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MANAGEMENT

SCIENCE

AND

H A N D B O O K

OPERATIONS

RESEARCH

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: A Practical Approach

Michael W. Carter and Camille C. Price

Operations Research and Management Science Handbook

A. Ravi Ravindran

Operations Research Calculations Handbook

Dennis Blumenfeld

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

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Library of Congress Cataloging-in-Publication Data Operations research and management science handbook / editor, A. Ravi Ravindran. p. cm. -- (Operations research series) Includes bibliographical references and index. ISBN 978-0-8493-9721-9 (alk. paper)

1. Operations research--Handbooks, manuals, etc. I. Ravindran, Ravi. II. Title. III. Series. T57.6.A32 1982 658.4’034--dc22 2007019976

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Dedication

This book is dedicated to the memory of Professor G. V. Loganathan,

author of Chapter 24, who was killed in the Virginia Tech

campus tragedy on April 16, 2007.

viii Contents

Contents xi

xii Contents

• 4.3 Minimum Cost Flow Problem 4 -
• 4.4 Shortest Path Problem 4 -
• 4.5 Maximum Flow Problem 4 -
• 4.6 Assignment Problem 4 -
• 4.7 Minimum Spanning Tree Problem 4 -
• 4.8 Minimum Cost Multicommodity Flow Problem 4 -
• 4.9 Conclusions 4 -
• Abu S. M. Masud and A. Ravi Ravindran 5 - 5 Multiple Criteria Decision Making
  • 5.1 Some Definitions 5 -
  • 5.2 The Concept of “Best Solution” 5 -
  • 5.3 Criteria Normalization 5 -
  • 5.4 Computing Criteria Weights 5 -
    • Alternatives 5 - 5.5 Multiple Criteria Methods for Finite
  • 5.6 Multiple Criteria Mathematical Programming Problems 5 -
  • 5.7 Goal Programming 5 -
  • 5.8 Method of Global Criterion and Compromise Programming 5 -
  • 5.9 Interactive Methods 5 -
  • 5.10 MCDM Applications 5 -
  • 5.11 MCDM Software 5 -
  • 5.12 Further Readings 5 -
• Cerry M. Klein 6 - 6 Decision Analysis
  • 6.1 Introduction 6 -
  • 6.2 Terminology for Decision Analysis 6 -
  • 6.3 Decision Making under Risk 6 -
  • 6.4 Decision Making under Uncertainty 6 -
  • 6.5 Practical Decision Analysis 6 -
  • 6.6 Conclusions 6 -
  • 6.7 Resources 6 -
• Jos´e A. Ventura 7 - 7 Dynamic Programming
  • 7.1 Introduction 7 -
  • 7.2 Deterministic Dynamic Programming Models 7 -
  • 7.3 Stochastic Dynamic Programming Models 7 -
  • 7.4 Conclusions 7 -
• Susan H. Xu 8 - 8 Stochastic Processes
  • 8.1 Introduction 8 -
  • 8.2 Poisson Processes 8 -
  • 8.3 Discrete-Time Markov Chains 8 -
  • 8.4 Continuous-Time Markov Chains 8 -
  • 8.5 Renewal Theory 8 - Contents ix
    • Stochastic Models 8 - 8.6 Software Products Available for Solving
• Natarajan Gautam 9 - 9 Queueing Theory
  • 9.1 Introduction 9 -
  • 9.2 Queueing Theory Basics 9 -
  • 9.3 Single-Station and Single-Class Queues 9 -
  • 9.4 Single-Station and Multiclass Queues 9 -
  • 9.5 Multistation and Single-Class Queues 9 -
  • 9.6 Multistation and Multiclass Queues 9 -
  • 9.7 Concluding Remarks 9 -
