Operations Research – Quantitative Analysis for Business Decisions

895

Author: Kumar A C S

ISBN: 9789380381442

Copy Right Year: 2015

Pages:  960

Binding: Soft Cover

Publisher:  Yes Dee Publishing

SKU: 9789380381442 Category:

Description

This book provides a clear understanding of the basic principles of the various principles of Operations Research. It would serve as a comprehensive textbook on the subject, which would fill the gap being experienced by the students on the subject at present. The contents of the book are so designed that they will satisfy the syllabus requirements for the B.Tech. and MBA programmes of all Indian Universities.

Additional information

Weight 1.15 kg
Dimensions 23 × 16 × 5 cm

Table of Content

Foreword
Preface
Acknowledgements
CHAPTER 1 INTRODUCTION TO OPERATIONS RESEARCH
1.1 Origin and Development of Operations Research
1.2 Meaning of Operations Research
1.3 Various Definitions of Operations Research
1.4 Scope of Operations Research
1.4.1 Agriculture
1.4.2 Finance
1.4.3 Industry
1.4.4 Production Management
1.4.5 Marketing Management
1.4.6 Personnel Management
1.5 Principal Characteristics of Operations Research
1.5.1 Inter-disciplinary Approach
1.5.2 Holistic Approach
1.5.3 Imperfectness of Solutions
1.5.4 Use of Scientific Research
1.5.5 Optimization of the Total Output
1.6 Models in Operations Research
1.7 Classification of Operations Research Models
1.7.1 Iconic (Physical) Models
1.7.2 Analogue Models
1.7.3 Mathematical (Symbolic) Models
1.7.4 Combined Analogue and Mathematical Models
1.8 Phases of Operations Research
1.8.1 Formulating the Problem
1.8.2 Constituting the Model
1.8.3 Deriving the Solution from the Model
1.8.4 Testing and Updating the Model
1.8.5 Controlling the Solution
1.8.6 Implementing the Solution
1.9 Advantages of Operations Research
1.9.1 Optimal Use of the Production Factors
1.9.2 Improved Quality of the Solution
1.9.3 Preparation of Future Managers
1.9.4 Scope for Modification of Solution
1.9.5 Possibility of Alternate Solutions
1.10 Limitations of Operations Research
1.10.1 Limited Practical Application
1.10.2 Reliability of the Proposed Solution
1.10.3 Cost of Time and Money
1.10.4 Lack of Feasibility of Combining Two or More Objectives
Summary
Review Questions
Objective Questions
Descriptive Questions
CHAPTER 2 ALLOCATION—LINEAR PROGRAMMING
2.1 Allocation
2.1.1 Additive Property
2.1.2 Multiplicative Property
2.2 Formulation of Problems in Linear Programming Model
2.2.1 LP Formulation for Product Mix Problem
2.2.2 LP Formulation Problem on Transportation
2.2.3 LP Formulation Problem on Inventory
2.2.4 LP Formulation Problem on Marketing
2.2.5 LP Formulation Problem on Advertising
2.2.6 LP Formulation Problem on Agriculture
2.3 Solution of LP Problems
2.3.1 Solution by Graphical Method
2.3.2 Special Cases in LP Problems
2.3.2.1 Degenerate solution
2.3.2.2 Unbounded solution
2.3.2.3 Multiple (alternate) optimal solutions
2.3.2.4 Inconsistent constraints
2.4 Simplex Method
2.4.1 General Form of LP Problem
2.4.2 Some Important Definitions
2.4.3 Solution of LP Problems by Simplex Method
2.4.3.1 Steps in the simplex  procedure
2.4.3.2 Starting simplex table
2.4.3.3 Optimality test
2.5 Artificial Variables Technique
2.5.1 Two-Phase Method
2.5.1.1 Phase I: Elimination of the artificial variables
2.5.1.2 Phase II: Application of simplex method
2.5.2 Big-M Method
2.6 Unrestricted Variables
2.7 Unbounded Solution
2.8 Degeneracy in Linear Programming
2.8.1 Resolution of Degeneracy by Generalized Simplex Method
Summary
Review Questions
Objective Questions
