Question 1

In the LP formulation of a maximal flow problem, a conservation-of-flow constraint ensures that an arc's flow capacity is not exceeded.

Accepted Answer

A) True 
 B)False  False

Question 2

If a transportation problem has four origins and five destinations, the LP formulation of the problem will have nine constraints.

Accepted Answer

A) True 
 B)False  True

Question 3

Consider a shortest route problem in which a bank courier must travel between branches and the main operations center.When represented with a network,

Accepted Answer

A) the branches are the arcs and the operations center is the node. 
B) the branches are the nodes and the operations center is the source. 
C) the branches and the operations center are all nodes and the streets are the arcs. 
D) the branches are the network and the operations center is the node. 
A) the branches are the arcs and the operations center is the node. 
B) the branches are the nodes and the operations center is the source. 
C) the branches and the operations center are all nodes and the streets are the arcs. 
D) the branches are the network and the operations center is the node. C

Question 4

Constraints in a transshipment problem

Accepted Answer

A) correspond to arcs. 
B) include a variable for every arc. 
C) require the sum of the shipments out of an origin node to equal supply. 
D) All of the alternatives are correct. 
A) correspond to arcs. 
B) include a variable for every arc. 
C) require the sum of the shipments out of an origin node to equal supply. 
D) All of the alternatives are correct.

Question 5

The number of units shipped from origin i to destination j is represented by

Accepted Answer

A) xij. 
B) xji. 
C) cij. 
D) cji. 
A) xij. 
B) xji. 
C) cij. 
D) cji.

Question 6

Transshipment problem allows shipments both in and out of some nodes while transportation problems do not.

Accepted Answer

A) True 
 B)False

Question 7

The parts of a network that represent the origins are

Accepted Answer

A) the capacities 
B) the flows 
C) the nodes 
D) the arcs 
A) the capacities 
B) the flows 
C) the nodes 
D) the arcs

Question 8

The assignment problem constraint x31 + x32 + x33 + x34 < 2 means

Accepted Answer

A) agent 3 can be assigned to 2 tasks. 
B) agent 2 can be assigned to 3 tasks. 
C) a mixture of agents 1, 2, 3, and 4 will be assigned to tasks. 
D) there is no feasible solution. 
A) agent 3 can be assigned to 2 tasks. 
B) agent 2 can be assigned to 3 tasks. 
C) a mixture of agents 1, 2, 3, and 4 will be assigned to tasks. 
D) there is no feasible solution.

Question 9

A transportation problem with 3 sources and 4 destinations will have 7 decision variables.

Accepted Answer

A) True 
 B)False

Question 10

The objective of the transportation problem is to

Accepted Answer

A) identify one origin that can satisfy total demand at the destinations and at the same time minimize total shipping cost. 
B) minimize the number of origins used to satisfy total demand at the destinations. 
C) minimize the number of shipments necessary to satisfy total demand at the destinations. 
D) minimize the cost of shipping products from several origins to several destinations. 
A) identify one origin that can satisfy total demand at the destinations and at the same time minimize total shipping cost. 
B) minimize the number of origins used to satisfy total demand at the destinations. 
C) minimize the number of shipments necessary to satisfy total demand at the destinations. 
D) minimize the cost of shipping products from several origins to several destinations.

Question 11

The problem which deals with the distribution of goods from several sources to several destinations is the

Accepted Answer

A) maximal flow problem 
B) transportation problem 
C) assignment problem 
D) shortest-route problem 
A) maximal flow problem 
B) transportation problem 
C) assignment problem 
D) shortest-route problem

Question 12

A dummy origin in a transportation problem is used when supply exceeds demand.

Accepted Answer

A) True 
 B)False

Question 13

Arcs in a transshipment problem

Accepted Answer

A) must connect every node to a transshipment node. 
B) represent the cost of shipments. 
C) indicate the direction of the flow. 
D) All of the alternatives are correct. 
A) must connect every node to a transshipment node. 
B) represent the cost of shipments. 
C) indicate the direction of the flow. 
D) All of the alternatives are correct.

Question 14

Converting a transportation problem LP from cost minimization to profit maximization requires only changing the objective function; the conversion does not affect the constraints.

Accepted Answer

A) True 
 B)False

Question 15

Which of the following is not true regarding the linear programming formulation of a transportation problem?