• Farhad Azadivar and Atul Rangarajan 10 - 10 Inventory Control
  • 10.1 Introduction 10 -
  • 10.2 Design of Inventory Systems 10 -
  • 10.3 Deterministic Inventory Systems 10 -
  • 10.4 Stochastic Inventory Systems 10 -
  • 10.5 Inventory Control at Multiple Locations 10 -
  • 10.6 Inventory Management in Practice 10 -
  • 10.7 Conclusions 10 -
  • 10.8 Current and Future Research 10 -
• Hari P. Thadakamalla, Soundar R.T. Kumara, and R´eka Albert 11 - 11 Complexity and Large-Scale Networks
  • 11.1 Introduction 11 -
  • 11.2 Statistical Properties of Complex Networks 11 -
  • 11.3 Modeling of Complex Networks 11 -
  • 11.4 Why “Complex” Networks 11 -
  • 11.5 Optimization in Complex Networks 11 -
  • 11.6 Conclusions 11 -
• Catherine M. Harmonosky 12 - 12 Simulation
  • 12.1 Introduction 12 -
  • 12.2 Basics of Simulation 12 -
  • 12.3 Simulation Languages and Software 12 -
  • 12.4 Simulation Projects—The Bigger Picture 12 -
  • 12.5 Summary 12 -
• Rex K. Kincaid 13 - 13 Metaheuristics for Discrete Optimization Problems
  • 13.1 Mathematical Framework for Single Solution Metaheuristics 13 -
  • 13.2 Network Location Problems 13 -
  • 13.3 Multistart Local Search 13 -
  • 13.4 Simulated Annealing 13 -
  • 13.5 Plain Vanilla Tabu Search 13 -
  • 13.6 Active Structural Acoustic Control (ASAC) 13 -
  • 13.7 Nature Reserve Site Selection 13 - x Contents
  • 13.8 Damper Placement in Flexible Truss Structures 13 -
  • 13.9 Reactive Tabu Search 13 -
  • 13.10 Discussion 13 -
• H. J. Greenberg and Tod Morrison 14 - 14 Robust Optimization
  • 14.1 Introduction 14 -
  • 14.2 Classical Models 14 -
  • 14.3 Robust Optimization Models 14 -
  • 14.4 More Applications 14 -
  • 14.5 Summary 14 -
• Adedeji B. Badiru 15 - 15 Project Management
  • 15.1 Introduction 15 -
  • 15.2 Critical Path Method 15 -
  • 15.3 PERT Network Analysis 15 -
  • 15.4 Statistical Analysis of Project Duration 15 -
  • 15.5 Precedence Diagramming Method 15 -
  • 15.6 Software Tools for Project Management 15 -
  • 15.7 Conclusion 15 -
• Qianmei Feng and Kailash C. Kapur 16 - 16 Quality Control
  • 16.1 Introduction 16 -
  • 16.2 Quality Control and Product Life Cycle 16 -
  • 16.3 New Trends and Relationship to Six Sigma 16 -
  • 16.4 Statistical Process Control 16 -
  • 16.5 Process Capability Studies 16 -
  • 16.6 Advanced Control Charts 16 -
  • 16.7 Limitations of Acceptance Sampling 16 -
  • 16.8 Conclusions 16 -
• Lawrence M. Leemis 17 - 17 Reliability
  • 17.1 Introduction 17 -
  • 17.2 Reliability in System Design 17 -
  • 17.3 Lifetime Distributions 17 -
  • 17.4 Parametric Models 17 -
  • 17.5 Parameter Estimation in Survival Analysis 17 -
  • 17.6 Nonparametric Methods 17 -
  • 17.7 Assessing Model Adequacy 17 -
  • 17.8 Summary 17 -
• Bobbie L. Foote and Katta G. Murty 18 - 18 Production Systems
  • 18.1 Production Planning Problem 18 -
  • 18.2 Demand Forecasting 18 -
  • 18.3 Models for Production Layout Design 18 -
  • 18.4 Scheduling of Production and Service Systems 18 -
