Introduction to
Management Science
with Spreadsheets
Stevenson and Ozgur
First Edition
Part 2 Deterministic Decision Models
Chapter 8
Network Optimization
Models
McGraw-Hill/Irwin
Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved.
Networks
• Network
–A set of nodes and connecting arcs or branches. Can
be useful in representing various systems, such as
distribution systems, production systems, and
transportation systems.
• Network models are an important approach for
problem solving because:
–They can be used to model a wide range of problems.
–They are relatively simple to work with
–They provide a visual portrayal of a problem.
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McGraw-Hill/Irwin 8–2
Frequently Used Algorithms
• Shortest-Route Algorithm
–Used for determining the shortest time, distance, or
cost from an origin to a destination through a network.
• Minimum Spanning Tree Algorithm
–Used in determining the minimum distance (cost, time)
needed to connect a set of locations into a single
system.
• Maximal Flow Algorithm
–Used for determining the greatest amount of flow that
can be transmitted through a system in which various
branches, or connections, have specified flow capacity
limitations.
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McGraw-Hill/Irwin 8–3
Figure 8–1
A Simple Network Diagram
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McGraw-Hill/Irwin 8–4
Example 8-1
Labeling Procedure
A label is developed for each node. The labels
consist of two numbers separated by a comma:
The first number refers to the distance from Node
1 to the labeled node along a certain path, while
the second number refers to the node that
immediately precedes this node along that path.
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McGraw-Hill/Irwin 8–5
Example 8-1 (cont’d)
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McGraw-Hill/Irwin 8–6
Example 8-1 (cont’d)
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McGraw-Hill/Irwin 8–7
Figure 8–2
Network for Tri-State Shipping Company Shortest-Route
Problem
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McGraw-Hill/Irwin 8–8
Figure 8–3
Network for Oil Pipeline Problem
Note: Arc lengths are not precisely proportional to the distances shown on the arcs.
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McGraw-Hill/Irwin 8–9
Example 8-3
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McGraw-Hill/Irwin 8–10
Example 8-3 (cont’d)
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McGraw-Hill/Irwin 8–11
Example 8-3 (cont’d)
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Figure 8–4
A Flow Network
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Figure 8–5
Updated Flow Network
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Figure 8–6
Second Revision of the Network
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Figure 8–7
Third Revision of Flow Network
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Figure 8–8
Final Solution for Flow Network Example
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Figure 8–9
Flow Network for Demonstration of Reverse Flow
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Figure 8–10
Flow Network for Demonstration of Reverse Flow
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Figure 8–11
Revised Flow Network
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Table 8–1
Branches of the Network and Flow Capacities of the Branches
for the Turkmen Oil Ltd. Maximal Flow Problem
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Figure 8–12
Network Diagram for the Maximal Flow Problem for Turkmen
Oil Ltd.
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McGraw-Hill/Irwin 8–22