Course Outline Indian Institute of Management Calcutta Programme: MBA Name of the Course: Operations Research (OM-103) for Sections B & C Core / Elective: Core Cap (for Elective): Not Applicable Credit: 3 credits Academic Year & Term: 2022-23, PGP-1, Term 2 Course Coordinator: Prof. Sumanta Basu Email: sumanta@iimcal.ac.in Instructor: Prof. Megha Sharma (Sessions 1 – 10) Instructor: Prof. Bodhibrata Nag (Sessions 11 – 20) Affiliation: IIM Calcutta Affiliation: IIM Calcutta Email: megha@iimcal.ac.in Email: bnag@iimcal.ac.in Introduction to Course /Course Description Course Objective and Key-takeaways from the course Operations Research is a discipline devoted to applying scientific methods to decision making. Operations Researchers utilize mathematical modeling techniques in concert with empirical observation and occasional experimentation to arrive at solutions to management problems in government and industry. This course introduces students to Operations Research through a combination of lectures and computer models using EXCEL/LINDO. Model formulation and use of the computer will be emphasized in applications to a broad spectrum of management problems. Programme Level Learning Goals (7) - Possess state-of-the-art knowledge of theory and practice in all functional fields of management and the ability to think critically, and apply them to diagnose and find solutions to organisational problems, even in unfamiliar or uncertain situations (Critical Thinking) - Acquire capacity to apply their professional knowledge and skills to diagnose and resolve business problems in actual organizational settings (Problem Solving) - Be able to appreciate the dynamics of Information Technology acquisition and absorption by present day business organizations and develop ability to use modern IT enabled decision support tools for improved understanding of business (Technological Competencies) International Components in your course: cases used in the course are drawn from international business practices Pre-requisites: None Required Text Book(s): “Introduction to Operations Research: Concepts and Cases” by F.S. Hillier, G.J. Lieberman, B. Nag and P. Basu, Latest Edition, McGraw Hill [HLNB] Recommended Text Book(s): None Course Pack Distribution to students: None Technology enabled learning component for your course Sessions 1-10: We will use MS Excel Solver for solving linear and integer programs. Sessions 11-20: We will use MS Excel Solver for solving problems in network optimization, queuing models, project scheduling, and goal programming problems. Session Plan S No. 1 2 3 4 5 6 7 Topic Introduction to Linear Programs (LP) • What is a linear program? • How to formulate simple linear programs? • Solving linear programs through graphical methods • Solving linear programs using MS Excel Solver Intended learning outcome The participants should be able to identify conditions that make an optimization model qualify as a linear program. They should be able to solve 2 variables LP using the graphical method and be able to use Excel solver for larger LPs. References [HLNB]: Chapter 3 Linear Programs • Anomalies: Unbounded, infeasible, and multiple optimal solutions • Advanced Formulation • Sensitivity analysis and interpretation Participants should be able to identify the common anomalies in LP, their causes and implications for real life problems. Ability to perform sensitivity analysis and understand its implication in practice Ability to formulate dual of a given linear program, and given the optimal solution to primal problem, ability to identify dual optimal solution. Participants should be able to identify special structures in LP that can be solved more efficiently. [HLNB]: Chapter 3, Chapter 6 Participants should be able to solve the transportation problem manually so as to realize why these problems are more efficient to solve. [HLNB]: Chapter 9 Participants should be able to perform sensitivity analysis and draw meaningful managerial insights. [HLNB]: Chapter 9 Understanding of the intricacies that make integer programs difficult to solve and how the LP [HLNB]: Chapter 12 Linear Programming Duality • Formulating Duals of Linear Programs • Primal-Dual Relationship Transportation & Assignment Problems • Problem Structure • Problem Formulation: LP, Network, Parameter Table • Balancing the Transportation Problem • Formulations Transportation & Assignment Problems • Basic Feasible Solution • Formulating the Dual • Optimality Conditions • Stepping Stone Method Transportation & Assignment Problems • Sensitivity Analysis • Assignment Problem Integer Linear Programs (ILP) • Does rounding-off an LP solution work? Optional reading: [HLNB]: Chapters 1 & 2 Problem Set-1 (to be uploaded) Problem Set-2 (to be uploaded) [HLNB]: Chapter 6 Problem Set-3 (to be uploaded) [HLNB]: Chapter 9 Problem Set-4 (to be uploaded) Problem Set-5 (to be uploaded) S No. 8 9 Topic • Formulating Binary Conditions Integer Linear Programs • Formulating if-else conditions • Solving ILP using MS Excel Solver Solving Integer Linear Programs • Branch and Bound Method Intended learning outcome relaxation may or may not be a good solution for ILP. Familiarity with modeling techniques that enable seemingly non-linear constraints to be formulated as integer linear constraints Participants should be able to solve integer linear program using the Branch and Bound Method Participant should be able to identify efficient and inefficient decision-making units. 10 Data Envelopment Analysis 11-12 Network Optimization To assist students learn the methodology of solving shortest path and spanning tree problems 13-14 Network Optimization: Applications in Project Management To assist students learn different project planning tools such as Critical Path Method and PERT 15-16 Dynamic Programming 17-18 Simulation 19-20 Graph Theory To provide introductory session on dynamic programming and its applications to the participants To assist students learn the concepts of discrete event simulation as applied to queuing systems To assist students learn about methodologies for solving the Traveling Salesman Problems References [HLNB]: Chapter 12 Problem Set-6 (to be uploaded) [HLNB]: Chapter 12 Problem Set-7 (to be uploaded) Reading material to be distributed in class Problem Set-8 (to be uploaded) Chapter 10 on Network Optimization Models in [HLNB] Problem Set-9 (to be uploaded) Additional reading material would be provided Problem Set-10 (to be uploaded) Chapter 11 [HLNB] Problem Set-11 (to be uploaded) Chapter 17 & 20 [HLNB] Problem Set-12 (to be uploaded) Ch. 9 [HLNB] Additional reading material would be provided Problem Set-13 (to be uploaded) Evaluation Components ü Components - ü Weightage Pre-Mid Term Quiz 20% Mid-Term Exam 30% Post-Mid Term Quiz 20% End-Term Exam 30% There will be two quizzes Pre-Mid Term conducted by Prof. Megha Sharma. The best of the two quizzes’ scores will be considered as the score for Pre-Mid Term quizzes (weightage 20%). There will be one quiz Post-Mid Term conducted by Prof. Bodhibrata Nag, which will be both computer and pen-paper based (weightage 20%).
