Operations research : an introduction

Operations research an introduction

This book elucidates the basic concepts and applications of operations research. Written in a lucid, well-structured and easy-to-understand language, the key topics are explained with adequate depth and self-explanatory flow charts. A wide range of solved examples and end-of-chapter exercises makes...

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Detalles Bibliográficos
Autor principal: Mariappan, P., Dr (-)
Formato: Libro electrónico
Idioma:Inglés
Publicado: Delhi, India ; Chennai, India ; Chandigarh, India : Pearson 2013.
Edición:1st edition
Colección:Always learning.
Materias:
Operations research > Mathematics > Problems, exercises, etc.
Programming (Mathematics)
College textbooks.
Ver en Biblioteca Universitat Ramon Llull:https://discovery.url.edu/permalink/34CSUC_URL/1im36ta/alma991009628246806719
Tabla de Contenidos:
  • Cover
  • Contents
  • Foreword
  • Preface
  • About the Author
  • Chapter 1: Introduction
  • 1.1 The History of Operations Research
  • 1.2 The Meaning of Operations Research
  • 1.3 Models of Operations Research
  • 1.4 Scope of Operations Research
  • 1.4.1 Agriculture
  • 1.4.2 In Organisation/Industry
  • 1.4.3 In Military Operations
  • 1.4.4 Planning
  • 1.4.5 In Transport
  • 1.4.6 In Hospitals
  • 1.4.7 In Production Management
  • 1.4.8 In Marketing
  • 1.4.9 In Finance
  • 1.4.10 L.I.C.
  • 1.5 Phases of OR
  • 1.6 Limitations of Operations Research
  • Exercise Problems
  • Review Questions
  • Chapter 2: Linear Programming Problem (LPP)
  • 2.1 Introduction
  • 2.2 General Model of the Linear Programming Problem
  • 2.3 Characteristics of an LPP
  • 2.4 Assumptions of Linear Programming
  • 2.4.1 Limitations of Linear Programming
  • 2.5 Formulation of an LPP
  • 2.6 Standard Form of an LPP
  • 2.6.1 Conversion of an LPP into Standard Form with Maximization Objective
  • 2.7 Solution to an LPP
  • 2.8 Types of Possible Solutions to an LPP
  • 2.8.1 Basic Solution
  • 2.8.2 Basic Feasible Solution
  • 2.8.3 Basic Infeasible Solution
  • 2.8.5 Unique Optimum Solution
  • 2.8.6 Multiple Optimum Solution
  • 2.8.7 Basic and Non-Basic Variables
  • 2.8.8 Degenerate Solution
  • 2.8.4 Optimal Solution
  • 2.9 Convex Set and Extreme Point
  • 2.9.1 Important Points to be Remembered
  • 2.10 Graphical Solution to an LPP
  • 2.11 Simplex Methods
  • 2.11.1 Simplex Method-I/Ordinary Simplex Method
  • 2.12 Penalty Method/Big-M Method/Charnes Method
  • 2.13 Two-phase Method
  • 2.14 The Duality Concept in a Linear Programming
  • 2.14.1 Definition of the Dual problem
  • 2.14.2 Standard Form of the Primal
  • 2.14.3 Standard Form of the Dual
  • 2.14.4 Structural and Computational Relationship Between Primal and Dual Problems
  • 2.14.5 In Matrix Notation (Primal & Dual).
  • 2.14.6 Shadow Price (Dual Price/Accounting Price)
  • 2.14.7 Economic Importance of Shadow Price
  • 2.15 Dual Simplex Method (DSM)
  • 2.15.1 Canonical Form of an LPP
  • 2.16 The Revised Simplex Method (RSM)
  • 2.16.1 Type 1
  • 2.16.2 Type-II
  • 2.16.3 Type-III
  • Exercise Problems
  • Answers to the Exercise Problems
  • Review Questions
  • Chapter 3: Sensitivity Analysis (or) Post-Optimal Analysis
  • 3.1 Introduction
  • 3.2 Change in the Objective Function Co-efficient of a Non-basic Variable
  • 3.3 Change in the Objective Function Co-efficient of a Basic Variable
  • 3.4 Change in the Right-hand Side of a Constraint
  • 3.5 Change in the Column of a Non-basic Variable
  • 3.6 Adding a New Constraint
  • 3.7 Adding a New Variable
  • Exercise Problems
  • Answers to the Exercise Problems
  • Review Questions
  • Chapter 4: Transportation Problem
  • 4.1 Introduction
  • 4.1.1 The Transportation Problem can be Described as Follows
  • 4.2 Conversion of a TP into an Equivalent LPP Form
  • 4.3 Formulation of a Transportation Problem
  • 4.4 Concepts of Feasibility Basicness, and Degeneracy in the Solution
