CRC 91824 C000.tex 7/10/2008 18: 27 Page i OPERATIONS RESEARCH METHODOLOGIES CRC 91824 C000.tex 7/10/2008 18: 27 Page ii The Operations Research Series Series Editor: A Ravi Ravindran Dept of Industrial & Manufacturing Engineering The Pennsylvania State University, USA Integer Programming: Theory and Practice John K Karlof Operations Research Applications A Ravi Ravindran Operations Research: A Practical Approach Michael W Carter and Camille C Price Operations Research Calculations Handbook Dennis Blumenfeld Operations Research and Management Science Handbook A Ravi Ravindran Operations Research Methodologies A Ravi Ravindran Forthcoming Titles Applied Nonlinear Optimization in Modeling Environments Janos D Pinter Operations Research Calculations Handbook, Second Edition Dennis Blumenfeld Probability Models in Operations Research Richard C Cassady and Joel A Nachlas CRC 91824 C000.tex 7/10/2008 18: 27 Page iii OPERATIONS RESEARCH METHODOLOGIES EDITED BY A RAVI RAVINDRAN Boca Raton London New York CRC Press is an imprint of the Taylor & Francis Group, an informa business This material was previously published in Operations Research and Management Science Handbook © 2008 by Taylor and Francis CRC Press Taylor & Francis Group 6000 Broken Sound Parkway NW, Suite 300 Boca Raton, FL 33487-2742 © 2009 by Taylor & Francis Group, LLC CRC Press is an imprint of Taylor & Francis Group, an Informa business No claim to original U.S Government works Version Date: 20130925 International Standard Book Number-13: 978-1-4200-9183-0 (eBook - PDF) This book contains information obtained from authentic and highly regarded sources Reasonable efforts have been made to publish reliable data and information, but the author and publisher cannot assume responsibility for the validity of all materials or the consequences of their use The authors and publishers have attempted to trace the copyright holders of all material reproduced in this publication and apologize to copyright holders if permission to publish in this form has not been obtained If any copyright material has not been acknowledged please write and let us know so we may rectify in any future reprint Except as permitted under U.S Copyright Law, no part of this book may be reprinted, reproduced, transmitted, or utilized in any form by any electronic, mechanical, or other means, now known or hereafter invented, including photocopying, microfilming, and recording, or in any information storage or retrieval system, without written permission from the publishers For permission to photocopy or use material electronically from this work, please access www.copyright.com (http:// www.copyright.com/) or contact the Copyright Clearance Center, Inc (CCC), 222 Rosewood Drive, Danvers, MA 01923, 978-750-8400 CCC is a not-for-profit organization that provides licenses and registration for a variety of users For organizations that have been granted a photocopy license by the CCC, a separate system of payment has been arranged Trademark Notice: Product or corporate names may be trademarks or registered trademarks, and are used only for identification and explanation without intent to infringe Visit the Taylor & Francis Web site at http://www.taylorandfrancis.com and the CRC Press Web site at http://www.crcpress.com CRC 91824 C000.tex 7/10/2008 18: 27 Page v Contents Preface ix Acknowledgments xi Editor xiii Contributors xv History of Operations Research xvii Linear Programming Katta G Murty 1.1 Brief History of Algorithms for Solving Linear Equations, Linear Inequalities, and LPs 1.2 Applicability of the LP Model: Classical Examples of Direct Applications 1.3 LP Models Involving Transformations of Variables 1.4 Intelligent Modeling Essential to Get Good Results, an Example from Container Shipping 1.5 Planning Uses of LP Models 1.6 Brief Introduction to Algorithms for Solving LP Models 1.7 Software Systems Available for Solving LP Models 1.8 Multiobjective LP Models 1-1 1-1 1-4 1-12 1-18 1-22 1-26 1-31 1-31 Nonlinear Programming Theodore B Trafalis and Robin C Gilbert 2-1 2.1 Introduction 2-1 2.2 Unconstrained Optimization 2-3 2.3 Constrained Optimization 2-15 2.4 Conclusion 2-19 Integer Programming Michael Weng 3-1 3.1 Introduction 3-1 3.2 Formulation of IP Models 3-3 3.3 Branch and Bound Method 3-7 3.4 Cutting Plane Method 3-12 3.5 Other Solution Methods and Computer Solution 3-15 Network Optimization Mehmet Bayram Yildirim 4.1 Introduction 4.2 Notation 4.3 Minimum Cost Flow Problem 4-1 4-1 4-2 4-3 v CRC 91824 C000.tex 7/10/2008 18: 27 Contents vi 4.4 4.5 4.6 4.7 4.8 4.9 Page vi Shortest Path Problem Maximum Flow Problem Assignment Problem Minimum Spanning Tree Problem Minimum Cost Multicommodity Flow Problem Conclusions 4-4 4-8 4-13 4-14 4-18 4-19 Multiple Criteria Decision Making Abu S M Masud and A Ravi Ravindran 5.1 Some Definitions 5.2 The Concept of “Best Solution” 5.3 Criteria Normalization 5.4 Computing Criteria Weights 5.5 Multiple Criteria Methods for Finite Alternatives 5.6 Multiple Criteria Mathematical Programming Problems 5.7 Goal Programming 5.8 Method of Global Criterion and Compromise Programming 5.9 Interactive Methods 5.10 MCDM Applications 5.11 MCDM Software 5.12 Further Readings 5-1 5-3 5-4 5-5 5-6 5-8 5-15 5-19 5-27 5-29 5-34 5-35 5-35 Decision Analysis Cerry 6.1 6.2 6.3 6.4 6.5 6.6 6.7 M Klein Introduction Terminology for Decision Analysis Decision Making under Risk Decision Making under Uncertainty Practical Decision Analysis Conclusions