Accepted Answer

A) Costs appear only in the objective function. 
B) The number of variables is (number of origins) x (number of destinations). 
C) The number of constraints is (number of origins) x (number of destinations). 
D) The constraints' left-hand side coefficients are either 0 or 1. 
A) Costs appear only in the objective function. 
B) The number of variables is (number of origins) x (number of destinations). 
C) The number of constraints is (number of origins) x (number of destinations). 
D) The constraints' left-hand side coefficients are either 0 or 1.

Question 16

Consider a maximal flow problem in which vehicle traffic entering a city is routed among several routes before eventually leaving the city.When represented with a network,

Accepted Answer

A) the nodes represent stoplights. 
B) the arcs represent one way streets. 
C) the nodes represent locations where speed limits change. 
D) None of the alternatives is correct. 
A) the nodes represent stoplights. 
B) the arcs represent one way streets. 
C) the nodes represent locations where speed limits change. 
D) None of the alternatives is correct.

Question 17

Which of the following is not true regarding an LP model of the assignment problem?

Accepted Answer

A) Costs appear in the objective function only. 
B) All constraints are of the > form. 
C) All constraint left-hand side coefficient values are 1. 
D) All decision variable values are either 0 or 1. 
A) Costs appear in the objective function only. 
B) All constraints are of the > form. 
C) All constraint left-hand side coefficient values are 1. 
D) All decision variable values are either 0 or 1.

Question 18

In the general linear programming model of the assignment problem,

Accepted Answer

A) one agent can do parts of several tasks. 
B) one task can be done by several agents. 
C) each agent is assigned to its own best task. 
D) one agent is assigned to one and only one task. 
A) one agent can do parts of several tasks. 
B) one task can be done by several agents. 
C) each agent is assigned to its own best task. 
D) one agent is assigned to one and only one task.

Question 19

The assignment problem is a special case of the

Accepted Answer

A) transportation problem. 
B) transshipment problem. 
C) maximal flow problem. 
D) shortest-route problem. 
A) transportation problem. 
B) transshipment problem. 
C) maximal flow problem. 
D) shortest-route problem.

Question 20

The shortest-route problem is a special case of the transshipment problem.

Accepted Answer

A) True 
 B)False

Exam 6: Distribution and Network Problems

In the LP formulation of a maximal flow problem, a conservation-of-flow constraint ensures that an arc's flow capacity is not exceeded.

If a transportation problem has four origins and five destinations, the LP formulation of the problem will have nine constraints.

Consider a shortest route problem in which a bank courier must travel between branches and the main operations center.When represented with a network,

Constraints in a transshipment problem

The number of units shipped from origin i to destination j is represented by

Transshipment problem allows shipments both in and out of some nodes while transportation problems do not.

The parts of a network that represent the origins are

The assignment problem constraint x31 + x32 + x33 + x34 < 2 means

A transportation problem with 3 sources and 4 destinations will have 7 decision variables.

The objective of the transportation problem is to

The problem which deals with the distribution of goods from several sources to several destinations is the

A dummy origin in a transportation problem is used when supply exceeds demand.

Arcs in a transshipment problem

Converting a transportation problem LP from cost minimization to profit maximization requires only changing the objective function; the conversion does not affect the constraints.

Which of the following is not true regarding the linear programming formulation of a transportation problem?

Consider a maximal flow problem in which vehicle traffic entering a city is routed among several routes before eventually leaving the city.When represented with a network,

Which of the following is not true regarding an LP model of the assignment problem?

In the general linear programming model of the assignment problem,

The assignment problem is a special case of the

The shortest-route problem is a special case of the transshipment problem.

Introduction

Introduction to Linear Programming

LP Sensitivity Analysis and Interpretation of Solution

Linear Programming Applications

Advanced Linear Programming Applications

Integer Linear Programming

Nonlinear Optimization Models

Project Scheduling: Pertcpm

Inventory Models

Waiting Line Models

Simulation

Decision Analysis

Multicriteria Decisions

Forecasting

Markov Processes

LP: Simplex Method

Simplex-Based Sensitivity Analysis and Duality

Solution Procedures for Transportation and Assignment Problems

Minimal Spanning Tree

Dynamic Programming

Filters

The assignment problem constraint x₃₁ + x₃₂ + x₃₃ + x₃₄ < 2 means