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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: Using QM: 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:

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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:

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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.

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