networksimplexalgorithm

# networksimplexalgorithm - 15.082 and 6.855J Network Simplex...

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15.082 and 6.855J Network Simplex Animations

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2 Calculating A Spanning Tree Flow 1 3 6 4 5 2 7 1 3 -6 -4 1 2 3 A tree with supplies and demands. (Assume that all other arcs have a flow of 0) What is the flow in arc (4,3)?
3 Calculating A Spanning Tree Flow 1 3 6 4 5 2 7 1 3 -6 -4 1 2 3 To calculate flows, iterate up the tree, and find an arc whose flow is uniquely determined. What is the flow in arc (5,3)? 2

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4 Calculating A Spanning Tree Flow 1 3 6 4 5 2 7 1 3 -6 -4 1 2 3 What is the flow in arc (3,2)? 2 3
5 Calculating A Spanning Tree Flow 1 3 6 4 5 2 7 1 3 -6 -4 1 2 3 What is the flow in arc (2,6)? 2 3 6

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6 Calculating A Spanning Tree Flow 1 3 6 4 5 2 7 1 3 -6 -4 1 2 3 What is the flow in arc (7,1)? 2 3 6 4
7 Calculating A Spanning Tree Flow 1 3 6 4 5 2 7 1 3 -6 -4 1 2 3 What is the flow in arc (1,6)? 2 3 6 4 3

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8 Calculating A Spanning Tree Flow 1 3 6 4 5 2 7 1 3 -6 -4 1 2 3 Note : there are two different ways of calculating the flow on (1,2), and both ways give a flow of 4. Is this a coincidence? 2 3 6 4 4 3
9 Calculating Simplex Multipliers for a Spanning Tree 1 3 6 4 5 2 7 5 -6 -2 -4 1 3 Here is a spanning tree with arc costs. How can one choose node potentials so that reduced costs of tree arcs is 0? Recall: the reduced cost of (i,j) is c ij - π i + π j

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10 1 3 6 4 5 2 7 5 -6 -2 -4 1 3 One can set π 1 arbitrarily. We will let π i = 0. What is the simplex multiplier for node 2? There is a redundant constraint in the minimum cost flow problem. 0 Calculating Simplex Multipliers for a Spanning Tree
Calculating Simplex Multipliers for a Spanning Tree 1 3 6 4 5 2 7 5 -6 -2 -4 1 3 What is the simplex multiplier for node 7? 0

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## This note was uploaded on 03/15/2010 for the course IE 505 taught by Professor Yok during the Spring '10 term at Galatasaray Üniversitesi.

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networksimplexalgorithm - 15.082 and 6.855J Network Simplex...

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