# 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
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
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
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
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) -∞
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 = ∞
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
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
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
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
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...