Descriptive Questions
Exercise Problems
CHAPTER 3 DUALITY IN LINEAR PROGRAMMING
3.1 General Rules for Converting the Primal into Dual
3.2 Fundamental Duality Theorems
3.3 Problems to Write the Dual from the Given Primal Problem
3.4 Problems to Solve the Dual to Find the Optimal Solution of the Primal
Summary
Review Questions
Objective Questions
Descriptive Questions
Exercise Problems
CHAPTER 4 ASSIGNMENT MODEL
4.1 Statement of the Problem
4.2 Mathematical Formulation of the Assignment Problem
4.3 Reduction Theorem
4.4 Solution Procedure of the Assignment Problem
4.5 Travelling Salesman Problem
Summary
Review Questions
Objective Questions
Descriptive Questions
Exercise Problems
CHAPTER 5 SEQUENCING
5.1 Introduction
5.2 Johnson’s Algorithm
5.2.1 Processing of n Jobs through m Machines
5.2.2 Processing of n Jobs, and 2 Machines, with the Same Processing Order Through the Two Machines for all the n Jobs
5.2.3 Processing of n Jobs, and 3 Machines, with the Same Processing Order Through the Three Machines for all the n Jobs
5.2.4 Processing of n Jobs, and m Machines, with the Same Processing Order Through all the m Machines for all the n Jobs
5.2.5 Processing of 2 Jobs, through m Machines, and the Processing Order of the 2 Jobs through all the m Machines being not Necessarily the Same
Summary
Review Questions
Objective Questions
Descriptive Questions
Exercise Problems
CHAPTER 6 TRANSPORTATION PROBLEM
6.1 Mathematical Formulation of the Problem
6.2 To find the Basic Feasible Solution (BFS)
6.2.1 North-West Corner Method
6.2.2 Least Cost Entry Method
6.2.3 Unit Cost Penalty Method or Vogel’s Approximation Method (VAM)
6.3 Unbalanced Transportation Problem
6.4 Degeneracy in Transportation Problems
Summary
Review Questions
Objective Questions
Descriptive Questions
Exercise Problems
CHAPTER 7 REPLACEMENT
7.1 Replacement of Capital Cost Items
7.2 Replacement of Capital Cost Items when Money’s Worth (over time) is Considered
7.3 Replacement of Low-Cost Items in Bulk Quantities (Group Replacement)
Summary
Review Questions
Objective Questions
Descriptive Questions
Exercise Problems
CHAPTER 8 INVENTORY CONTROL
8.1 Objective of an Inventory Problem
8.1.1 Controllable Variables
8.1.2 Uncontrollable Variables
8.1.2.1 Cost variables
8.1.2.2 Other variables
8.2 Need of Inventory
8.3 Inventory Models
8.3.1 Deterministic Models
8.3.2 Probabilistic Models
8.4 MODEL I: Economic Lot Size Model with Uniform Rate of Demand, Infinite Production Rate and Having No Shortages
8.4.1 Description of the Model
8.5 MODEL II: Economic Lot Size Model with Different Rates of Demand in Different Production Cycles, Infinite Production Rate and having No Shortages
8.6 MODEL III: Economic Lot Size Model with Uniform Rate of Demand, Finite Rate of Replenishment and Having no Shortages
8.7 MODEL IV: Deterministic Models with Shortages and Backlogging (Fixed Time Model) with Uniform Rate of Demand ‘Q’ to be fulfilled in Constant Time t–Infinite Rate of Production and having Shortages which are to be Fulfilled
8.8 MODEL V: ELS Model with Uniform Rate of Demand, Infinite Rate of Production having Shortages which are to be Fulfilled (Varying Time Model)
8.9 MODEL VI: ELS Model with Uniform Rate of Demand, Finite Rate of Production having Shortages which are to be Fulfilled
8.10 MODEL VII: Single Period Model with Discontinuous or Instantaneous Demand and No Set-up Cost Model
8.11 MODEL VIII: Single Period Model with Uniform Rate of Demand (No Set-up Cost Model)
8.12 MODEL IX: General Single Period Model of Profit Maximization with Time-Independent Cost
