Outline:
1. Convex sets, Extreme points, Convex and concave functions, properties - Linear Programming Problems: Formulation, Graphical solution, Fundamental properties of solutions - Simplex Method- Big-M Method - Two phase Method - Revised Simplex Method.
2. Duality - Primal and Dual LPP problems – Properties - Dual Simplex Method - Sensitivity analysis - Discrete changes in cost vector in requirement vector – Coefficient-matrix Parametric programming - Parameterization of cost vector and requirement vector.
3. Transportation Problem - Methods of generating Basic Feasible solution – Optimality - Modi method - Assignment Problem - Routing problems - Traveling Salesman problem.
4. Integer programming Problem - Gomory's method - Branch and bound. method. Linear Fractional programming – Variable transformation method - Updated objective function method - Bounded variable technique.
5. Simulation - Nature and need for simulation - Monte Carlo method - generation of pseudo random numbers by mid-square method, congruence multiplier method - Test for randomness - generating random variables for known probability distributions - Uniform, Exponential, Erlangian, Poisson, Normal Distributions - Applications to simple problems in Operations Research.
Books:
1. F.S.Hillier & G.J. Lieberman, "Introduction to Mathematical programming", McGraw-Hill International Edition.
2. H.A.Taha- "Operations Research: An Introduction", 6thEdition, Macmillan.
