## OPERATIONAL RESEARCH

Description

Operations Research is an applied mathematics subject and is also a course in many engineering and management programmes. This course is designed for those who want to learn Operational Research (OR) and practitioners in their respective professionals. Operations Research introduces several topics like Linear Programming, Transportation problems, Assignment problems, and advanced duality issues. Here you will learn organization operations and use mathematical modelling, computer software or other analytical approaches to find more effective ways of working. Thus, at the end of this course, you will understand and formulate linear programming problems and applications.

Operations research (OR) is an analytical method of problem-solving and decision making. This is useful in the management of organizations. In operations research, problems are broken down into essential components and then solved in defined steps by mathematical analysis.

Syllabus

• Unit-1: Introduction to Operations Research
• Introduction
• Scope of Operations Research
• Features of Operations Research
• Phases of Operations Research
• Types of Operations Research Models
• Operations Research Methodology
• Operations Research Techniques and Tools
• Unit-2: Linear Programming
• Introduction
• Linear Programming Problem
• Requirements of LPP
• Mathematical Formulation of LPP
• Graphical Methods to Solve Linear Programming Problems
• Applications
• Limitations
• Unit-3: Graphical Analysis of Linear Programming Problems
• Introduction
• Graphical Analysis
• Some Basic Definitions
• Graphical Methods to Solve LPP
• Unit-4: Simplex Method
• Introduction
• Standard Form of LPP
• The fundamental theorem of LPP
• A solution of LPP – Simplex Method
• Big M-Method
• Solved Problems on Minimization
• Unit-5: Duality
• Dual of an LP
• Writing the Dual
• Duality Results
• Primal-Dual Relationship
• Formulation of Dual Problem
• Unit-6: Transportation problem
• Balanced Transportation Problem
• Northwest Method
• Least Cost Method
• Vogel’s Approximation Method
• Transportation Algorithm (MODI Method)
• Degeneracy
• Unbalanced Transportations Problem
• Unit-7: Assignment Problem
• Balanced Assignment Problem
• The Hungarian Algorithm
• Unbalanced Assignment Problem
• Unit-8: PERT/CPM
• Network Scheduling by PERT / CPM
• Network and Basic Components
• Rules of Network Construction
• CPM Analysis
• PERT
• The distinction between PERT and CPM
• Unit-9: Queuing Theory
• Introduction
• Mathematical Analysis of Queuing Process
• Properties of Queuing System
• Notations
• Service System
• Single Channel Models
• Multiple Service Channels
• Applications of Queuing Theory
• Limitations of Queuing Theory
• Unit-10: Game Theory
• Games and Strategies – Pure and Mixed Game
• Principle of Dominance
• Maximin – Minimax Principle