chapter9 (1)

# chapter9 (1) - Network Optimization Models IE 220 Spring...

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Network Optimization Models IE 220 – Spring 2011 – Prof. Katya Scheinberg Chapter 9

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Chapter 9: Network Optimization Models Outline Outline Introduction (Section 9.1) Terminology of Networks (Section 9.2) The Shortest Path Problem (Section 9.3) The Minimum Spanning Tree Problem (Section 9.4) The Maximum Flow Problem (Section 9.5) The Minimum-Cost Flow Problem (Section 9.6) Chapter 9: Network Optimization Models 2
Chapter 9: Network Optimization Models Introduction (Section 9.1) Outline Introduction (Section 9.1) Terminology of Networks (Section 9.2) The Shortest Path Problem (Section 9.3) The Minimum Spanning Tree Problem (Section 9.4) The Maximum Flow Problem (Section 9.5) The Minimum-Cost Flow Problem (Section 9.6) Chapter 9: Network Optimization Models 3

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Chapter 9: Network Optimization Models Introduction (Section 9.1) Seervada Park Example Map of roads in Seervada Park : O A B C E D T 2 5 4 7 2 4 3 4 1 1 5 7 I O is the origin (entrance to the park). I T is a “scenic wonder.” I Other circles are spots where roads meet. I Numbers give distance (in miles) between intersections. Chapter 9: Network Optimization Models 4
Chapter 9: Network Optimization Models Introduction (Section 9.1) Problems to Address The park operates trams that run from O to T . Park management wants to answer the following questions: 1. What is the shortest route from O to T ? Chapter 9: Network Optimization Models 5

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Chapter 9: Network Optimization Models Introduction (Section 9.1) Problems to Address The park operates trams that run from O to T . Park management wants to answer the following questions: 1. What is the shortest route from O to T ? 2. The park wants to lay telephone cables so that all intersections have an emergency phone. All intersections must be connected to the network. The cost to lay cable is proportional to the distance. What is the cheapest network? Chapter 9: Network Optimization Models 5
Chapter 9: Network Optimization Models Introduction (Section 9.1) Problems to Address The park operates trams that run from O to T . Park management wants to answer the following questions: 1. What is the shortest route from O to T ? 2. The park wants to lay telephone cables so that all intersections have an emergency phone. All intersections must be connected to the network. The cost to lay cable is proportional to the distance. What is the cheapest network? 3. Suppose the park imposes a maximum limit on the number of tram rides that can traverse each road per day. What is the maximum number of tram rides that can be operated per day? Chapter 9: Network Optimization Models 5

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Chapter 9: Network Optimization Models Introduction (Section 9.1) Network Models I These are all examples of network models . I The map itself is called a network . I Network models arise in lots of applications. I They often have properties that allow us to solve them eﬃciently.
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chapter9 (1) - Network Optimization Models IE 220 Spring...

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