UMA031 OPTIMIZATION TECHNIQUES
Scope of Operations Research: Introduction to linear and non-linear programming formulation
of different models.
Linear Programming: Geometry of linear programming, Graphical method, Linear programming (LP) in standard form, Solution of LP by simplex and revised simplex methods, Exceptional cases in LP, Duality theory, Dual Simple method, Sensitivity analysis.
Network Analysis: Transportation problem (with transshipment), Assignment problem, Traveling-salesman problem, Shortest route problem, Minimal spanning tree, Maximum flow problem.
Integer Programming: Branch and bound algorithm, Traveling salesman problem.
Dynamic programming: Forward recursions, General problem, Reliability problem, Capital budgeting problem, Cargo-loading problem.
CPM and PERT: Drawing of networks, Removal of redundancy, Network computations, Free slack, Total slack, Crashing, Resource allocation.
Programming: Characteristics, Concepts of convexity, maxima and minima of
functions of n-variables using Lagrange multipliers and Kuhn-Tuker conditions,
One dimensional search methods, Fibonacci, golden section method and gradient
methods for unconstrained problems.
Software: Introduction to software for optimization techniques (TORA).
Ravindran A, Phllips D.T. and Solberg J.J. Operation Research: Principles and Practice, John Wiley (2007).