Master Linear Programming Methods Using Simplex Method

Learn Linear programming model and problems using Simplex method

What you'll learn

Construct Linear programming method using simplex method

Create a simplex table using simplex method

Establish a basic initial feasible solution and complete the creation of simplex table

Perform optimality test for an LP model using the Simplex method

Solve LP problem using simplex method when there are multiple optimal solutions or degeneracy

Solve LP problem using the simplex method in case of minimization objective, degeneracy infeasibility.

Solve linear programming problems using the Big M method

Requirements

You don’t need any perquisites for taking this course

Description

Rarely the resources to run a company are available in the unlimited quantities. There is always a restriction. Each resource – labour, money, material, equipment is available in its specific quantity which sets a limit on its use. The problem most commonly face by the management is to decide the manner in which these limited resources should be used to achieve the desired objective i.e. profit maximization/cost minimization etc. Here linear programming technique proves to be of great help to the management in the decision-making process. It is a mathematical technique for allotting limited resources of a firm in an optimal manner. This technique embraces almost every functional area of the business-like production, finance, marketing, distribution etc. in every type of industry.A few areas of application of linear programming technique are production scheduling, assembly line balancing, make or buy decisions, media selection, profit planning, portfolio selection, manpower scheduling, flight scheduling, environment protection, diet problems etc.In this course, you will learn the simplex method to solve linear programming problems. The different type of problems includes maximization, minimization, multiple optimal solutions, degeneracy, infeasible solution and unrestricted variables etc. You will also learn how to handle linear programming problems using simplex method when the constraints have ‘greater than equal to’ or simply ‘an equal to’ sign which is also known as Big M method.

Overview

Section 1: Simplex method - Introduction

Lecture 1 Simplex method - Step 1 - Construct an LP Model

Lecture 2 Simplex method - Step 2 - Standardization of the problem

Lecture 3 Simplex method - Step 3 - Create a Simplex table

Lecture 4 Simplex method - Step 4 - Establish a basic initial feasible solution

Lecture 5 Simplex method - Step 5 - Perform optimality test

Lecture 6 Simplex method - Step 6 - Iterate towards optimal solution

Lecture 7 Simplex method - Step 7 - Repeat Steps 5 and 6

Section 2: Examples of Simplex method

Lecture 8 Simplex method - Example 1 - Maximization - Part 1

Lecture 9 Simplex method - Example 1 - Maximization - Part 2

Lecture 10 Simplex method - Example 2 - Tie for key columns

Lecture 11 Simplex method - Example 3 - Multiple optimal solutions

Lecture 12 Simplex method - Example 4 - Degeneracy

Lecture 13 Simplex method - Example 5 - Minimization

Lecture 14 Simplex method - Example 6 - Infeasible solution

Lecture 15 Simplex method - Example 7 - Unrestricted variables

Section 3: Big M method

Lecture 16 Simplex method - Fundamentals of Big M method

Lecture 17 Simplex method - Big M - Example 1

Lecture 18 Simplex method - Big M - Example 2

Lecture 19 Simplex method - Big M - Example 3

The course can be useful for students studying operations management, professionals working in IT industry.