Linear Programming Using MATLAB®

Description

This book offers a theoretical and computational presentation of a variety of linear programming algorithms and methods with an emphasis on the revised simplex method and its components. A theoretical background and mathematical formulation is included for each algorithm as well as comprehensive numerical examples and corresponding MATLAB® code. The MATLAB® implementations presented in this book are sophisticated and allow users to find solutions to large-scale benchmark linear programs. Each algorithm is followed by a computational study on benchmark problems that analyze the computational behavior of the presented algorithms. As a solid companion to existing algorithmic-specific literature, this book will be useful to researchers, scientists, mathematical programmers, and students with a basic knowledge of linear algebra and calculus. The clear presentation enables the reader to understand and utilize all components of simplex-type methods, such as presolve techniques, scaling techniques, pivoting rules, basis update methods, and sensitivity analysis. Front Matter ....Pages i-xvii Introduction (Nikolaos Ploskas, Nikolaos Samaras)....Pages 1-11 Linear Programming Algorithms (Nikolaos Ploskas, Nikolaos Samaras)....Pages 13-71 Linear Programming Benchmark and Random Problems (Nikolaos Ploskas, Nikolaos Samaras)....Pages 73-134 Presolve Methods (Nikolaos Ploskas, Nikolaos Samaras)....Pages 135-217 Scaling Techniques (Nikolaos Ploskas, Nikolaos Samaras)....Pages 219-275 Pivoting Rules (Nikolaos Ploskas, Nikolaos Samaras)....Pages 277-302 Basis Inverse and Update Methods (Nikolaos Ploskas, Nikolaos Samaras)....Pages 303-328 Revised Primal Simplex Algorithm (Nikolaos Ploskas, Nikolaos Samaras)....Pages 329-381 Revised Dual Simplex Algorithm (Nikolaos Ploskas, Nikolaos Samaras)....Pages 383-435 Exterior Point Simplex Algorithm (Nikolaos Ploskas, Nikolaos Samaras)....Pages 437-490 Interior Point Methods (Nikolaos Ploskas, Nikolaos Samaras)....Pages 491-540 Sensitivity Analysis (Nikolaos Ploskas, Nikolaos Samaras)....Pages 541-563 Back Matter ....Pages 565-637