MC4007 Operations Research Syllabus:
MC4007 Operations Research Syllabus – Anna University PG Syllabus Regulation 2021
COURSE OBJECTIVES:
To provide the concept and an understanding of basic concepts in Operations Research techniques for Analysis and Modeling in Applications.
To understand , develop and solve mathematical model of linear programming problems
To understand , develop and solve mathematical model of Transport and assignment problems
To Understand network modeling for planning and scheduling the project activities
UNIT I LINEAR PROGRAMMING MODELS
Formulation of LPP, Graphical solution of LPP. Simplex Method, Artificial variables: big-M method, degeneracy and unbound solutions.
UNIT II TRANSPORTATION AND ASSIGNMENT MODELS
Formulation – Methods for finding basic Feasible Solution – Optimality Test – MODI method – Degeneracy in Transportation Problem -Unbalanced Transportation Problem. Assignment Method: Mathematical formulation of assignment models – Hungarian Algorithm – Variants of the Assignment problem
UNIT III SCHEDULING BY PERT AND CPM
Introduction – Rules to frame a Network – Fulkerson’s Rule to numbering of events – Activity, Times – Critical Path Computation – Slack and Float – PERT- Steps and computing variance, Merits and demerits of PERT, CPM- Time estimating & Limitations, Comparison between PERT & CPM.
UNIT VI QUEUEING MODELS
Characteristics of Queueing Models–Poisson Queues-(M /M/1):(FIFO/∞/∞), (M / M / 1) : (FIFO / N / ∞), (M / M / C) : (FIFO / ∞ / ∞), (M / M / C) : (FIFO / N / ∞)models.
UNIT V GAME THEORY
Competitive game, rectangular game, saddle point, minimax (maximin) method of optimal strategies- value of the game. Solution of games with saddle points, dominance principle. Rectangular games without saddle point – mixed strategy for 2 X 2 games.
SUGGESTED ACTIVITIES:
1. Do some research on nutrients that are essential for a balanced diet. Select three or four nutrients and constraints on it. Explore the framework of LPP. Formulate an LPP with suitable objective function and constraints.
2. Identify some electricity distribution centers and areas which have requirements. Think of the objective and try to provide the solution framework.
3. Break down the stages of completing a construction of a house (like Start, Framing, Plumbing etc…) and find the minimum days to complete the construction.
4. Try to observe the customer arrival rate in a departmental store near your residence for a week. Also the service rate rendered. Make your inference on appointing an extra salesgirl.
5. Decision making is very crucial. Consider the situation where two companies share a market, in which they currently make Rs 50, 00,000 each. Both need to determine whether they should advertise. For each company advertising costs Rs 20, 00,000 and captures Rs 30, 00, 000 from the competitor provided the competitor doesn’t advertise. What should the companies do?
COURSE OUTCOMES:
CO1:Understand and apply linear programming to solve operational problem with constraints
CO2:Apply transportation and assignment models to find optimal solution
CO3:Prepare project scheduling using PERT andCPM
CO4:Identify and analyze appropriate queuing models to reduce the waiting time in queue.
CO5:Choose the best strategy using decision making methods under game theory.
TOTAL: 45 PERIODS
REFERENCES
1. Taha H.A., “Operations Research: An Introduction”, 10th Edition, Prentice Hall of India, New Delhi, 2017
2. KantiSwarup, P.K. Gupta, Man Mohan, “Operations Research”, 15th Revised Edition, S. Chand& Sons Education Publications, New Delhi, 2017
3. Ronald L Rardin, Optimization In Operations Research, 2nd Edition, Pearson Education, India, 2018
4. Jatinder Kumar, Optimization Techniques in Operations Research, LAP LAMBERT Academic Publishing, 2015
5. D.S.Hira and P.K.Gupta, Operations Research, 5th Edition, S.Chand& Sons, 2015.