Contents

Preface

Chapter 1 Origin and History of Operations Research
1.1 Introduction
1.2 Evolution of Operations Research
1.2.1 World War II
1.2.2 Patrick Maynard Stuart Blackett – The Father of Operations Research
1.2.3 George Bernard Dantzig and Simplex Method
1.2.4 Post-World War II
1.3 History of Operations Research in India
1.4 Definitions of Operations Research
1.5 Models
1.5.1 Evolution of Models
1.5.2 Mathematical Model and Its Importance
1.5.3 Types of Models
1.5.4 Model Building Process
1.6 Applications of Operations Research
1.7 Advantages of Operations Research
1.8 Limitations of Operations Research
1.9 Computer Applications in Operations Research
Review Questions

Chapter 2 Linear Programming – Formulation & Applications
2.1 Linear Programming – Problem Formulation [Mathematical Modeling]
2.2 Mathematical Models
2.3 Mathematical Model Development
2.4 Assumptions in Linear Programming Problems
2.4.1 Proportionality Assumption
2.4.2 Additivity Assumption
2.4.3 Continuity / Divisibility Assumption
2.5 Applications of Linear Programming Problems
2.6 Investment Decisions
2.6.1 Investment Decision by an Individual
2.6.2 Portfolio Construction
2.6.3 Investments in Projects
2.7 Marketing Related Decisions
2.7.1 Market Research Decision - I
2.7.2 Market Research Decision - II
2.7.3 Media Planning
2.8 Stocking / Inventory Decisions
2.8.1 Vegetable Vendor Problem
2.9 Product Mix Decisions
2.9.1 Coffee Product Mix Decision
2.9.2 Toys Manufacturing Decision
2.9.3 Food Product Manufacturing Decision
2.9.4 Food Product Manufacturing Decision with Resource Re-allocation
2.9.5 Cement Manufacturing Decision
2.9.6 Make or Buy Decision
2.10 Applications in Diet Related Decisions
2.10.1 Fit n Slim Diet Problem
2.11 Applications in Agricultural Related Decisions
2.11.1 Land Allocation for Green Farming
2.12 Applications in Transportation Related Decisions
2.12.1 Bangalore Backers Transportation Problem
Review Questions

Chapter 3 Linear Programming - Graphical Solution
3.1 Definitions
3.2 Graphical Solution Procedure of LP Problems
3.3 Some Special Cases LP Problems and their Solution through Graphical Methods
Review Questions

Chapter 4 Linear Programming - Simplex Method
4.1 Definitions
4.2 Simplex Method
4.3 Simplex Algorithm
4.4 Illustration of Algebra of Simplex Method
4.5 Simplex Method – In Tabular Form
4.6 Big ‘M’ Method [Charne’s Penalty Method]
4.7 Big ‘M’ Method-Simplex Algorithm
4.8 Solution Through Simplex Method for Special Cases of Linear Programming Problems
4.9 Two-Phase Method
Review Questions

Chapter 5 Introduction to Duality
5.1 Duality
5.2 Primal-dual Solutions and their Relations
5.3 Dual-Simplex Method
Review Questions

Chapter 6 Sensitivity Analysis
Case-1: Changes made in RHS of Constraints
Case-2: Changes made in Objective Function Coefficients
Review Questions

Chapter 7 Transportation Problems
7.1 Transportation Problems-An Introduction
7.2 Mathematical Formulation of Transportation Problems
7.3 Assumptions in Transportation Problems
7.4 Transportation Problem Formulation - Example
7.5 Transportation Problem – Methods of Obtaining Initial Solution
7.6 Transportation Problem – Methods of Obtaining Optimum Solution
7.7 Transportation Problem – Variations in the Transportation Models
7.8 Transhipment Problem – Variations in the Transportation Models
Review Questions

