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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: 411

SUMMARY

Course Status : Upcoming
Course Type : Core
Duration : 15 weeks
Start Date : 13 Jan 2020
End Date : 25 Apr 2020
Exam Date : 10 May 2020
Enrollment Ends : 28 Feb 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.

    INSTRUCTOR BIO







    Professor Bibhas C. Giri

    Jadavpur University
    Dr. Bibhas C. Giri is a Professor of the Department of Mathematics, Jadavpur University, Kolkata. He did his M.Sc. in Mathematics and Ph.D. in Operations Research, from Jadavpur University. He has been teaching Operations Research course at PG level since 2005. Professor Giri has published so far 10 book chapters and about 200 research papers in international journals, which have been cited over 6650 times in total (google scholar citation), and supervised 12 Ph.D. students. He is the recipient of Alexander von Humboldt Fellowship, Germany; Fulbright Fellowship, US.A. and Commonwealth Fellowship, U.K.. He has successfully run this MOOCs course in 2019 in Swayam platform with 702 enrollments.

    COURSE CERTIFICATE

    The course is free to enroll and learn. If you want a certificate, you have to register and appear in the exam in person at any of the designated exam centres.
    The exam is optional for a fee of Rs 1000/- (Rupees one thousand only).
    Date and Time of Exam: 10 May, 2020, Morning session 9am to 12 noon.
    The online registration form has to be filled and the certification exam fee needs to be paid. More details will be made available when the exam registration form is published. If there are any changes, it will be mentioned then.
    Please check the form for more details on the cities where the exams will be held, the conditions you agree to when you fill the form etc. 

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