|Subject Code||Subject Name||Teaching Scheme (Contact Hours per week)||Credits Assigned|
|Internal Assessment||End Sem. Exam.|
[ Once in a semester ]
|Test 1||Test 2||Average|
Objectives Operations research is a scientific approach to analyzing problems and making decisions. It uses mathematics and mathematical modeling on computers to forecast the implications of various choices and identify the best alternatives.
Outcomes Operations research methodology is applied to a broad range of problems in both the public and private sectors. Many problems deal with the allocation of scarce human resources, money, materials, equipment or facilities. Applications include staff scheduling, vehicle routing, warehouse location, product distribution, quality control, traffic light phasing, police patrolling, preventive maintenance scheduling, economic forecasting, design of experiments, power plant fuel allocation, stock portfolio optimization, cost- effective environmental protection, inventory control and university course scheduling.
Unit No Contents No of. Hrs.
Unit I Nature of Operation Research : History ,Nature of OR ,Impact of OR
Unit II 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
Unit III 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
,Solution to Problems based onDegeneracy, Alternative optima ,Unbounded solutions ,Infeasible solutions
Unit IV Dual Problem :Relation between primal and dual problems, Dual simplex method, Sensitivity analysis
Unit V Transportation problem :Starting solutions. North-west corner Rule – lowest cost methods – Vogels approximation method, MODI Method, Minimization and Maximization problem
Unit VI Assignment problem :Hungarian method (Minimization and Maximization)
Travelling salesman problem :Branch & Bound technique, Hungarian method
Unit VII Sequencing Problem :2 machines n jobs ,3 machines n jobs , n machines m jobs
Unit VIII PERT and CPM :Arrow network ,Time estimates, earliest expected time, latest allowable occurrence time, latest allowable occurrence time and slack time,
Critical path ,Probability of meeting scheduled date of completion of project
,Calculation of CPM network ,Various floats for activities ,Project crashing
Unit IX Replacement theory :Replacement of items that deteriorate ,
Replacement of items that fail group replacement and individual replacement.
Unit X Decision Theory: Classification of Decisions, Steps in decision theory approach, Decision making under certainty, Decision making under uncertainty, Decision making under risk, Decision making under conflict, SIMONS’s Model
Unit XI Game theory: Two person Zero sum games, Solving simple games 2 Hrs.
Instructions for Students’ Assignments: Each candidate will submit a journal which will have case studies on Decision Theory, PERT-CPM and Replacement theory.
- Hillier F., and Lieberman, G.J. “Introduction to Operation Research”, Holden Day
- Operations Research Applications and Algorithms Waynel L. Winston Thomson
- Kambo, N.S., “Mathematical Programming Techniques”, McGraw Hill
- Operations Research : Principles and Practice 2nd edition Ravindran Wiley Production
- Operations Research, 1e, Prasad, Cengage Learning
- Optimization methods K.V. Mital& Mohan New Age
- KantiSwaroop, Gupta P.K. Man Mohan, “Operations Research”, Sultan Chand and Sons
- Taha, H.A. “Operations Research – An Introduction”, McMillan Publishing Company, NY
- Operation Research – S.D. Sharma
- Operations Research by P. K. Gupta &Hira S. Chand
- Principles of Operation Research ( with applications to managerial decisions) – H.M Wagher, PHI, New Delhi
- Operation Research –Ravindran