X56 = 0

B) X46 + X56 = 1

C) X46 + X56 - X61 = 1

D) X46 + X56 - X61 = -1

E) X46 + X56 - X61 = 0

Answer: E

Page Ref: 185

Topic: Maximal Flow Problem

Difficulty: Moderate

5) Refer to the figure. What is the maximum capacity associated with arc X61? A) +1

B) -1

C) 0

D) +∞

E) -∞

Answer: D

Page Ref: 184

Topic: Maximal Flow Model

Difficulty: Moderate

6) Refer to the figure. What is the constraint associated with node 1? A) -X12 - X13 = 1

B) X61 - X12 - X13 = -1

C) X61 - X12 - X13 = 1

D) X61 - X12 - X13 = 0

E) X61 - X12 - X13 = ∞

Answer: D

Page Ref: 184

Topic: Maximal Flow Model

Difficulty: Moderate

7) Refer to the figure. What is the constraint associated with node 2? A) X12 - X24 = 0

B) X12 - X32 - X24 = 0

C) X12 + X32 - X24 = 1

D) X12 - X32 + X24 = 0

E) X12 + X32 - X24 = 0

Answer: E

Page Ref: 184

Topic: Maximal Flow Model

Difficulty: Moderate

8) Which of the following statements concerning the transshipment model are FALSE? A) A supply node is one where the total flow into the node is less than the total flow out of the node. B) A transshipment node is one where the total flow into the node equals the total flow of the node. C) The flow balance for a demand node should show a positive RHS value. D) The flow balance for a transshipment node should show a negative RHS value. E) The flow balance for a supply node should show a negative RHS value. Answer: D

Page Ref: 174

Topic: Transshipment Model

Difficulty: Moderate

Use the information below to answer the following questions.

Consider the following shortest path problem where node 1 is the starting node and node 6 is the destination node.

9) Refer to the figure. What is the constraint associated with node 1? A) X21+ X31 - X12 - X13 = -1

B) X21 + X31 - X12 - X13 = +1

C) + X31- X12 - X13 = 0

D) X12 + X13 = 0

E) -X12 + X13 = -1

Answer: A

Page Ref: 188

Topic: Shortest-Path Model

Difficulty: Moderate

10) Refer to the figure. What is the constraint associated with node 6? A) X64 + X65 - X46 - X56 = +1

B) X64 + X65 - X46 - X56 = 0

C) X46 + X56 - X64 - X65 = +1

D) -X64 - X65 = -1

E) -X46 + X56 = 0

Answer: C

Page Ref: 188

Topic: Shortest-Path Model

Difficulty: Moderate

11) Refer to the figure. Excluding the non-negativity constraint, this model has: A) 6 decision variables

B) 7 decision variables

C) 8 decision variables including the dummy arc

D) 5 decision variables

E) none of the above

Answer: E

Page Ref: 188

Topic: Shortest-Path Model

Difficulty: Challenging

12) What is the constraint associated with job A for the following assignment problem?

Machine

123

A$3$4$2

JobB$1$3$5

C$6$4$2

Let Xij = 1 if job i is assigned to machine j, otherwise 0.

A) 3XA1 + 4XA2 + 2XA3 = 1

B) 3XA1 + 4XA2 + 2XA3 = 0...

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