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Linear Programming

By Dr. ANEESH KUMAR. K   |   Mahatma Gandhi College, Iritty- Kannur, Kerala.
Learners enrolled: 120
           Linear programming refers to the technique of finding an optimal solution to a problem with limited resources, where all the relationships between the variables under consideration are linear. Linear programming has been used successfully in the solution of problems concerned with assignment of personnel, blending of materials, distribution and transportation, and investment portfolios.
          The course “LINEAR PROGRAMMING” helps one to get an insight in operations research modeling and to learn from the very beginning of linear programming. This course starts with fundamental concepts involved in LPP and discusses various methods for solving Linear Programming Problems. This course includes Assignment problem, Transportation problem and their mathematical formulations and various methods for solution. The course also discusses the Theory of Games. Various types of
game problems and the methods for solving such problems are also considered. Those who wish to familiarize LPP and related problems can make use of this course only with the knowledge of higher secondary level mathematics as a prerequisite.
Summary
Course Status : Upcoming
Course Type : Elective
Language for course content : English
Duration : 16 weeks
Category :
  • Mathematics
Credit Points : 5
Level : Undergraduate
Start Date : 20 Jan 2025
End Date : 30 Apr 2025
Enrollment Ends : 28 Feb 2025
Exam Date : 25 May 2025 IST
NCrF Level   : 5.0
Exam Shift :

Shift - I

Note: This exam date is subject to change based on seat availability. You can check final exam date on your hall ticket.


Page Visits



Course layout

Weeks Weekly Lecture Topics (Module Titles)

1 Day 1 Introduction to Operations Research and Linear Programming Problems
Day 2 Mathematical Preliminaries
Day 3 Mathematical formulation of LPPs-1
Day 4 Mathematical formulation of LPPs-2
Day 5 Assignment I

2 Day 1 Basic assumptions, applications, advantages and limitations of Linear Programming 
Day 2 Some important theorems related to LPP
Day 3 Solution of LPP – Graphical Method
Day 4 Solution of LPP – Graphical Method-II
Day 5 Assignment II

3 Day 1 Simplex method -1
Day 2 Simplex method -2
Day 3 More Problems on Simplex method (Simplex method -3)
Day 4 Simplex method in tableau format-I
Day 5 Assignment III

4 Day 1 Simplex method in tableau format – II 
Day 2 Artificial variable techniques – Two phase method.
Day 3 Artificial variable techniques - Big M Method
Day 4 Interactive session
Day 5 Assignment IV

5 Day 1 Artificial Variable Techniques More Problems (Solving more LPPs using two phase and Big M method.)
Day 2 Degeneracy in Simplex Method.
Day 3 Duality in LPP
Day 4 More theorems on Duality
Day 5 Assignment V

6 Day 1 Dual simplex method and Economical Interpretation of Dual
Day 2 Transportation Problem
Day 3 North-West corner rule (Transportation Problem-Initial basic feasible solution)
Day 4 Row minima method, Column Minima method and Least Cost method. (Transportation Problem-Initial basic feasible solution)
Day 5 Assignment VI

7 Day 1 Vogels Approximation method. (Transportation Problem-Initial basic feasible solution)
Day 2 Unbalanced Transportation Problem, Loops in Transportation Table
Day 3 Optimal solution for a Transportation Problem
Day 4 Discussion
Day 5 Assignment VII

8 Day 1 Degeneracy in Transportation Problems 
Day 2 Maximization transportation problems and an Introduction to Assignment Problems
Day 3 Solution of Assignment Problem - Hungarian method
Day 4 Unbalanced and Maximization Assignment Problems
Day 5 Assignment VIII

9 Day 1 Game Theory – An Introduction
Day 2 Games with Mixed Strategies
Day 3 Dominance in Games
Day 4 Games Problems – Graphical Method
Day 5 Assignment IX

10 Day 1 Linear Programming Formulation of a Game Problem 
Day 2 More Problems on Linear Programming Method of  Solving Games
Day 3 Mathematical Formulation of Linear Programming Problems – More examples
Day 4 Interactive session
Day 5 Assignment X

11 Day 1 Graphical Solution of Linear Programming Problems – More examples
Day 2 Solution to Linear Programming Problem by Simplex Method – Special cases
Day 3 Simplex Method – LPP with more than two variables
Day 4
Day 5 Assignment XI

12 Day 1 Additional problems on Two Phase and Big M Method
Day 2 Dual Simplex Method – More Problems
Day 3 Transportation Problem – Initial Basic Feasible Solution-More problems using N-W Corner, Row Minima and Least Cost Methods.
Day 4  
Day 5 Assignment XII

13 Day 1 Transportation Problem – Initial Basic Feasible Solution-More problems using Vogel’s Approximation Method
Day 2 Optimal Solution for Transportation Problems- Additional Problems -I
Day 3 Optimal Solution for Transportation Problems- Additional Problems -II
Day 4 Interactive session
Day 5 Assignment XIII

 14 Day 1 Assignment Problems 
Day 2 Assignment Problems-Additional problems 
Day 3 Solving More Game Problems Using Graphical Method
Day 4
Day 5 Assignment XIV

 15 Day 1 Linear Programming Formulation of Game Problems –Additional example
Day 2 Interactive session
Day 3 Assignment XV
Day 4

Books and references

1. Mokhtar S, Bazaraa, John J Jarvis and Hanif D Sherali, Linear Progmming and Network Flows, 2 nd Edn John Wiley and Sons, India 2004.
2. F S Hillier and G J Lieberman, Introduction to Operations Research, 9 th edn. TataMc Graw Hill Singapore 2009.
3. Hamdy A Taha, Operations Research- An Introduction, 8 th Edn Prentice-Hall India 2006.
4. G Hadley, Linear Programming, Narosa Publishing House New Delhi 2002.
5. Kanti Swaroop.P.K.,Gupta and Man Mohan: Operations Research (Sulthan Chand and Sons, New Delhi), 1998.

Instructor bio

Dr. ANEESH KUMAR. K

Mahatma Gandhi College, Iritty- Kannur, Kerala.
Dr.Aneesh Kumar.K,  an Associate Professor in Statistics with 19 years of experience in teaching, awarded Ph.D from University of Calicut under the guidance of Dr.M.Manoharan. He has published his research works in various national and international journals and authored five books for the benefit of UG level students in Statistics.





Course certificate

Course Completion  will carry 70% weightage of end term exam and 30% weightage of internal assessments. A minimum 40% in each is required to qualify for the Course Completion Certificate.


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