Swayam Central

# Operations Research

By Professor Bibhas C. Giri   |   Jadavpur University

Operations Research (OR) is a systematic approach of solving problems involving operations of a system by using scientific tools and techniques. It is a well-developed field with a sophisticated array of techniques that are routinely used to solve various real world problems. OR helps to make decisions better. It is regularly used in several areas such as inventory and supply chain management, marketing management, healthcare, telecommunication, finance, transportation, energy and so on. Active areas may also be at the intersection of these and many other disciplines. There are many advantages of studying OR, such as improving decision making, better control, higher productivity, better coordination, etc. In business, very few things are certain, and managers must often make decision based on their instincts instead of being able to use reliable data. OR techniques fill this void with methods that quantify issues and give business managers a better basis for making decisions. This course is a fifteen-week program introducing a number of OR tools and techniques. The objective of the course is to provide students with knowledge and skills needed to apply these tools and techniques for decision making in organizations. The course focuses on mathematical modelling and therefore, emphasis will be given to model formulation and analysis.

Learners enrolled: 1615

### SUMMARY

 Course Status : Ongoing Course Type : Core Duration : 15 weeks Start Date : 13 Jan 2020 End Date : 25 Apr 2020 Exam Date : 10 May 2020 Enrollment Ends : 08 Mar 2020 Category : Mathematics Level : Postgraduate

### COURSE LAYOUT

Week 1:  Chapter 1 – Linear  Programming  Problem
Module-1:
Mathematical Formulation of LPP and Graphical Method for Solving LPP
Module-2:  Simplex Method for Solving LPP and Big-M Method

Week 2: Chapter 1 – Linear  Programming  Problem
Module-3:
Some Special Cases in LPP
Module-4: Duality, and Solving LPP using Duality in Simplex Method
Module-5: Dual Simplex Method and Revised Simplex Method
Week 3: Chapter 2 – Transportation  and  Assignment  Problems
Module-1: Mathematical Formulation and Initial BFS of Transportation Problem
Module-2: Optimality Test by Stepping Stone Method and MODI Method, and Some Special Cases of Transportation Problem
Module-3: Assignment Problem and Its Solution by Hungarian Method, and Travelling Salesman Problem

Week 4:  Chapter 3 – Game  Theory
Module-1: Basic Concept and Terminologies, Two-person Zero-sum Game, and Game with Pure and Mixed Strategies
Module-2: Dominance Principle, Arithmetic Method, and Graphical Method for Solving  (2× n) Game
Module-3: Graphical Method for Solving (m×2) Game and Solution of  Game by Simplex Method

Week 5:  Chapter 4 – Job Sequencing  and  Replacement  Theory
Module-1:  Basic Terminologies and Assumptions of Job Sequencing, and Processing of n Jobs through 2 and 3 Machines
Module-2:  Processing n Jobs through m Machines, and Processing 2 Jobs through m Machines - Graphical Method
Module-3:  Introduction to Replacement Theory and Determination of Optimal Replacement Time
Module-4:  Selection of the Best Machine, and Individual and Group Replacement Policies

Week 6:  Chapter 5 – Inventory  Theory
Module-1: Economic Order Quantity and EOQ Models without Shortage
Module-2: EOQ models with Shortage and EPQ Models with/without Shortages
Week 7:  Chapter 5 – Inventory  Theory
Module-3:
Multi-item Inventory Models, Purchase Inventory Model, and Inventory Models with Price Breaks
Module-4: Newsboy Problem and Probabilistic Inventory Model with Instantaneous Demand and No Set up Cost
Module-5: Probabilistic Inventory Model with Uniform Demand and No Set up Cost, and Buffer Stock in Probabilistic Inventory Model

Week 8:  Revision, Assignment and Evaluation
Week 9:  Chapter 6 – Queuing  Theory
Module-1:
Basic Characteristics of Queuing System and Probability Distribution of Arrivals
Module-2
:  Probability Distribution of Departures and Model I (M|M|1):(∞|FCFS)
Module-3:
Model I. (General): (M|M|1): (∞|FCFS), and Model II. (M|M|1): (N|FCFS)
Module-4:
Model III - (M|M|s): (∞|FCFS), and Model IV - (M|Ek|1): ( ∞|FCFS)

Week 10:  Chapter 7 – Network  Analysis
Module-1:
Basic Components of Network and Critical Path Method (CPM)
Module-2: Total Float and Free Float of Activity, and CPM Model: Time-cost Optimization

Week 11:  Chapter 7 – Network  Analysis
Module-3:
Program Evaluation and Review Technique (PERT)
Module-4: LP and Dual LP Solutions to Network Problem

Week 12:  Chapter 8 – Dynamic  Programming
Module-1:
Basic Concept and Terminology, and Dynamic Programming Models I and II
Module-2: DP Model III, Solution of Discrete DP Problem and Solution of LPP by DP

Week 13:  Chapter 9 – Integer Programming
Module-1:
Introduction to Integer Programming, and Gomory's Cutting Plane Method for All IPP
Module-2
: Gomory's Cutting Plane Method for Mixed IPP, and Branch and Bound Method

Week 14:  Chapter 10 – Nonlinear  Programming
Module-1:
NLPP with Equality Constraints: Lagrange Multiplier Method
Module-2
: NLPP with Inequality Constraints: Kuhn-Tucker (KT) Conditions, and Quadratic Programming
Module-3
: Wolfe's Modified Simplex Method and Beale's Method

Week 15:  Revision, Assignment and Evaluation

### BOOKS AND REFERENCES

Taha, H.A., “Operations Research – An Introduction”, Prentice Hall, (7th Edition), 2002.
Hillier, F.S., Lieberman, G.J. , Nag, B., Basu, P.,  “Introduction to Operations Research”, McGraw Hill (10th Edition), 2017.
Sharma, S.D., “Operations Research”, Kedar Nath Ram Nath & Co. (15th Edition), 2010.
Ravindran, A. , Phillips, D. T and Solberg, J. J. , “Operations Research: Principles and Practice”, John Willey and Sons, 2nd Edition, 2009.