Revised Primal Simplex Algorithm

Nikolaos Ploskas and Nikolaos Samaras
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Nikolaos Ploskas: University of Macedonia
Nikolaos Samaras: University of Macedonia

Chapter Chapter 8 in Linear Programming Using MATLAB®, 2017, pp 329-381 from Springer

Abstract: Abstract The simplex algorithm is one of the top ten algorithms with the greatest influence in the twentieth century and the most widely used method for solving linear programming problems (LPs). Nearly all Fortune 500 companies use the simplex algorithm to optimize several tasks. This chapter presents the revised primal simplex algorithm. Numerical examples are presented in order for the reader to understand better the algorithm. Furthermore, an implementation of the algorithm in MATLAB is presented. The implementation is modular allowing the user to select which scaling technique, pivoting rule, and basis update method will use in order to solve LPs. Finally, a computational study over benchmark LPs and randomly generated sparse LPs is performed in order to compare the efficiency of the proposed implementation with MATLAB’s simplex algorithm.

Date: 2017
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DOI: 10.1007/978-3-319-65919-0_8

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