1. Chapter 7
Network Flow Models

2. Shortest Route Problem
Given distances between nodes, find the shortest route between any pair of nodes.

3. Example: p.282 (291)

4. Solution Methods Dijkstra algorithm: Using QM: Introduced in book.
Not required for this course
Using QM:
Required for this course
Data input format -

5. 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.)

6. 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.

8. 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.

9. 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.

11. 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.