Syllabus (MATHEMATICS)

Course Type: ME-6

Semester: 5

Course Code: BMTMMEB35T

Course Title: Linear Programming Problem

(L-P-Tu): 4-0-0

Credit: 4

Practical/Theory: Theory

Course Objective: To be done.

Learning Outcome: Course Outcomes (CO): The whole course will have the following outcomes: Upon successful completion of this course, students will be able to CO1: solve linear programming problems (LPP) using appropriate techniques and optimization solvers, interpret the

Syllabus:

Linear Programming Problem [Credit: 4, 60 L]

General introduction to optimization problem, Definition of L.P.P., Mathematical formulation of the problem, Canonical & Standard form of L.P.P., Graphical solution of L. P.P.

Basic solutions, feasible solution, basic feasible & optimal solutions, Reduction of a feasible solution to basic feasible solution.

Fundamental theorems of L.P.P., Improved basic feasible solutions, Unbounded solution, Condition of optimality, Simplex method, Simplex algorithm, Artificial variable technique (Big M method, Two phase method).

Concept of duality, Fundamental properties of duality, Fundamental theorem of duality, Duality & Simplex method.

Transportation Problem (T.P.), Initial basic feasible solutions (different methods like North West corner, Row minima, Column minima, Matrix minima & Vogel’s Approximation method), Loops in T.P. table and their properties, Optimal solutions, Degeneracy in T.P., Unbalanced T.P.

Assignment Problem, optimal solution by Hungarian Method.

Reference Books

1. Ghosh & Chakraborty, An Introduction to Linear Programming & Game Theory, Maulik Library
2. Karak, P. M., Linear Programming with Game Theory, New Central Book Agency
3. Sharma, J. K., Operations Research – Theory and Applications

Swarup, Gupta & Man Mohan – Operations Research.