This preview shows pages 1–4. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: CO350 Linear Programming Chapter 9: The Revised Simplex Method 29th June 2005 Chapter 9: Revised Simplex Method 1 Motivation The most computationally intensive part of the simplex method is pivoting ; i.e., the construction of the new tableau. Tableau: z P j N c j x j = v x i + P j N a ij x j = b i ( i B ) In a tableau, there are n m nonbasic c j s one v , ( n m ) m a ij s, m b i s. In all, there are ( m + 1)( n m + 1) numbers in a tableau. However, we only need n m nonbasic c j s to decide entering variable x k , and m a ik s and m b i s to decide leaving variable x r . In all, we only need n + m numbers. Revised Simplex Method An implementation of the simplex method that computes only the necessary coefficients instead of the whole tableau. Chapter 9: Revised Simplex Method 2 Entering variable We need to compute nonbasic c j . By definition, a tableau is derived from z c T x = Ax = b using elementary row operations. Thus there exists y = [ y 1 , y 2 , . . . , y m ] T such that the zrow z P j N c j x j = v is equivalent to the linear combination z c T x + y T Ax = y T b ; i.e. z ( c A T y ) T x = y T b Comparing coefficients of basic...
View Full
Document
 Fall '97
 Wolkowicz

Click to edit the document details