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.
Table of Contents
Introduction. Introduction. Vector Spaces and Matrices. Vector. Matrix. Linear Equations. Matrix Inversion. Eigen values and Eigen vectors. Exercises. MATLAB. Introduction. Basic feature. Basic Operations in MATLAB. Selection Statements and Loop Statements. User Defined Function. MATLAB Functions Defined in This Book. Exercises. Introduction to Linear Programming. Introduction. Simple Examples of Linear programs. Convex Sets. Graphical Solution of Linear Programming problem. Exercises. Contents. The Simplex Method. Standard Form of Linear Programming Problem. Basic Solutions. Properties of Basic Solutions. Simplex Algorithm. Two Phase Simplex Method. Exercises. The Revised Simplex Method. Introduction. Matrix Form of the Revised Simplex Method. The Revised Simplex Algorithm. Exercise. Duality. Dual Linear Programs. Properties of Dual Problems. The Dual Simplex Method. Exercises. The Transportation Problem. Introduction. Balanced Transportation Problem. North West Corner Method. Least Cost Method. Vogel's Approximation Method. Optimal Solution from BFS. Exercises. The Assignment Problem. Introduction. Hungarian Method. Exercises. Answer Keys. Bibliography. Index
Dr Shashi Kant Mishra is a Professor of Mathematics at the Institute of Science at Banaras Hindu Univeristy. His areas of research are generalized convexity, vector optimization, nonsmooth optimization and variational Inequalities.