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11 - Numerical Solution of LP Problems Using the Simplex Method

from Part III - Formulation and Solution of Linear Programming (LP) Problems

Published online by Cambridge University Press:  17 December 2020

Vassilios S. Vassiliadis
Affiliation:
University of Cambridge
Ehecatl Antonio del Rio Chanona
Affiliation:
Imperial College London
Ye Yuan
Affiliation:
Huazhong University of Science and Technology
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Summary

The chapter aims to introduce completely the theory behind the simplex method for Linear Programming, by building slowly the material from the solution set of rectangular linear (affine) systems of equations to vertex solutions.The simplex method is introduced as a natural way to progress from one vertex to the next, on the constraint polytope, always improving the objective until the optimal solution is reached.Use of artificial variables and the two-phase simplex method is made to deal with finding an initial feasible basis for the simplex method.Pathological cases of LP problems are also considered, and how the simplex method would detect them is highlighted.

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Chapter
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Optimization for Chemical and Biochemical Engineering
Theory, Algorithms, Modeling and Applications
, pp. 123 - 132
Publisher: Cambridge University Press
Print publication year: 2021

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