Resources 6-1 6-1 6-2 6-3 6-17 6-21 6-28 6-29 Dynamic Programming Jos´e 7.1 7.2 7.3 7.4 A Ventura 7-1 Introduction 7-1 Deterministic Dynamic Programming Models 7-3 Stochastic Dynamic Programming Models 7-19 Conclusions 7-24 Stochastic Processes Susan 8.1 8.2 8.3 8.4 8.5 H Xu 8-1 Introduction 8-1 Poisson Processes 8-7 Discrete-Time Markov Chains 8-14 Continuous-Time Markov Chains 8-27 Renewal Theory 8-39 CRC 91824 C000.tex 7/10/2008 18: 27 Page vii Contents vii 8.6 Software Products Available for Solving Stochastic Models 8-46 10 11 12 13 Queueing Theory Natarajan Gautam 9.1 Introduction 9.2 Queueing Theory Basics 9.3 Single-Station and Single-Class Queues 9.4 Single-Station and Multiclass Queues 9.5 Multistation and Single-Class Queues 9.6 Multistation and Multiclass Queues 9.7 Concluding Remarks 9-1 9-1 9-2 9-8 9-21 9-28 9-34 9-37 Inventory Control Farhad Azadivar and Atul Rangarajan 10.1 Introduction 10.2 Design of Inventory Systems 10.3 Deterministic Inventory Systems 10.4 Stochastic Inventory Systems 10.5 Inventory Control at Multiple Locations 10.6 Inventory Management in Practice 10.7 Conclusions 10.8 Current and Future Research 10-1 10-1 10-4 10-9 10-20 10-27 10-34 10-35 10-36 Complexity and Large-Scale Networks Hari 11.1 11.2 11.3 11.4 11.5 11.6 P Thadakamalla, Soundar R.T Kumara, and R´eka Albert Introduction Statistical Properties of Complex Networks Modeling of Complex Networks Why “Complex” Networks Optimization in Complex Networks Conclusions 11-1 11-1 11-6 11-11 11-16 11-18 11-26 Simulation Catherine M Harmonosky 12.1 Introduction 12.2 Basics of Simulation 12.3 Simulation Languages and Software 12.4 Simulation Projects—The Bigger Picture 12.5 Summary 12-1 12-1 12-3 12-15 12-20 12-22 Metaheuristics for Discrete Optimization Problems Rex K Kincaid 13.1 Mathematical Framework for Single Solution Metaheuristics 13.2 Network Location Problems 13.3 Multistart Local Search 13.4 Simulated Annealing 13.5 Plain Vanilla Tabu Search 13.6 Active Structural Acoustic Control (ASAC) 13.7 Nature Reserve Site Selection 13-1 13-3 13-3 13-5 13-6 13-8 13-10 13-13 CRC 91824 C000.tex 7/10/2008 18: 27 Page viii Contents viii 13.8 Damper Placement in Flexible Truss Structures 13-21 13.9 Reactive Tabu Search 13-29 13.10 Discussion 13-35 14 Robust Optimization H J 14.1 14.2 14.3 14.4 14.5 Greenberg and Tod Morrison Introduction Classical Models Robust Optimization Models More Applications Summary 14-1 14-1 14-2 14-10 14-16 14-30 Index I-1 CRC 91824 C000.tex 7/10/2008 18: 27 Page ix Preface Operations research (OR), which began as an interdisciplinary activity to solve complex problems in the military during World War II, has grown in the past 50 years to a fullfledged academic discipline Now OR is viewed as a body of established mathematical models and methods to solve complex management problems OR provides a quantitative analysis of the problem from which the management can make an objective decision OR has drawn upon skills from mathematics, engineering, business, computer science, economics, and statistics to contribute to a wide variety of applications in business, industry, government, and military OR methodologies and their applications continue to grow and flourish in a number of decision-making fields The objective of this book is to provide a comprehensive overview of OR models and methods in a single volume This book is not an OR textbook or a research monograph The intent is that the book becomes the first resource a practitioner would reach for when faced with an OR problem or question The key features of this book are as follows: • • • • • • • • Single source guide to OR techniques Comprehensive resource, but concise Coverage of emerging OR methodologies Quick reference guide to students, researchers, and practitioners Bridges theory and practice References to computer software availability Designed and edited with nonexperts in mind Unified and up-to-date coverage ideal for ready reference This book contains 14 chapters that cover not only the fundamental OR models and methods such as linear, nonlinear, integer and dynamic programming, networks, simulation, queueing, inventory, stochastic processes, and decision analysis, but also emerging OR techniques such as multiple criteria optimization, metaheuristics, robust optimization, and complexity and large-scale networks Each chapter gives an overview of a particular OR methodology, illustrates successful applications, and provides references to computer software availability Each chapter in this book is written by leading authorities in the field and is devoted to a topic listed as follows: • • • • • • • • • • • Linear programming Nonlinear programming Integer programming Network optimization Multiple criteria decision making Decision analysis Dynamic programming Stochastic processes Queueing theory Inventory control Complexity and large-scale networks ix .. .CRC 91824 C000.tex 7/10/2008 18: 27 Page i OPERATIONS RESEARCH METHODOLOGIES CRC 91824 C000.tex 7/10/2008 18: 27 Page ii The Operations Research Series Series Editor:... Karlof Operations Research Applications A Ravi Ravindran Operations Research: A Practical Approach Michael W Carter and Camille C Price Operations Research Calculations Handbook Dennis Blumenfeld Operations. .. basic approach of operations research is employed As more research went into the development of OR, the researchers were able to CRC 91824 C000.tex 7/10/2008 History of Operations Research 18: 27