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Chapter 7

Chapter 7. Network Flow Models. Shortest Route Problem. Given distances between nodes, find the shortest route between any pair of nodes. Example: p.282 (291). Solution Methods. Dijkstra algorithm: Introduced in book. Not required for this course Using QM: Required for this course

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Chapter 7

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  1. Chapter 7 Network Flow Models

  2. Shortest Route Problem • Given distances between nodes, find the shortest route between any pair of nodes.

  3. Example: p.282 (291)

  4. Solution Methods • Dijkstra algorithm: • Introduced in book. • Not required for this course • Using QM: • Required for this course • Data input format -

  5. Discussion • What if the ‘cost’, instead of ‘distance’, between two nodes are given, and we want to find the ‘lowest-cost route’ from a starting node to a destination node? • What if the cost from a to b is different from the cost from b to a? (QM does not handle this situation.)

  6. Minimal Spanning Tree Problem • Given costs (distances) between nodes, find a network (actually a “tree”) that covers all the nodes with minimum total cost. • Applications:

  7. Example: p.290 (299) Solution Method: Using QM.

  8. Shortest Route vs. Minimal Spanning • The minimal spanning tree problem is to identify a set of connected arcs that cover all nodes. • The shortest route problem is to identify a route from a particular node to another, which typically does not pass through every node.

  9. Maximal Flow Problem • Given flow-capacities between nodes, find the maximum amount of flows that can go from the origin node to the destination node through the network. • Applications:

  10. Example: p.294 (303) Solution Method: Using QM.

  11. Network Flow Problem Solving • Given a problem, we need to tell what ‘problem’ it is (shortest route, minimal spanning tree, or maximal flow); then use the corresponding module in QM to solve it.

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