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Linear Programming and Resource Allocation Modeling
book

Linear Programming and Resource Allocation Modeling

by Michael J. Panik
November 2018
Intermediate to advanced content levelIntermediate to advanced
448 pages
12h 24m
English
Wiley
Content preview from Linear Programming and Resource Allocation Modeling

9Analyzing Structural Changes

9.1 Introduction

Oftentimes, one is faced with the task of adding or deleting certain variables or structural constraints in a problem for which an optimal basic feasible solution has been found. As in the preceding chapter, rather than resolve completely the adjusted problem, we shall use the information contained within the optimal simplex matrix of the original linear program to determine the effects of the said changes upon the feasibility or optimality of the solution at hand.

9.2 Addition of a New Variable

We first look to the effect on the optimal solution of a given linear programming problem of the introduction of a new variable xn + 1, with cn + 1 and an + 1 representing its associated objective function coefficient and vector of structural constraint coefficients, respectively. In particular, we are now confronted with solving a problem of the form

images

If XB = B−1b represents an optimal basic feasible solution to the problem

images

then we may also view it as a basic feasible solution to the former problem with xn + 1 deemed nonbasic or zero. Moreover, this solution will be optimal if images Obviously then, if the current solution is no longer optimal ...

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Publisher Resources

ISBN: 9781119509448Purchase book