Chapter 8 Assignment Problems
8.1 Introduction
8.2 General Structure of an Assignment Problem
8.3 Solution Methods for Assignment Problem
8.4 Assignment Algorithm / Hungarian Method
8.5 Unbalanced Assignment Problem / Asymmetric Assignment
8.6 Assignment Problem – Maximisation Models
8.7 Assignment Problems with Restrictions / Constraints
8.8 Travelling Salesperson Problem
8.9 General Structure of a Travelling Salesperson Problem
Review Questions

Chapter 9 Project Planning & Network Analysis [PERT/CPM]
9.1 Introduction to Project Management
9.2 Brief History of CPM/PERT
9.3 Project Scheduling - Network Analysis
9.4 Float
9.5 Project Activities with Deterministic Time Estimates [Critical Path Method]
9.6 Project Activities with Probabilistic Time Estimates [PERT]
9.7 Crashing Project Activities
9.8 Resource Levelling
Review Questions

Chapter 10 Introduction to Integer Linear Programming
10.1 Classification of Integer Programming Problems [IPP]
10.2 Branch and Bound Method
10.3 Gomory’s Cutting Plane Algorithm
Review Questions

Chapter 11 Inventory Models
11.1 Introduction
11.2 Categories of Inventory
11.3 Just-in-Time (JIT)
11.4 Inventory Models
11.5 Material Requirement Planning (MRP)
Review Questions

Chapter 12 Game Theory – An Introduction
12.1 Introduction
12.2 Two-person Zero-sum Game
12.2.1 Pure Strategies and Mixed Strategies
12.3 Modified Dominance Property
Review Questions

Chapter 13 Queuing Theory
13.1 Introduction
13.2 Overview of Components of Different Queueing Systems
13.3 Components of Queuing Systems
13.4 Kendall – Lee Notation
13.5 Little’s Law
13.6 Poisson Queues
Review Questions

Chapter 14 Replacement Theory
14.1 Introduction
14.2 Replacement Situations
14.3 Various Costs Associated with Maintenance / Replacement Problems
14.4 Replacement of Items whose Maintenance Cost Increases with Time and the Value of Money Remains the Same
14.5 Replacement of Items whose Maintenance Cost Increases with Time and the Time Value of Money taken into Considerations
14.6 Group Replacement Policy
Review Questions

Chapter 15 Markov Processes
15.1 Stochastic Process
15.2 State and State Variables
15.3 Markov Process
15.4 Markovian Property
15.5 Transition Probabilities
Review Questions

Chapter 16 Dynamic Programming
16.1 Introduction
16.2 Bellman’s Principle of Optimality
16.3 Characteristics of Dynamic Programming
16.4 Forward Procedure and Backward Procedure in Dynamic Programming
16.5 Applications of Dynamic Programming
16.6 Workforce Size Model
16.7 Inventory Model
16.8 Cargo Loading Problem
16.9 Capital Budgeting Problem
Review Questions

Chapter 17 Decision Theory
17.1 Introduction
17.2 Good Vs Bad Decisions
17.3 Decision Making Process
17.4 Terminologies in Decision Theory
17.5 Types of Decision-Making Environments
17.5.1 Decision-Making under Certainty
17.5.2 Decision-Making under Uncertainty
17.5.3 Decision-Making under Risk
17.6 Expected Value of Monetary Value
17.7 Expected Opportunity Loss
17.8 Expected Value of Perfect Information (EVPI)
17.9 Decision Trees
17.10 Posterior Probabilities and Bayesian Analysis
Review Questions

Chapter 18 Sequencing Problem
18.1 Introduction
18.2 Notations
18.3 Terminologies
18.4 Assumptions
18.5 Processing n Jobs in Two Machines
18.6 Processing n Jobs through Three Machines
18.7 Processing 2 Jobs through M Machines
18.8 Processing n Jobs through M Machines using Johnson and Bellman’s Method
Review Questions

Chapter 19 Simulation
19.1 Introduction
19.2 Types of Simulation
19.3 The Simulation Process
19.4 Advantages of Simulation
19.5 Disadvantages of Simulation
19.6 Monte Carlo Simulation
19.7 Methods of Generating Random Numbers
19.8 Applications of Simulations in Management
19.9 Statistical Study Vs Simulation Study
Review Questions