Chapter 7 - MA3252 LINEAR AND NETWORK OPTIMIZATION Topic 7:...

Info iconThis preview shows pages 1–5. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: MA3252 LINEAR AND NETWORK OPTIMIZATION Topic 7: The Network Simplex Method 1 / 19 In this topic, we develop the details of the simplex method applied to network flow problems (known as the network simplex method). This can lead to a much faster algorithm than standard simplex method. 2 / 19 Consider the uncapacitated minimum cost flow problem: min c x s.t. Ax = b x ≥ A is the node-arc incidence matrix of a directed graph G ( V , E ) where n = | V | and m = | E | . The size of the matrix A is n × m as opposed to earlier conventions. b is the supply vector and c is the cost vector Assumptions: 1 ∑ i ∈ V b i = 0 else the flow is infeasible. 2 Graph G ( V , E ) is connected else the network can be decomposed into smaller networks that can be solved independently. 3 / 19 Trees and Basic Feasible Solutions Network flow problems can be solved very efficiently because the basis matrices have a special structure that can be described nicely in terms of the network. To understand this structure, we analyze the node-arc incidence matrix. Each column of the incidence matrix A has exactly two nonzero entries, one equal to +1 and one equal to -1, indicating the start and end node of the arc. Adding up the rows of A gives the zero vector, indicating that the rows of A are linearly dependent....
View Full Document

This note was uploaded on 12/02/2011 for the course MATH 3252 taught by Professor Tanbanpin during the Spring '10 term at National University of Singapore.

Page1 / 19

Chapter 7 - MA3252 LINEAR AND NETWORK OPTIMIZATION Topic 7:...

This preview shows document pages 1 - 5. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online