Chapter 7
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Transcript of 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– Data input format -
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
• 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)
Solution Method: Using QM.
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
• 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)
Solution Method: Using QM.
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.