ME 1803 : OPERATIONS RESEARCH 

Syllabus

Module I 
Linear Algebra : Review of the properties of matrices and matrix operations, partitioning of matrices, vectors and Euclidean spaces, unit vectors, sum vectors, linear dependence, bases, spanning set, rank, product form of inverse, simultaneous equations, basic solutions, point sets, lines and hyper planes, convex sets, extreme points, fundamental theorem of linear programming. 

Module II 
Linear Programming : Fundamentals Theorems of Linear programming, Mathematical formulation of the problem, Assumption of Linear programming, graphical Method. Simplex Method – Slack & surplus variables, basic feasible solution, reduction of a feasible solution to basic feasible solution, artificial variables, optimality conditions. Charnes ‘M’Method. 

Module III 
Transportation Problems : Definition of a transportation model, North-west Corner Rule, Least Cost or Matrix Minima Method, Vogel’s approximation method, Degeneracy in Transportation problem. Assignment Problems Theorems of Assignment problem, Zero assignments, Unbalanced problems. Comparison with Transportation Models.

Module IV 
Game Theory : Von Neuman’s theorem, saddle points, pure and mixed strategies, formulation of primal and dual LP problems for mixed strategies, dominance, graphical solutions. Queueing Theory : Basic structures of queueing models, exponential and poisson distribution, Kendall’s Notation, Queueing models – M/M/1 and M/M/K. Simulation : Definition, Simulation Models – Monte-Carlo Simulation, Application of Simulation, Advantages and limitations of Simulation. 

References: 
1) Operations Research, Goel and Mittal, Pragti Prakasan, Meerut 
2) Operations Research, Kanti Swarup, Gupta and Manmohan, Sultan Chand and Sons  Publishers, New Delhi. 
3) Operations Research , S Kalavathy , Vikas Publishing House 
4) Introduction to operational research , C. R. Kothari Vikas Publishing House 
5) Resource Management , N.G. Nair 

Type of Questions for University Examination
Q1. Eight short answer questions of 5 marks each with two questions from each of the four modules. (8x5 = 40 marks) 
Q2 to Q5 : Two questions A & B of 15 marks from each module with option to answer either A or B. (4x15 = 60 marks