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Linear Programming

Mahathma Gandhi College, Iritty , CEC via Swayam

Description

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.

Abstract Algebra

Syllabus

Weeks Weekly Lecture Topics (Module Titles) 1 Day 1 1. Introduction to Operations Research and Linear Programming Problems. Day 22.Mathematical Preliminaries Day 33.Mathematical formulation of LPPs-1 Day 4Interaction based on the three modules covered Day 5Objective Assignment 2 Day 1 4.Mathematical formulation of LPPs-2 Day 25.Assumptions of Linear Programming Day 36.Some important theorems related to LPP Day 4Interaction based on the three modules covered Day 5Subjective Assignment 3 Day 1 7.Solution of LPP – Graphical Method Day 28.Solution of LPP – Graphical Method: More problems Day 39.Simplex method -1 Day 4Interaction based on the three modules covered Day 5Objective Assignment 4 Day 1 10.Simplex method -2 Day 211.More problems on simplex method. Day 312.Simplex method in tableau format-I Day 4Interaction based on the three modules covered Day 5Subjective Assignment 5 Day 1 13.Simplex method in tableau format – II Day 214. Artificial variable techniques – Two phase method. Day 315.Artificial variable techniques - Big M Method Day 4Interaction based on the three modules covered Day 5Objective Assignment 6 Day 1 16. Solving more LPPs using two phase and Big M method. Day 217. Degeneracy in LPP Day 318.Duality in LPP Day 4Interaction based on the three modules covered Day 5Subjective Assignment

7 Day 1 19. Theorems on Duality in LPP, Day 220.Dual simplex method, Economical Interpretation of duality Day 321. Transportation Problem. Day 4Interaction based on the three modules covered Day 5Objective Assignment 8 Day 1 22.North-West corner rule Day 223. Row minima method, Column Minima method and Least Cost method. Day 324.Vogel’s approximation method Day 4Interaction based on the three modules covered Day 5Subjective Assignment 9 Day 1 25. Unbalanced transportation problem, Degeneracy in transportation problem. Day 226.Optimal solution to Transportation Problem Day 327.More Transportation Problems. Day 4Interaction based on the three modules covered Day 5Objective Assignment 10 Day 1 28.Assignment problems Day 229.Hungarian method Day 330.Optimal Assignment Day 4Interaction based on the three modules covered Day 5Subjective Assignment 11 Day 1 30.Maximization and Unbalance assignment problems Day 231.Game theory – an introduction Day 332.Solving two person zero sum game problems Day 4Interaction based on the three modules covered Day 5Objective Assignment 12 Day 1 33.Games with mixed strategies Day 235.Graphical solution to game problems Day 336.LP formulation of a game problem and Dominance in Game problems Day 4Interaction based on the three modules covered Day 5Subjective Assignment 13Day 1 Day 2 Day 3 Day 4Interaction based on the modules covered so far Day 5