8.13 MODEL X: Purchase Inventory Model with One Price Break
8.14 MODEL XI: Purchase–Inventory Model with Two Price Breaks
8.15 Purchase Inventory Model with Multiple Price Breaks
8.15.1 To find the Optimal Order Quantity q which Minimizes the Total Cost
8.16 ABC Analysis
Summary
Review Questions
Objective Questions
Descriptive Questions
Exercise Problems
CHAPTER 9 QUEUING MODELS
9.1 Objective of Queuing Models
9.2 Service Mechanism
9.3 Operating Characteristics of a Queuing System
9.4 Queing Theory
9.4.1 Important Definitions
9.4.2 State of the System
9.4.3 Poisson Process
9.4.4 Poisson Arrivals
9.4.5 Inter-Arrival Time/Service Time Distributions (Used in Queuing Theory)
9.4.6 Erlang Distribution
9.5 Queing Theory
9.5.1 Terminology of Queing Theory
9.5.2 Objectives of Queuing Theory
9.5.3 Basic Elements of Queuing System
9.6 Queing Models
9.6.1 Poisson Arrivals and Exponential Service Times
9.7 Basic Equations of Queuing System
9.8 Classification of Queing Models
9.9 MODEL I: {(M/M/1):(∞/FCFS)}
9.9.1 Characteristics of Model 1
9.10 MODEL II: {(M/M/1):(N/FCFS)}-(Finite Queue Model)
9.10.1 Characteristics of Model II
9.11 MODEL III: {(M/M/S):(∞/FCFS)}
9.11.1 System of Differential Difference Equations
9.11.2 Solution of Equations
9.11.3 Characteristics of Model III
9.12 MODEL IV: {(M/M/S):(N/FCFS)}
9.12.1 Characteristics of Model IV
9.13 MODEL V: {(M/M/S):(M/GD)}
9.13.1 Characteristics of the Model for S = 1
9.13.2 Characteristics of the Model for S > 1
9.14 MODEL VI: {(M/Ek/1):(∞/FCFS)}
9.14.1 Characteristics of the Model
Summary
Review Questions
Objective Questions
Descriptive Questions
Exercise Problems
CHAPTER 10 THEORY OF GAMES OR COMPETITIVE STRATEGIES
10.1 A Simple Illustration to Understand the Theory of Games
10.2 Features of Competitive Games
10.2.1 Zero-Sum Game
10.2.2 Two-Person Zero-Sum Game (Rectangular Game)
10.2.3 Pay-Off Matrix (Gain Matrix)
10.2.4 Strategy of a Player
10.2.5 Difference between the Course of Action and Strategy of a Player
10.2.6 Pure Strategy
10.2.7 Mixed Strategy
10.2.8 Value of the Game (n)
10.3 Maximin or Minimax Criterion of Optimality
10.4 Saddle Point
10.5 Game Theory—Problems
10.5.1 Problems with Saddle Point
10.6 Mixed Strategies
10.7 Dominance Property: Rules of Dominance
10.8 Solution of Problems without Saddle Point
10.9 Problems without Saddle Point—Solution using Dominance
10.10 Solution of Problems by Graphical Method
10.11 Solution Methodology for Problems without Saddle Point, without Dominance, and which can NOT be reduced to either (2 × n) size or (m × 2) size
10.12 Solution of Theory of Games Problems without saddle point 637
10.13 Solution of Rectangular Games without Saddle Point by Approximate Method (Iterative Method)
10.14 Algebraic Method
10.15 Solution of Game Theory Problem By Converting into L.P. Problem
10.16 Game Theory—Additional Problems
Summary
Review Questions
Objective Questions
Descriptive Questions
Exercise Problems
CHAPTER 11 DECISION ANALYSIS
11.1 Definition of Decision Analysis
11.2 Steps in Decision-Making
11.3 Different Environments in which Decisions may be Made
11.3.1 Decision-Making Under Conditions of Certainty
11.3.2 Decision-Making Under Conditions of Uncertainty
11.3.3 Decision-Making Under Conditions of Risk
11.4 Criteria for Decision-Making Under Uncertainty
11.4.1 Maximax Criterion
11.4.2 Maximin Criterion
11.4.3 Minimax Criterion
11.4.4 Minimax Regret Criterion
11.4.5 The Criterion of Realism
11.5 Decision-Making Under Conditions of Risk
11.5.1 Solution Methods for Decision-Making Under Risk Environment
11.5.1.1 Expected value criterion