• C. Randy Hudson and Adedeji B. Badiru 19 - 19 Energy Systems
  • 19.1 Introduction 19 -
  • 19.2 Definition of Energy 19 -
  • 19.3 Harnessing Natural Energy 19 -
  • 19.4 Mathematical Modeling of Energy Systems 19 -
  • 19.5 Linear Programming Model of Energy Resource Combination 19 -
  • 19.6 Integer Programming Model for Energy Investment Options 19 -
  • 19.7 Simulation and Optimization of Distributed Energy Systems 19 -
  • 19.8 Point-of-Use Energy Generation 19 -
  • 19.9 Modeling of CHP Systems 19 -
  • 19.10 Economic Optimization Methods 19 -
  • 19.11 Design of a Model for Optimization of CHP System Capacities 19 -
  • 19.12 Capacity Optimization 19 -
  • 19.13 Implementation of the Computer Model 19 -
  • 19.14 Other Scenarios 19 -
• Jane L. Snowdon and Giuseppe Paleologo 20 - 20 Airline Optimization
  • 20.1 Introduction 20 -
  • 20.2 Schedule Planning 20 -
  • 20.3 Revenue Management 20 -
  • 20.4 Aircraft Load Planning 20 -
  • 20.5 Future Research Directions and Conclusions 20 -
• Aliza R. Heching and Alan J. King 21 - 21 Financial Engineering
  • 21.1 Introduction 21 -
  • 21.2 Return 21 -
  • 21.3 Estimating an Asset’s Mean and Variance 21 -
  • 21.4 Diversification 21 -
  • 21.5 Efficient Frontier 21 -
  • 21.6 Utility Analysis 21 -
  • 21.7 Black–Litterman Asset Allocation Model 21 -
  • 21.8 Risk Management 21 -
  • 21.9 Options 21 -
  • 21.10 Valuing Options 21 -
  • 21.11 Dynamic Programming 21 -
  • 21.12 Pricing American Options Using Dynamic Programming 21 -
  • 21.13 Comparison of Monte Carlo Simulation and Dynamic Programming 21 -
  • 21.14 Multi-Period Asset Liability Management 21 -
  • 21.15 Conclusions 21 -
• Donald P. Warsing 22 - 22 Supply Chain Management
  • 22.1 Introduction 22 -
  • 22.2 Managing Inventories in the Supply Chain 22 -
  • 22.3 Managing Transportation in the Supply Chain 22 -
  • 22.4 Managing Locations in the Supply Chain 22 -
  • 22.5 Managing Dyads in the Supply Chain 22 -
  • 22.6 Discussion and Conclusions 22 -
• Sowmyanarayanan Sadagopan 23 - 23 E-Commerce
  • 23.1 Introduction 23 -
  • 23.2 Evolution of E-Commerce 23 -
  • 23.3 OR/MS and E-Commerce 23 -
  • 23.4 OR Applications in E-Commerce 23 -
  • 23.5 Tools–Applications Matrix 23 -
  • 23.6 Way Forward 23 -
  • 23.7 Summary 23 -
• G.V. Loganathan 24 - 24 Water Resources
  • 24.1 Introduction 24 -
  • 24.2 Optimal Operating Policy for Reservoir Systems 24 -
  • 24.3 Water Distribution Systems Optimization 24 -
  • 24.4 Preferences in Choosing Domestic Plumbing Materials 24 -
  • 24.5 Stormwater Management 24 -
  • 24.6 Groundwater Management 24 -
  • 24.7 Summary 24 -
• Jeffery D. Weir and Marlin U. Thomas 25 - 25 Military Applications
  • 25.1 Introduction 25 -
  • 25.2 Background on Military OR 25 -
  • 25.3 Current Military Applications of OR 25 -
  • 25.4 Concluding Remarks 25 -
• P. Balasubramanian 26 - 26 Future of OR/MS Applications: A Practitioner’s Perspective
  • 26.1 Past as a Guide to the Future 26 -
  • 26.2 Impact of the Internet 26 -
  • 26.3 Emerging Opportunities 26 -

