# Linear Programming

By Dr.ANEESH KUMAR. K   |   MAHATMA GANDHI COLLEGE, IRITTY
Learners enrolled: 958
The course “Linear Programming” starts with a general introduction to Operations Research and an introduction to Linear Programming Problems (LPP) in particular.  The mathematical preliminaries and related theorems related to LPP are discussed.  Mathematical formulation of LPP and the methods for solving LPP like graphical and simplex methods are discussed.  Duality in LPP is considered.  Transportation Problems (TP), Assignment Problems and various methods of solving such problems are discussed in detail.  The methods for solving TP included North-West corner rule, least cost method, and Vogel’s approximation method.  Hungarian method for solving assignment problems is considered.  The methods for optimizing the solutions are also included.
Theory of games is discussed in detail.  Various types of game problems and the methods for solving game problems including LPP methods, graphical method and dominance property are discussed.

Summary
 Course Status : Ongoing Course Type : Elective Duration : 15 weeks Start Date : 23 Jan 2023 End Date : 19 Apr 2023 Exam Date : Enrollment Ends : 15 Mar 2023 Category : Mathematics Credit Points : 4 Level : Undergraduate

### Course layout

Weeks Weekly Lecture Topics (Module Titles)

1 Day 1 1. Introduction to Operations Research and Linear Programming Problems.
Day 2 2.Mathematical Preliminaries
Day 3 3.Mathematical formulation of LPPs-1
Day 4 Interaction based on the three modules covered
Day 5 Objective Assignment

2 Day 1 4.Mathematical formulation of LPPs-2
Day 2 5.Assumptions of Linear Programming
Day 3 6.Some important theorems related to LPP
Day 4 Interaction based on the three modules covered
Day 5 Subjective Assignment

3 Day 1 7.Solution of LPP – Graphical Method
Day 2 8.Solution of LPP – Graphical Method: More problems
Day 3 9.Simplex method -1
Day 4 Interaction based on the three modules covered
Day 5 Objective Assignment

4 Day 1 10.Simplex method -2
Day 2 11.More problems on simplex method.
Day 3 12.Simplex method in tableau format-I
Day 4 Interaction based on the three modules covered
Day 5 Subjective Assignment

5 Day 1 13.Simplex method in tableau format – II
Day 2 14. Artificial variable techniques – Two phase method.
Day 3 15.Artificial variable techniques  - Big M Method
Day 4 Interaction based on the three modules covered
Day 5 Objective Assignment

6 Day 1 16. Solving more LPPs using two phase and Big M method.
Day 2 17. Degeneracy in LPP
Day 3 18.Duality in LPP
Day 4 Interaction based on the three modules covered
Day 5 Subjective Assignment

7 Day 1 19. Theorems on Duality in LPP,
Day 2 20.Dual simplex method, Economical Interpretation of duality
Day 3 21. Transportation Problem.
Day 4 Interaction based on the three modules covered
Day 5 Objective Assignment

8 Day 1 22.North-West corner rule
Day 2 23. Row minima method, Column Minima method and Least Cost method.
Day 3 24.Vogel’s approximation method
Day 4 Interaction based on the three modules covered
Day 5 Subjective Assignment

9 Day 1 25. Unbalanced transportation problem, Degeneracy in transportation problem.
Day 2 26.Optimal solution to Transportation Problem
Day 3 27.More Transportation Problems.
Day 4 Interaction based on the three modules covered
Day 5 Objective Assignment

10 Day 1 28.Assignment problems
Day 2 29.Hungarian method
Day 3 30.Optimal Assignment
Day 4 Interaction based on the three modules covered
Day 5 Subjective Assignment

11 Day 1 30.Maximization and Unbalance assignment problems
Day 2 31.Game theory – an introduction
Day 3 32.Solving two person zero sum game problems
Day 4 Interaction based on the three modules covered
Day 5 Objective Assignment

12 Day 1 33.Games with mixed strategies
Day 2 35.Graphical solution to game problems
Day 3 36.LP formulation of a game problem and Dominance in Game problems
Day 4 Interaction based on the three modules covered
Day 5 Subjective Assignment

13 Day 1
Day 2
Day 3
Day 4 Interaction based on the  modules covered so far
Day 5

### Books and references

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

### Dr.ANEESH KUMAR. K

MAHATMA GANDHI COLLEGE, IRITTY
Dr. Aneesh Kumar K, has 22 years of experience in teaching Undergraduate level Statistics, Operations Research etc.  He has developed study material for many Universities in Kerala for their School of Distance Education.  Awarded Ph.D. from the University of Calicut in 2007 for the works under Dr. M. Manoharan- University of Calicut.

### Course certificate

Assessment/Assignment marks will be considered for Internal Marks and will carry 30 percent for overall Result.

End Term Exam- will have 100 questions and will carry 70 percent of  overall Result.

*All students, who obtain 40% marks in in-course assessment and 40% marks in end-term proctored exam separately, will be eligible for certificate and credit transfer.