Operations Research is the study of scientific approaches to decision-making. Through mathematical modeling, it seeks to design, improve and operate complex systems in the best possible way. The mathematical tools used for the solution of such models are either deterministic or stochastic, depending on the nature of the system modeled. In addition, the course will learn very powerful modeling and solution techniques for decision-making problems that are used today by many successful companies to help them save/earn millions of dollars. The module covers topics that include: linear programming, transportation, assignment, inventory control, replacement theory and game theory. Analytic techniques and computer packages will be used to solve problems facing business managers in decision environments.
Objectives
The general objectives of this course to provide a broad orientation of the field of optimization, with emphasis on basic theory and methods for continuous and discrete optimization problems in finite dimension, and it also gives some insight into its use for analyzing practical optimization problems.
Course Units
7 Units · 48 Hrs
Introduction
History of Operations Research
Stages of Development of Operations Research
Relationship between Manager and OR Specialist
OR Tools and Techniques
Applications of Operations Research
Limitations of Operations Research
Introduction to Linear Programming
Linear Programming Problem Formulation
Formulation with Different Types of Constraints
Graphical Analysis of Linear Programming
Graphical Linear Programming Solution
Multiple Optimal Solutions
Unbounded Solution
Infeasible Solution
Basics of Simplex Method
Simplex Method Computation
Simplex Method with More Than Two Variables
Primal and Dual Problems
Economic Interpretation
Transportation Problems Definition
Transportation Problem Linear Form
North West Corner Method
Least Cost Method
Vogel's Approximation Method
Degeneracy in Transportation
Modified Distribution Method (MODI)
Unbalanced Transportation Problems
Profit Maximization Problems
Transshipment Problems
Assignment Problem Structure
Hungarian Method
Unbalanced Assignment Problem
Infeasible Assignment Problem
Maximization Assignment Problem
Crew Assignment Problem
Basis of Queuing Theory
Elements of Queuing Theory
Kendall's Notation
Operating Characteristics of a Queuing System
Classification of Queuing Models
Inventory Classification
Inventory Costs
Economic Order Quantity (EOQ)
Inventory Models with Deterministic Demand
ABC Analysis
Introduction
Replacement of Capital Equipment Depreciated with Time
Replacement by Alternative Equipment
Group Replacement Policy
Individual Replacement Policy
Introduction
Characteristics of Game Theory
Two Person Zero Sum Games
Pure Strategy
Dominance Theory
Mixed Strategies (2×2 Games)
Mixed Strategies (m×2 Games)
Algebraic Method
Graphical Method
Teaching Methods
The general teaching pedagogy includes class lectures, presentations, group works, case studies, guest lecturers research works, project works, assignments (Theoretical and Practical). The teaching faculty will determine the choice of teaching pedagogy and encouraged to select software tools as per the requirements of topics for practical activities.
References & Books
Hillier, F.S.& Lieberman, G.J. (1995). Introduction to Operations Research, 7th edition. The McGraw-Hill Companies, Inc.
Natarajan, A. M.; Balasubramani, P. & Tamilarasi, A. (2007). Operations Research. Pearson Education Inc.
Sharma, J.K. (2009). Operational Research: Theory and Application. Macmillan Publishers India Ltd.
Taha, H.A. (2017). Operations Research: A Introduction, 10th edition, Global edition, Pearson Education, Inc. Pearson Prentice Hall.
Wagner, H. N. (2003). Operations Research by, Prentice hall. N D Vohra, Tata McGraw-Hill.
Winston, L.W. (2004). Operations Research: Applications and Algorithms, Indian University, 4th edition.