xiv Preface

Part II of the handbook contains 11 chapters discussing the OR/MS applications in specific areas. They include:

• Airlines
• E-commerce
• Energy systems
• Finance
• Military
• Production systems
• Project management
• Quality control
• Reliability
• Supply chain management
• Water resources

Part II ends with a chapter on the future of OR/MS applications. The handbook is an ideal reference book for OR/MS practitioners in business, industry, government, and academia. It can also serve as a supplemental text in undergraduate and graduate OR/MS courses at the university level.

A. Ravi Ravindran University Park, Pennsylvania

Acknowledgments

First and foremost I would like to thank the authors, who have worked diligently in writing the various handbook chapters that are comprehensive, concise, and easy to read, bridging the gap between theory and practice. The development and evolution of this handbook have also benefited substantially from the advice and counsel of my colleagues and friends in academia and industry, who are too numerous to acknowledge individually. They helped me identify the key topics to be included in the handbook, suggested chapter authors, and served as reviewers of the manuscripts. I express my sincere appreciation to Atul Rangarajan, an industrial engineering doc- toral student at Penn State University, for serving as my editorial assistant and for his careful review of the page proofs returned by the authors. Several other graduate stu- dents also helped me with the handbook work, in particular, Ufuk Bilsel, Ajay Natarajan, Richard Titus, Vijay Wadhwa, and Tao Yang. Special thanks go to Professor Prabha Sharma at the Indian Institute of Technology, Kanpur, for her careful review of several chapter manuscripts. I also acknowledge the pleasant personality and excellent typing skills of Sharon Frazier during the entire book project. I thank Cindy Carelli, Senior Acquisitions Editor, and Jessica Vakili, project coordinator at CRC Press, for their help from inception to publication of the handbook. Finally, I wish to thank my dear wife, Bhuvana, for her patience, understanding, and support when I was focused completely on the handbook work.

A. Ravi Ravindran

xv

Contributors

R´eka Albert Pennsylvania State University University Park, Pennsylvania

Farhad Azadivar University of Massachusetts–Dartmouth North Dartmouth, Massachusetts

Adedeji B. Badiru Air Force Institute of Technology Dayton, Ohio

P. Balasubramanian Theme Work Analytics Bangalore, India

Qianmei Feng University of Houston Houston, Texas

Bobbie L. Foote U.S. Military Academy (Retd.) West Point, New York

Natarajan Gautam Texas A&M University College Station, Texas

Robin C. Gilbert University of Oklahoma Norman, Oklahoma

H. J. Greenberg University of Colorado at Denver and Health Sciences Center Denver, Colorado

Catherine M. Harmonosky Pennsylvania State University University Park, Pennsylvania

Aliza R. Heching IBM T. J. Watson Research Center Yorktown Heights, New York

C. Randy Hudson Oak Ridge National Laboratory Oak Ridge, Tennessee

Kailash C. Kapur University of Washington Seattle, Washington

Rex K. Kincaid College of William and Mary Williamsburg, Virginia

Alan J. King IBM T. J. Watson Research Center Yorktown Heights, New York

Cerry M. Klein University of Missouri–Columbia Columbia, Missouri

Soundar R. T. Kumara Pennsylvania State University University Park, Pennsylvania

Lawrence M. Leemis College of William and Mary Williamsburg, Virginia

G. V. Loganathan Virginia Tech Blacksburg, Virginia

Abu S. M. Masud Wichita State University Wichita, Kansas

Tod Morrison University of Colorado at Denver and Health Sciences Center Denver, Colorado

Katta G. Murty University of Michigan Ann Arbor, Michigan

Giuseppe Paleologo IBM T. J. Watson Research Center Yorktown Heights, New York

Atul Rangarajan Pennsylvania State University University Park, Pennsylvania

A. Ravi Ravindran Pennsylvania State University University Park, Pennsylvania

Sowmyanarayanan Sadagopan Indian Institute of Information Technology Bangalore, India

