7-1 copyright © 2013 pearson education shortest route, minimal spanning tree and maximal flow...
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7-1Copyright © 2013 Pearson Education
Shortest Route, Minimal Spanning Tree and
Maximal Flow Models
Chapter 7
7-2Copyright © 2013 Pearson Education
Chapter Topics
■ Network Components
■ The Shortest Route Problem
■ The Minimal Spanning Tree Problem
■ The Maximal Flow Problem
7-3
THE MAXIMAL FLOW PROBLEM
Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall
7-4Copyright © 2013 Pearson Education
Figure 7.18 Network of railway system
The Maximal Flow ProblemDefinition and Example Problem Data
Problem: Maximize the amount of flow of items from an origin to a destination.
a directed branch
undirected branch
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Figure 7.19 Maximal flow for path 1-2-5-6
The Maximal Flow ProblemSolution Approach (1 of 5)
Step 1: Arbitrarily choose any path through the network from origin to destination and ship as much as possible.
7-6Copyright © 2013 Pearson EducationFigure 7.20 Maximal flow for path 1-4-6
The Maximal Flow ProblemSolution Approach (2 of 5)
Step 2: Re-compute branch flow in both directions
Step 3: Select other feasible paths arbitrarily and determine maximum flow along the paths until flow is no longer possible.
7-7Copyright © 2013 Pearson EducationFigure 7.21 Maximal flow for path 1-3-6
The Maximal Flow ProblemSolution Approach (3 of 5)
Continue
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Figure 7.22 Maximal flow for path 1-3-4-6
The Maximal Flow ProblemSolution Approach (4 of 5)
Continue
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Figure 7.23 Maximal flow for railway network
The Maximal Flow ProblemSolution Approach (5 of 5)
Optimal Solution
7-10Copyright © 2013 Pearson Education
The Maximal Flow ProblemSolution Method Summary
1. Arbitrarily select any path in the network from the origin to the destination.
2. Adjust the capacities at each node by subtracting the maximal flow for the path selected in step 1.
3. Add the maximal flow along the path to the flow in the opposite direction at each node.
4. Repeat steps 1, 2, and 3 until there are no more paths with available flow capacity.
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