  • 4.4.1 Basic and Non-basic Cells
  • 4.5 Methods Used to Find the Solution to a Transportation Problem
  • 4.6 Description of Various Methods to Find the Initial Basic Feasible Solution
  • 4.6.1 North West Corner Rule
  • 4.6.2 Row Minima Method
  • 4.6.3 Column Minima Method
  • 4.6.4 Least Cost Method/Matrix Minima Method
  • 4.6.5 Vogel's Approximation Method
  • 4.6.6 Effectiveness of Various Methods
  • 4.7 Stepping Stone Method/Modified Distributive Method
  • 4.8 Transshipment Problems
  • 4.9 Sensitivity Analysis for Transportation Problem
  • 4.9.1 Change in the Objective Function Coefficient by a Non-basic Variable
  • 4.9.2 Change in the Objective Function Coefficient of a Basic Variable
  • 4.9.3 Increasing Both Supply Si and Demand dj by Δ
  • Exercise Problems.
  • Answers to the Exercise Problems
  • Review Questions
  • Chapter 5: Assignment Problem
  • 5.1 Introduction
  • 5.2 General Model of the Assignment Problem
  • 5.3 Conversion into an Equivalent LPP
  • 5.4 Solution to the Assignment Problem
  • 5.5 Travelling Salesman Problem
  • Exercise Problems
  • Answers to the Exercise Problems
  • Review Questions
  • Chapter 6: PERT - CPM
  • 6.1 Introduction
  • 6.1.1 Activity
  • 6.1.2 Activity Duration/Activity Time
  • 6.1.3 Event
  • 6.1.4 Network/Arrow Diagram of a Project
  • 6.2 Method for Construction of a Network
  • 6.3 Numbering the Nodes
  • 6.3.1 Dummy Activity
  • 6.3.2 Precedence Relationships
  • 6.4 Critical Path Method (CPM)
  • 6.4.1 ES and EC Time of an Activity
  • 6.4.2 Latest Start (LS) and Latest Completion (LC) Time of an Activity
  • 6.4.3 Total Slack (TS)
  • 6.4.4 Free Slack (FS)
  • 6.4.5 Independent Float (IF)
  • 6.4.6 Critical Activity and Critical Path
  • 6.5 Project Evaluation Review Technique (PERT)
  • 6.6 PERT-Cost
  • 6.6.1 Crashing
  • 6.6.2 Project Cost
  • 6.7 Resource Levelling
  • Exercise Problems
  • Answers to the Exercise Problems
  • Review Questions
  • Chapter 7: Sequencing
  • 7.1 Introduction
  • 7.1.1 Assumptions
  • 7.2 Johnson's Method (Rule)
  • 7.3 Graphical Method
  • Exercise Problems
  • Answers to the Exercise Problems
  • Review Questions
  • Chapter 8: Queuing Theory
  • 8.1 Introduction
  • 8.2 Some Queuing Terminologies
  • 8.2.1 The Input/Arrival Process
  • 8.2.2 Queue Discipline
  • 8.2.3 Service Mechanism
  • 8.2.4 Service Channel
  • 8.2.5 Maximum Capacity of the Queue
  • 8.2.6 Classification of Queues
  • 8.2.7 Methods Used to Solve a Queuing Situation
  • 8.3 Model : 1 Single Server Model with Infinite Queue (M/M/1): (∞/FCFS)
  • 8.4 Model : 2 Single Server Model with Finite Queue (M/M/1): (N/FCFS)
  • 8.5 Model : 3 Multi-server Model with Infi nite Queue (M/M/C): (∞/FCFS).
  • 8.6 Model : 4 Multi-server Model with Finite Queue (M/M/C): (N/FCFS)
  • Exercise Problems
  • Answers to the Exercise Problems
  • Review Questions
  • Chapter 9: Dynamic Programming
  • 9.1 Introduction
  • 9.1.1 Methods Used to Solve a DP
  • 9.1.2 Characteristics of a DPP
  • 9.1.3 Merits and Demerits of a DPP
  • 9.1.4 Construction of a Recursive Equation
  • 9.2 Calculus Method to Solve a DPP
  • 9.3 Tabular Method to Solve a DPP
  • 9.4 DPP Application to Solve an LPP
  • Exercise Problems
  • Answers to the Exercise Problems
  • Review Questions
  • Chapter 10: Non-Linear Programming
  • 10.1 Introduction
  • 10.2 General Structure of an NLPP
  • 10.3 Formulation of an NLPP
  • 10.4 Methods to Solve an NLPP
  • 10.4.1 Lagrangian Method for Equality Constraints
  • 10.4.2 Sufficient Conditions
  • 10.4.3 Constrained Optimization with Two or More Equality Constraints
  • 10.5 Constrained Optimization with Inequality Constraints
  • 10.5.1 Kuhn-Tucker Conditions
  • 10.6 Quadratic Programming Problem (QPP)
  • 10.7 Wolfe's Method to Solve a QPP
  • 10.8 Beals Method to Solve a QPP
  • Exercise Problems
  • Answers to the Exercise Problems
  • Review Questions
  • Appendix A
  • Appendix B
  • Index.

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