Linear Programming - Operations Research

Linear Programming - Operations Research

I am a professor of Operations Research, teaching this subject from 1986 onwards. Linear Programming, Assignment Problem, Transportation Problem, Networking Techniques, and Game Theory are some of the major algorithms in Operations Research. My attempt, over the years, has been to teach without involving a great deal of mathematics, so that the student without any math background can also understand the algorithm easily. In the initial phase, I launched the courses on Linear Programming, Assignment Problem, Transportation Problem, and Sequencing at one go. Recently I launched a course on game theory, bringing out the essential part of game theory in a little over two hours.

This course is intended to provide you an opportunity about the manual process of solving simple linear programming problems, involving the simplest type of constraint, namely <= (read as ‘less than or equal to’) It starts with the graphical method of solving the Linear Programming Problem (LPP), with a detailed explanation as to what is an LPP, how to formulate it and solve it using a simple graph. In the very first lecture, I delved into the concept of LPP and how and where it is to be applied. This lecture deals with plotting the constraints as straight lines in their limiting case and from thereupon finding the solution space. The first lecture has two problems solved in it whereas the second lecture solves four such problems. All types of problems have been covered, including the special case of three variable problem solved using graphical method! The next lecture that is lecture number 3 is an important lecture in the sense that it introduces the student to the process of the simplex algorithm. Initially, a very simple problem involving two variables and two constraints has been solved using the simplex process. In the course of solving the problem, the method has been explained at length. The next simplex problem covered in the same lecture has three variables and three constraints. The subsequent lecture in video number 4 deals with a 3 variables, 3 constraints with multiple solutions. It will also train the student on how to detect multiple solutions. In this longish lecture, the second problem solved is by way of revision, and so are the next two, which are 3 variables, and 3 constraints problems. Similar practice problems make up this lecture, for example, two problems have only been formulated, since it’s beyond the scope of the course to solve them. These variations are covered in another of my course, which is a fairly advanced one, which is also available on Udemy for a subscription. Later on, in the same lecture, degeneracy has been covered at length, by solving a problem twice over. Towards the end of the lecture, the concept of duality has been explained in some detail. In lecture number five, an important topic of sensitivity analysis is taken for discussion. It’s very important to discuss this topic, not only to understand the simplex process completely but to understand the “what if” situations in businesses where LPP is applied. In lecture number 6, another simple problem on sensitivity analysis has been covered, apart from covering a problem on graphical method, just by way of revision.

The remaining parts of LPP have been covered in the other course of mine named ‘Linear Programming B Advanced’ available separately on Udemy. That course will cover more advanced topics using all types of constraints, using web tools for LPP solutions, and even using some mobile apps for solving LPP. If you have bought this course from Udemy, I am confident that you will enjoy it thoroughly, and please do remember to give feedback after you complete the course. Thanks, and best wishes for your academic pursuits.

Graphical and Simplex Methods

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What you will learn

• You will learn the basic tools of Operations Research (OR). OR is a bunch of mathematical tools to solve business related problems.
• You will learn the Graphical method to solve the Linear Programming Problem.
• These problems are typically to maximize or minimize the value of a given objective function subject to some restrictions (constraints).

Rating: 4.25

Level: All Levels

Duration: 10.5 hours

Instructor: Madhusudan Sohani