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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.
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.