Optimization - Advanced Linear Programming

Learning step by step skills of linear programming problem (LPP)

What you'll learn

You will learn the basic tools of Operations Research

You will learn in-depth simplex method of solving a linear programming problem

You will learn the most important topic in LPP, namely post-optimality analysis or sensitivity analysis

Requirements

High school level mathematics

Some exposure to optimisation tools

You need a pc or a laptop with a stable internet connection

You need an Android phone if you wish to use mobile apps

You need a 10 digit calculator to verify the results

You need exposure to high school level mathematics

Description

This course is intended to provide you an opportunity to learn about the manual process of solving simple linear programming problems, involving all types of constraints, and including unrestricted variables. It also introduces you to solving the problems by formulating the same in MS Excel, using the solver tool. To this extent, a formulated question in linear programming has been included, for solving, using excel solver tool.Starting with the first lecture, you will be exposed to the popular method of solving a linear programming problem (LPP as hereafter called) involving all constraints of the type ‘less than or equal to’; which is the easiest type of constraint to deal with. The questions involving other type of constraints namely ‘greater than or equal to’ or ‘equal to’ are more difficult to manually solve. They will be gradually introduced from the second lecture onwards. Right in the second lecture, you will get used to having ‘greater than or equal to’ constraint. In fact, the second video deals with a problem having two constraints and two variables, both the constraints being ‘greater than or equal to’. In the third video, mixed type of constraints are covered, which requires to be treated differently for each constraints. The fourth video will cover a problem which has constraints of all types, <=, >= and =. Additional twist in the problem is, it has a multiple solution. You will learn how to detect a multiple solution. In lecture 05, you will see a direct application of LPP to a business problem. On simplification, it will be possible to solve the problem, which has been solved in the lecture. It has got a slight twist in the end though.Lecture 6 will be quite a surprise for the unsuspecting student, since you will discover the utility of artificial variables in its true sense. You will learn that at times none out of slack, or surplus or artificial variables are needed to solve the problem. The seventh lecture will adequately and confirm the use of artificial variables, through two problems. The lecture at serial number 8 will demonstrate to you how a problem containing 72 numbers in the table could be reduced to a problem containing only 18 numbers. Of course this can be done, only if minimum values of variables are given.Degeneracy is a different class of problems. After this video lecture at serial number 9, you will be able to deal with a degenerate problem. Also, in this lecture is included a problem having unrestricted variable. This type of a problem cannot be solved by the conventional simplex method since the simplex algorithm is based on the assumption that all variables are non-negative. For the first time you will deal with a variable which can take both, positive and negative values!Lecture number 10 deals with a unique method of two phases. Here in this method the problem is solved in two parts. The first part or phase one, as it is called, will revolve around removing the artificial variables from the problem, by allotting them a simple contribution like + or – 1. After artificial variables are removed from the basis, the phase two starts, where in the decision variables are re-allotted their original contribution, the solution checked for optimality and improved if necessary, till it is optimal. This is a very interesting process, and actually offers an improvement over the conventional ‘big M’ method.Lecture number 11 deals with a very important aspect of LPP. The situations in business are not static, in the sense that if you obtain the solution to a problem it can not taken as sacrosanct, and you must offer the possibility of changes in the structure of the problem. It is very interesting to see how the optimal tableau offers answers to small changes in the structure of the problem. After viewing this video, you will be able to appreciate the importance of carrying out changes in the right-hand side of the constraints, even consider changes in the contribution of products. You can examine the introduction of new products within the given situation of existing products.Lecture number 12 is actually taken from one my other courses on Udemy. It will strengthen the concepts of carrying out post-optimality analysis or sensitivity analysis of a given LPP. Lecture 13 deals with viewing any primal problem through it’s dual. It’s actually like seeing the two sides of a coin. If ‘head’ is maximization, the ‘tail’ is minimization and vice-versa. You will be taken through simple steps of writing the dual of any problem from the given primal. The next lecture i.e., 14 will teach you the procedure of writing the dual if the primal is not in the standard form or has ‘=’ constraints. This lecture will delve on the uses of dual in practical situation when it’s more convenient to write and solve the dual of a problem than solving the original problem.Lecture number 15 is an important lecture in the sense that once you know how to solve the LPP manually, you can get into tools to solve them automatically. To this effect, this lecture deals with solving a problem through excel solver tool. It’s shown by taking a problem from start to finish through MS Excel Solver. Right in the beginning explanation has been given as to installation of Solver tool. Once you master this tool. It’s very easy to solve an LPP of any size. For many of you, this may be the most important lecture in the whole course. The lecture number 16 summarizes how to deal with a simple production planning problem. You need to decide how much production you should do with normal time or with over time being paid to the workers. Lecture number 17 showcases how to detect an infeasible problem of LPP, and its characteristics.Lecture 18 will showcase use of some android applications to solve the LPP. Actually two applications have been discussed right from the stage of downloading the same and using them. A demonstration has been given in this lecture by actually solving a problem using these two applications. In fact there are several applications floating on Google Play Store, and it’s difficult to make a choice. An attempt has been made to provide you the guidance for choosing the correct app.The next in the lecture is a demonstration of using live web-pages for finding the solution to LPPs. A problem each has been solved using these web-pages. In the last lecture, a problem has been solved to showcase what is known as blending problems. Particularly useful in petroleum industry!I hope that you will get the satisfaction of learning something new, and quite thoroughly. Enjoy the course and give your feedback to me by writing a review of my course. Thanks a lot for registering for this course. Best wishes!

Overview

Section 1: Introductory Section

Lecture 1 Introduction

Section 2: Introduction

Lecture 2 Constraints like >=

Lecture 3 Mixed type of constraints

Lecture 4 Mixed constraints, multiple solutions

Lecture 5 Mixed constraints again, a good practice problem

Lecture 6 All constraints of '=' type. No slack, surplus or artificial variables!

Lecture 7 Constraints like >=, but great simplification

Lecture 8 The lecture will introduce the student to the concept of simplifying the problem

Lecture 9 Degeneracy explained with an example, problem of 'unrestricted' variable solved

Lecture 10 Two phase method

Lecture 11 Sensitivity analysis explained with an example

Lecture 12 Sensitivity analysis explained with an example

Lecture 13 Duality in Linear Programming

Lecture 14 Duality - continued

Lecture 15 Solver tool

Lecture 16 A production scheduling problem for formulation

Lecture 17 An infeasible problem

Lecture 18 Mobile Apps for linear programming problem

Lecture 19 Online solutions

MBA students, learners of mathematical tools, students of operations research, modelling using mathematics, students of business problems which need optimization,Students of any Diploma courses, where Operations Research is one of the subjects,MBA or MS students having a paper in Optimisation or Linear Programming,Business people interested in solving complex problems involving use of linear programming. If they want to use Excel Solver, this is the course for them,People who wish to solve the LPP 'on the go' using mobile apps,Those students who are pursuing PhD in mathematical sciences