# M.C.A. Semester III: Operations Research

OPERATIONS RESEARCH

1. Nature of Operation Research • History • Nature of OR • Impact of OR • Application Areas

2. Overview of Modeling approach • Formulating the problem • Constructing a mathematical model • Deriving a solution • Testing a model and the solution • Establishing control over the solution • Implementation issues

3. Linear Programming • Introduction • Graphical solution • Graphical sensitivity analysis • The standard form of linear programming problems • Basic feasible solutions • Simplex algorithm • Artificial variables • Big M and two phase method • Degeneracy • Alternative optima • Unbounded solutions • Infeasible solutions

4. Dual Problem • Relation between primal and dual problems • Dual simplex method

5. Transportation problem • Starting solutions. North-west corner Rule – lowest cost methods – Vogels approximation method • MODI Method

6. Assignment problem • Hungarian method

7. Travelling salesman problem • Branch & Bound technique • Hungarian method

8. Sequencing Problem • 2 machines n jobs • 3 machines n jobs • n machines m job 9. Pert and CPM • Arrow network • Time estimates, earliest expected time, latest allowable occurrence time, latest allowable occurrence time and stack • Critical path • Probability of meeting scheduled date of completion of project • Calculation of CPM network • Various floats for activities • Project crashing

10. Integer programming • Branch and bound algorithm • Cutting plane algorithm

11. Deterministic Inventory Models • Static EOQ models • Dynamic EOQ models

12. Game theory • Two person Zero sum games • Solving simple games

13. Replacement theory • Replacement of items that deteriorate • Replacement of items that fail group replacement and individual replacement.

Term work/Assignment : Each candidate will submit a journal in which at least 10 assignments based on the above syllabus and the internal test paper. Test graded for 10 marks and Practicals graded for 15 marks.

Reference : 1. Gillet, B.E., “Introduction to Operation Research : a computer oriented algorithmic approach” Tata McGraw Hill, NY 2. Hillier F., and Lieberman, G.J. “Introduction to Operation Research”, Holden Day 3. Operations Research Applications and Algorithms Waynel L. Winston Thomson 4. Optimization methods K.V. Mital & Mohan New Age 5. Operations Research : Principles and Practice 2nd edition Ravindran Wiley Production 6. Kambo, N.S., “Mathematical Programming Techniques”, McGraw Hill 7. Kanti Swaroop, Gupta P.K. Man Mohan, “Operations Research”, Sultan Chand and Sons 8. Taha, H.A. “Operations Research – An Introduction”, McMillan Publishing Company, NY 9. Operation Research – S.D. Sharma 10. Operations Research by P.K.Gupta & Hira S. Chand