MA30014: Operation Research

MA30014
Course name	Operation Research
Offered by	Department of Mathematics
Credits	3
L-T-P	3-0-0
Professor(s)	M. P. Biswal
Venue(s)	NR 223
Previous Year Grade Distribution
11 14 22 26 16 16 1 EX A B C D P F
Semester	{{{semester}}}

Syllabus mentioned in ERP

Baseline model, linear programming problem, convex sets, convex functions and their properties, basic feasible solution, optimal solution, related theorems. Graphical method for solving two and three variable problems, simplex method, Big M method, degenerate LP problem, product form of inverse of a matrix, revised simplex method, duality theorems, complementary slackness principle, primal-dual simplex algorithm, sensitivity analysis, parametric programming, linear integer programming problem, Gomory cutting plane method, branch and bound algorithm, 0-1 implicit enumeration, transportation problem, assignment problem with their solution methodologies. Theory of games, two-person zero-sum games with and without saddle-points, pure and mixed strategies, graphical method of solution of a 2ï´n game, solution of an mï´n game by simplex method.

Concepts taught in class

Introduction

Operation Research is a branch of mathematics that deals with obtaining the best (optimum) results for equations or expressions under certain restrictions. Most common applications are in minimizing effort or cost, and maximizing output. Optimization Techniques are divided into two different types, namely Linear Models and Non-Linear Models. The mathematical statement of a linear model is stated as follows:

Find <math> x_1, x_2, x_3,..., x_n </math> so as to

<math>max/min : Z = \sum_{j=0}^{n} c_j x_j, j=1,2,3...n </math>

Subject to the conditions :

<math>\sum_{j=0}^{n} a_{ij} x_j (\le,=,\ge) b_i, i=1,2,3...m </math>

<math> x_j\ge0, j=1,2,3,...,n</math>