Network Flow Models

1
Chapter 7

• Network Flow Models

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Shortest Route Problem

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

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Example p.282 (291)
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Solution Methods

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

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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.)

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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.

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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.

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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.

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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.