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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

5Variations of the Standard Simplex Routine

This chapter presents a variety of computational devices which can be employed to solve linear programming problems which depart from the basic structure depicted in Chapter 3 (3.1). In particular, we shall consider “≥” as well as “=” structural constraints, the minimization of the objective, and problems involving unrestricted variables.

5.1 The M‐Penalty Method

Let us assume that we are faced with solving a linear program whose structural constraint system involves a mixture of structural constraints, e.g. the said problem with its mixed structural constraint system (involving “≤,” “≥,” and “=” structural constraints) might appear as

images

We noted in Chapter 3 that to convert a “≤” structural constraint to standard form (i.e. to an equality) we must add a nonnegative slack variable to its left‐hand side. A similar process holds for “≥” structural constraints – this time we will subtract a nonnegative surplus variable from its left‐hand side. So for x3 ≥ 0 a slack variable and x4 ≥ 0 a surplus variable, the preceding problem, in images form, becomes

images

The associated simplex matrix thus appears as

Since this matrix does not contain within ...

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Publisher Resources

ISBN: 9781119509448Purchase book