Jane L. Snowdon IBM T. J. Watson Research Center Yorktown Heights, New York

xix

xx Contributors

Hari P. Thadakamalla Pennsylvania State University University Park, Pennsylvania

Marlin U. Thomas Air Force Institute of Technology Wright-Patterson AFB, Ohio

Theodore B. Trafalis University of Oklahoma Norman, Oklahoma

Jos´e A. Ventura Pennsylvania State University University Park, Pennsylvania

Donald P. Warsing North Carolina State University Raleigh, North Carolina

Jeffery D. Weir Air Force Institute of Technology Wright-Patterson AFB, Ohio

Michael Weng University of South Florida Tampa, Florida

Susan H. Xu Pennsylvania State University University Park, Pennsylvania

Mehmet Bayram Yildirim Wichita State University Wichita, Kansas

xxii History of Operations Research and Management Science

and TIMS, merged to form the Institute of Operations Research and Management Sciences (INFORMS). Another factor that accelerated the growth of operations research was the introduction of OR/MS courses in the curricula of many universities and colleges in the United States. Graduate programs leading to advanced degrees at the master’s and doctorate levels were introduced in major American universities. By the mid-1960s many theoretical advances in OR techniques had been made, which included linear programming, network analysis, integer programming, nonlinear programming, dynamic programming, inventory theory, queueing theory, and simulation. Simultaneously, new applications of OR emerged in service organizations such as banks, health care, communications, libraries, and transportation. In addition, OR came to be used in local, state, and federal governments in their planning and policy-making activities. It is interesting to note that the modern perception of OR as a body of established models and techniques—that is, a discipline in itself—is quite different from the original concept of OR as an activity, which was preformed by interdisciplinary teams. An evolution of this kind is to be expected in any emerging field of scientific inquiry. In the initial formative years, there are no experts, no traditions, no literature. As problems are successfully solved, the body of specific knowledge grows to a point where it begins to require specialization even to know what has been previously accomplished. The pioneering efforts of one generation become the standard practice of the next. Still, it ought to be remembered that at least a portion of the record of success of OR can be attributed to its ecumenical nature.

Meaning of Operations Research

From the historical and philosophical summary just presented, it should be apparent that the term “operations research” has a number of quite distinct variations of meaning. To some, OR is that certain body of problems, techniques, and solutions that has been accumulated under the name of OR over the past 50 years and we apply OR when we recognize a prob- lem of that certain genre. To others, it is an activity or process, which by its very nature is applied. It would also be counterproductive to attempt to make distinctions between “oper- ations research” and the “systems approach.” For all practical purposes, they are the same. How then can we define operations research? The Operational Research Society of Great Britain has adopted the following definition:

Operational research is the application of the methods of science to com- plex problems arising in the direction and management of large systems of men, machines, materials and money in industry, business, government, and defense. The distinctive approach is to develop a scientific model of the system, incor- porating measurement of factors such as chance and risk, with which to predict and compare the outcomes of alternative decisions, strategies or controls. The purpose is to help management determine its policy and actions scientifically. The Operations Research Society of America has offered a shorter, but similar, description:

Operations research is concerned with scientifically deciding how to best design and operate man–machine systems, usually under conditions requiring the allo- cation of scarce resources. In general, most of the definitions of OR emphasize its methodology, namely its unique approach to problem solving, which may be due to the use of interdisciplinary teams or

History of Operations Research and Management Science xxiii

due to the application of scientific and mathematical models. In other words, each prob- lem may be analyzed differently, though the same basic approach of operations research is employed. As more research went into the development of OR, the researchers were able to classify to some extent many of the important management problems that arise in practice. Examples of such problems are those relating to allocation, inventory, network, queuing, replacement, scheduling, and so on. The theoretical research in OR concentrated on devel- oping appropriate mathematical models and techniques for analyzing these problems under different conditions. Thus, whenever a management problem is identified as belonging to a particular class, all the models and techniques available for that class can be used to study that problem. In this context, one could view OR as a collection of mathematical mod- els and techniques to solve complex management problems. Hence, it is very common to find OR courses in universities emphasizing different mathematical techniques of operations research such as mathematical programming, queueing theory, network analysis, dynamic programming, inventory models, simulation, and so on. For more on the early activities in operations research, see Refs. 1–5. Readers interested in the timeline of major contributions in the history of OR/MS are referred to the excellent review article by Gass [6].

References

1. Haley, K.B., War and peace: the first 25 years of OR in Great Britain, Operations Research, 50, Jan.–Feb. 2002.
2. Miser, H.J., The easy chair: what OR/MS workers should know about the early formative years of their profession, Interfaces, 30, March–April 2000.
3. Trefethen, F.N., A history of operations research, in Operations Research for Management, J.F. McCloskey and F.N. Trefethen, Eds., Johns Hopkins Press, Baltimore, MD, 1954.
4. Horner, P., History in the making, ORMS Today, 29, 30–39, 2002.
5. Ravindran, A., Phillips, D.T., and Solberg, J.J., Operations Research: Principles and Prac- tice, Second Edition, John Wiley & Sons, New York, 1987 (Chapter 1).
6. Gass, S.I., Great moments in histORy, ORMS Today, 29, 31–37, 2002.