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Neha Tikoo, Lovely Professional University Unit 3: Linear Programming Problem – Simplex Method

Unit 3: Linear Programming Problem – Simplex Method Notes

CONTENTS
Objectives
Introduction
3.1 Simplex Method of Linear Programming
3.1.1 Maximisation Cases
3.1.2 Minimization Cases
3.2 Big 'M' Method

3.3 Unconstrained Variables
3.3.1 Change in Objective Function Coefficients and Effect on Optimal Solution
3.3.2 Change in the Right-hand Side Constraints Values and Effect on Optimal
Solution
3.4 Special Cases in Linear Programming
3.4.1 Multiple or Alternative Optimal Solutions
3.4.2 Unbounded Solutions
3.4.3 Infeasibility

3.5 Summary
3.6 Keywords
3.7 Review Questions
3.8 Further Readings

Objectives

After studying this unit, you will be able to:

 Understand the meaning of word 'simplex' and logic of using simplex method
 Know how to convert a LPP into its standard form by adding slack, surplus and artificial
variables

 Learn how to solve the LPP with the help of Big M methodology
 Understand the significance of duality concepts in LPP and ways to solve duality problems

Introduction

In practice, most problems contain more than two variables and are consequently too large to be
tackled by conventional means. Therefore, an algebraic technique is used to solve large problems
using Simplex Method. This method is carried out through iterative process systematically step
by step, and finally the maximum or minimum values of the objective function are attained.
The simplex method solves the linear programming problem in iterations to improve the value
of the objective function. The simplex approach not only yields the optimal solution but also
other valuable information to perform economic and 'what if' analysis.

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