1. Stevenson and Ozgur First Edition Introduction to Management Science with Spreadsheets McGraw-Hill/Irwin Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved. Chapter 8 Network Optimization Models Part 2 Deterministic Decision Models

2. Copyright © 2007 The McGraw-Hill Companies. All rights reserved. McGraw-Hill/Irwin 8–2 NetworksNetworks 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.

3. Copyright © 2007 The McGraw-Hill Companies. All rights reserved. McGraw-Hill/Irwin 8–3 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.

4. Copyright © 2007 The McGraw-Hill Companies. All rights reserved. McGraw-Hill/Irwin 8–4 Figure 8–1A Simple Network Diagram

5. Copyright © 2007 The McGraw-Hill Companies. All rights reserved. McGraw-Hill/Irwin 8–5 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.

6. Copyright © 2007 The McGraw-Hill Companies. All rights reserved. McGraw-Hill/Irwin 8–6 Example 8-1 (cont’d)

7. Copyright © 2007 The McGraw-Hill Companies. All rights reserved. McGraw-Hill/Irwin 8–7 Example 8-1 (cont’d)

8. Copyright © 2007 The McGraw-Hill Companies. All rights reserved. McGraw-Hill/Irwin 8–8 Figure 8–2Network for Tri-State Shipping Company Shortest-Route Problem

9. Copyright © 2007 The McGraw-Hill Companies. All rights reserved. McGraw-Hill/Irwin 8–9 Figure 8–3Network for Oil Pipeline Problem Note: Arc lengths are not precisely proportional to the distances shown on the arcs.

10. Copyright © 2007 The McGraw-Hill Companies. All rights reserved. McGraw-Hill/Irwin 8–10 Example 8-3

11. Copyright © 2007 The McGraw-Hill Companies. All rights reserved. McGraw-Hill/Irwin 8–11 Example 8-3 (cont’d)

12. Copyright © 2007 The McGraw-Hill Companies. All rights reserved. McGraw-Hill/Irwin 8–12 Example 8-3 (cont’d)

13. Copyright © 2007 The McGraw-Hill Companies. All rights reserved. McGraw-Hill/Irwin 8–13 Figure 8–4A Flow Network

14. Copyright © 2007 The McGraw-Hill Companies. All rights reserved. McGraw-Hill/Irwin 8–14 Figure 8–5Updated Flow Network

15. Copyright © 2007 The McGraw-Hill Companies. All rights reserved. McGraw-Hill/Irwin 8–15 Figure 8–6Second Revision of the Network

16. Copyright © 2007 The McGraw-Hill Companies. All rights reserved. McGraw-Hill/Irwin 8–16 Figure 8–7Third Revision of Flow Network

17. Copyright © 2007 The McGraw-Hill Companies. All rights reserved. McGraw-Hill/Irwin 8–17 Figure 8–8Final Solution for Flow Network Example

18. Copyright © 2007 The McGraw-Hill Companies. All rights reserved. McGraw-Hill/Irwin 8–18 Figure 8–9Flow Network for Demonstration of Reverse Flow

19. Copyright © 2007 The McGraw-Hill Companies. All rights reserved. McGraw-Hill/Irwin 8–19 Figure 8–10Flow Network for Demonstration of Reverse Flow

20. Copyright © 2007 The McGraw-Hill Companies. All rights reserved. McGraw-Hill/Irwin 8–20 Figure 8–11Revised Flow Network

21. Copyright © 2007 The McGraw-Hill Companies. All rights reserved. McGraw-Hill/Irwin 8–21 Table 8–1Branches of the Network and Flow Capacities of the Branches for the Turkmen Oil Ltd. Maximal Flow Problem

22. Copyright © 2007 The McGraw-Hill Companies. All rights reserved. McGraw-Hill/Irwin 8–22 Figure 8–12Network Diagram for the Maximal Flow Problem for Turkmen Oil Ltd.