Unit 1

Basics of Operational Research: Origin & Development of Operational Research, Definition and Meaning of Operational Research, Different Phases of an Operational Research Study, Scope and Limitations of Operational Research, Mathematical Modeling of Real Life Problems.

Unit 2

Linear Programming: Linear Programming Problem Formulation, solution by Graphical Method, Theory of Simplex Method, Simplex Algorithm, Two phase Method, Charnes-M Method, Degeneracy, Theory of Duality, Dual-simplex method.

Unit 3

Transportation problem (TP) and its formulation. Finding basic feasible solution of TP using North- West Corner Rule, Least Cost and Vogel’s Approximation Method, MODI method for finding optimal solution for TP, Assignment problem and its formulation, Hungarian method for solving Assignment problem, Transshipment and Travelling salesmen problem.

Unit 4

Introduction to Dynamic Programming. The recursive Equation Approach, Characteristics of Dynamic Programming, Recursive nature of computations in Dynamic programming problem – Forward and Backward Recursion, Cargo-loading Model–Work-Force size model – Equipment Replacement model.

Unit 5

Network Representation, Critical Path (CPM) computations, Construction of the Time Schedule, Linear programming formulation of CPM – PERT calculations. Concepts of Game problem, Two- person zero-sum game, Pure and Mixed strategies, Saddle point and its existence Dominance. Fundamental Theorem of Rectangular games, Concept of Dominance and Graphical method of
solving Rectangular games. Relationship between rectangular game and Linear Programming Problem. Solving rectangular game by Simplex method.

Practical/Lab to be performed on a computer using Excel/Statistical packages

1. To solve Linear Programming Problem using Graphical Method with
   1. Unbounded solution
   2. Infeasible solution
   3. Alternative or multiple solutions.
2. Solution of LPP with simplex method.
3. Problem solving using Charnes-M method.
4. Problem solving using Two Phase method.
5. Illustration of following special cases in LPP using Simplex method
   1. Unrestricted variables
   2. Unbounded solution
   3. Infeasible solution
   4. Alternative or multiple solutions.
6. Problems based on Dual simplex method.
7. Solution of Transportation Problem.
8. Solution of Assignment Problem.
9. Solution of Travelling Salesman Problem.
10. Solution of Dynamic programming problems
11. Solution of game problems

Course Outcome:

CO1: Ability to understand Methodology of Operations Research.
CO2: Understand the basic concepts of linear programming, theory of duality and methods for solving linear programming problems.
CO3: Understand the Mathematical formation of transportation and assignment problems and solution methods.
CO4: Ability to solve Dynamic programming problems
CO5: Understand the network representation of project works and computation of PERT-CPM

Text Books

• Hamdy A. Taha, Operations Research – An Introduction, 8thEdition, Prentice Hall.
• KantiSwarup, P.K. Gupta and Man Mohan, Operations Research, 9thEdition, S Chand and Sons.

References

1. Ravindran, D. T. Phillips and James J. Solberg: Operations Research- Principles and Practice, John Wiley & Sons, 2005.
2. F.S. Hillier. G.J. Lieberman, Introduction to Operations Research- Concepts and Cases, 9th Edition, Tata Mc-Graw Hill, 2010
3. Ronald L. Rardin, Optimization in Operations Research, Prentice Hall, 1999