Introduction to Linear Programming with MATLAB®

"This book is based on the lecture notes of the author delivered to the students at the Institute of Science, Banaras Hindu University, India. It covers simplex, revised simplex, two-phase method, duality, dual simplex, complementary slackness, transportation and assignment problems with good number of examples, clear proofs, MATLAB codes and homework problems. The book will be useful for both students and practitioners."--Provided by publisher Cover -- Half Title -- Title -- Copyrights -- Contents -- Foreword -- Preface -- List of Figures -- List of Tables -- Chapter 1. Introduction -- 1.1 History of Linear Programming -- Chapter 2. Vector Spaces and Matrices -- 2.1 Vector -- 2.2 Matrix -- 2.3 Linear Equations -- 2.4 Matrix Inversion -- 2.5 Exercises -- Chapter 3. MATLAB -- 3.1 Introduction -- 3.2 Basic Feature -- 3.3 Basic Operations in MATLAB -- 3.4 Selection Statements and Loop Statements -- 3.5 User-De ned Function -- 3.6 MATLAB Functions De ned in This Book -- 3.7 Exercises -- Chapter 4. Introduction to Linear Programming -- 4.1 Introduction -- 4.2 Simple Examples of Linear Programs -- 4.3 Convex Sets -- 4.4 Graphical Solution of Linear Programming Problem -- 4.5 Exercises -- Chapater 5. The Simplex Method -- 5.1 Standard Form of Linear Programming Problem -- 5.2 Basic Solutions -- 5.3 Properties of Basic Solutions -- 5.4 Simplex Algorithm -- 5.5 Two-Phase Simplex Method -- 5.6 Exercises -- Chapter 6. The Revised Simplex Method -- 6.1 Introduction -- 6.2 Matrix Form of the Revised Simplex Method -- 6.3 The Revised Simplex Algorithm -- 6.4 Exercises -- Chapter 7. Duality -- 7.1 Dual Linear Programs -- 7.2 Properties of Dual Problems -- 7.3 The Dual Simplex Method -- 7.4 Exercises -- Chapter 8. The Transportation Problem -- 8.1 Introduction -- 8.2 Balanced Transportation Problem -- 8.3 Northwest Corner Method -- 8.4 Least Cost Method -- 8.5 Vogel's Approximation Method -- 8.6 Optimal Solution from BFS -- 8.7 Exercises -- Chapter 9. The Assignment Problem -- 9.1 Introduction -- 9.2 Hungarian Method -- 9.3 Exercises -- Answer Key -- Bibliography -- Index