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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

Chapter 7

Network Flow Models


Shortest route problem
Shortest Route Problem

  • Given distances between nodes, find the shortest route between any pair of nodes.


Example p 282 291
Example: p.282 (291)


Solution methods
Solution Methods

  • Dijkstra algorithm:

    • Introduced in book.

    • Not required for this course

  • Using QM:

    • Required for this course

    • Data input format -


Discussion
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.)


Minimal spanning tree problem
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:


Example p 290 299
Example: p.290 (299)

Solution Method: Using QM.


Shortest route vs minimal spanning
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.


Maximal flow problem
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:


Example p 294 303
Example: p.294 (303)

Solution Method: Using QM.


Network flow problem solving
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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