1 M.C.A. SEMESTER - III 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
2 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.
3 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
4 1 NATURE OF OPERATION RESEARCH (OR) Unit Structure : 1.0 1.1 1.2 1.3 1.4 1.5 Objectives Introduction History of OR Nature of OR Application Areas Unit End Exercise 1.0 OBJECTIVES After going through this unit you will be able to: Understand the need of introducing OR Define OR Understand History of OR Describe Nature of OR Know the application areas of OR 1.1 INTRODUCTION In any organization, managers have to take decisions while, planning the activities. Generally decisions were taken based on past experiences, the style of working of the manager and judgement. However, decisions taken in this manner had the risk of making wrong decisions which would affect the cost of the project. To overcome this difficulty managers have started using scientific methods to evaluate the various alternatives so that proper decisions can be taken. With the increased complexities of life, the business has grown tremendously in different directions and hence there is necessity to modify the organisations relevant to business. Decision making is a requirement in business and as any problem becomes complicated with large input data, the analysis becomes difficult and hence an effective use of systematic approach is needed. This has created the necessity of scientific methods for decision making in business.