11.5.1.2 Expected value combined with variance criterion
11.6 Decision-Making Under Uncertainty
11.6.1 Laplace Criterion
11.6.2 Maximin Criterion
11.6.3 Minimax Criterion
11.6.4 Savage Minimax Regret Criterion
11.6.5 Hurwicz Criterion
11.7 Decision-Making under Risk: [Expected Monetary Value (EMV) Criterion]
11.8 Decision Tree
11.8.1 Symbols Used in the Decision Tree Approach
Summary
Review Questions
Objective Questions
Descriptive Questions
Exercise Problems
CHAPTER 12 SIMULATION
12.1 Usefulness of Simulation
12.1.1 Analytical Complexity
12.1.2 Complex Interdependence
12.1.3 Effect of Change
12.1.4 Time Compression
12.1.5 Physical Simulation
12.2 Significant Parameters of Simulation
12.2.1 State Variables
12.2.2 Event
12.2.3 Static and Dynamic Simulation Models
12.3 Monte Carlo Simulation Technique
12.4 Normal Distribution
12.4.1 Characteristics of Normal Distribution
12.4.2 How to Calculate the Variance from the Available Data?
12.4.3 How to Measure the Area Under the Normal Curve?
12.5 Simulation Languages
12.6 Types of Simulation
12.7 Advantages of Simulation
Summary
Review Questions
Objective Questions
Descriptive Questions
Exercise Problems
CHAPTER 13 NETWORK ANALYSIS (CPM AND PERT)
13.1 Critical Path Method
13.2 Program Evaluation and Review Technique
13.3 Basic Concepts of Network Analysis
13.4 Types of Activities
13.5 Drawing a Network diagram
13.6 Rules for Numbering of the Events
13.6.1 D.R. Fulkerson’s Rule (for numbering of the events)
13.7 Hints for drawing the network diagrams
13.7.1 General Hints
13.7.2 Avoiding the Loop Network
13.7.3 Dummy Activity
13.8 Critical Path Method
13.8.1 Important Terminology in CPM
13.8.2 Float
13.8.3 Time–Cost Trade-off
13.8.4 Project Cost Analysis
13.8.5 Limitations of CPM
13.9 Program Evaluation and Review Technique (PERT)
13.9.1 Calculation of the Probabilities
13.10 Comparison between CPM and PERT
Summary
Review Questions
Objective Questions
Descriptive Questions
Exercise Problems
CHAPTER 14 DYNAMIC PROGRAMMING
14.1 Some Important Terms
14.2 Basic Features (Characteristics) of Dynamic Programming Problems 14.3 Model-I: Shortest Route Problem
14.4 Model-II: Optimal Sub-Division Problems
14.5 Bellman’s Principle of Optimality
14.6 Model-III: Solution of L.P. Problems by Dynamic Programming
14.7 Model-IV: Cargo Loading Problems
14.8 Model-V: Optimization of Study Days for Examination Preparation
14.9 Capital Budgeting Problem
14.10 Reliability Problems
14.11 Warehouse problem
14.12 Product Allocation Problem
14.13 Salesmen Allocation Problem

14.14 Advertising Media Problem
Summary
Review Questions
Objective Questions
Descriptive Questions
Exercise Problems
Appendices
Index

About The Author

Dr. A. Chandra Sekhara Kumar is a Professor of Mechanical Engineering who had retired as Vice Principal from Jawaharlal Nehru Technological University College of Engineering, Hyderabad. He has more than 40 years of teaching experience in B.I.T.S., Pilani, Higher College of Technology, Muscat, Sultanate of Oman  and J.N.T.U.H., Hyderabad put together. He had taught the subject of Theory of Machines for many batches of students of B.Tech., during his long service in J.N.T.U.H., Hyderabad. Besides, he is an active Researcher in the field of Production Engineering, and so far ten research scholars obtained Ph.D under his guidance, and another five research scholars are currently working under his supervision. He has nearly 75 research publications to his credit in various reputed International and National Journals and Conferences.

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