Introduction to operations research 9th edition

F or over four decades, Introduction to Operations Research has been the classic text on operations research Ninth Edition Introduction to Operations Research and the Institute for research for further reading All Excel® coverage has been updated for Excel 2007 The text website (www.mhhe.com/hillier) features the following material for students and instructors: Hillier Lieberman Operations Research Ninth Edition Frederick S Hillier Gerald J Lieberman MD DALIM 1000954 12/26/08 CYAN MAG YELO BLACK state of the art Introduction to Additional New Features: Operations Research New Emphasis on Real Applications Introduction to hil76299_fm_i-xxiv.qxd 12/16/08 06:51 PM Rev.Confirming Pages Page i INTRODUCTION TO OPERATIONS RESEARCH Ninth Edition FREDERICK S HILLIER Stanford University GERALD J LIEBERMAN Late of Stanford University hil76299_fm_i-xxiv.qxd 12/16/08 06:51 PM Rev.Confirming Pages Page ii INTRODUCTION TO OPERATIONS RESEARCH, NINTH EDITION Published by McGraw-Hill, a business unit of The McGraw-Hill Companies, Inc., 1221 Avenue of the Americas, New York, NY 10020 Copyright © 2010 by The McGraw-Hill Companies, Inc All rights reserved Previous editions © 2005, 2001, and 1995 No part of this publication may be reproduced or distributed in any form or by any means, or stored in a database or retrieval system, without the prior written consent of The McGraw-Hill Companies, Inc., including, but not limited to, in any network or other electronic storage or transmission, or broadcast for distance learning Some ancillaries, including electronic and print components, may not be available to customers outside the United States This book is printed on acid-free paper CCW/CCW ISBN 978-0-07-337629-5 MHID 0-07-337629-9 Global Publisher: Raghothaman Srinivasan Sponsoring Editor: Debra B Hash Director of Development: Kristine Tibbetts Developmental Editor: Lora Neyens Senior Marketing Manager: Curt Reynolds Project Manager: Melissa M Leick Senior Production Supervisor: Laura Fuller Senior Media Project Manager: Sandra M Schnee Associate Design Coordinator: Brenda A Rolwes Cover Designer: Studio Montage, St Louis, Missouri Compositor: Laserwords Private Limited Typeface: 10/12 Times Roman Printer: Courier Westford, Inc Library of Congress Cataloging-in-Publication Data Hillier, Frederick S Introduction to operations research / Frederick S Hillier, Gerald J Lieberman.—9th ed p cm Includes index ISBN 978-0-07-337629-5 — ISBN 0-07-337629-9 (hbk : alk paper) Operations research I Lieberman, Gerald J II Title T57.6.H53 2010 658.4'032—dc22 2008039045 www.mhhe.com hil76299_fm_i-xxiv.qxd 12/16/08 06:51 PM Page iii Rev.Confirming Pages ABOUT THE AUTHORS Frederick S Hillier was born and raised in Aberdeen, Washington, where he was an award winner in statewide high school contests in essay writing, mathematics, debate, and music As an undergraduate at Stanford University he ranked first in his engineering class of over 300 students He also won the McKinsey Prize for technical writing, won the Outstanding Sophomore Debater award, played in the Stanford Woodwind Quintet, and won the Hamilton Award for combining excellence in engineering with notable achievements in the humanities and social sciences Upon his graduation with a B.S degree in Industrial Engineering, he was awarded three national fellowships (National Science Foundation, Tau Beta Pi, and Danforth) for graduate study at Stanford with specialization in operations research After receiving his PhD degree, he joined the faculty of Stanford University, where he earned tenure at the age of 28 and the rank of full professor at 32 He also received visiting appointments at Cornell University, Carnegie-Mellon University, the Technical University of Denmark, the University of Canterbury (New Zealand), and the University of Cambridge (England) After 35 years on the Stanford faculty, he took early retirement from his faculty responsibilities in 1996 in order to focus full time on textbook writing, and now is Professor Emeritus of Operations Research at Stanford Dr Hillier’s research has extended into a variety of areas, including integer programming, queueing theory and its application, statistical quality control, and the application of operations research to the design of production systems and to capital budgeting He has published widely, and his seminal papers have been selected for republication in books of selected readings at least 10 times He was the first-prize winner of a research contest on “Capital Budgeting of Interrelated Projects” sponsored by The Institute of Management Sciences (TIMS) and the U.S Office of Naval Research He and Dr Lieberman also received the honorable mention award for the 1995 Lanchester Prize (best English-language publication of any kind in the field of operations research), which was awarded by the Institute of Operations Research and the Management Sciences (INFORMS) for the 6th edition of this book In addition, he was the recipient of the prestigious 2004 INFORMS Expository Writing Award for the 8th edition of this book Dr Hillier has held many leadership positions with the professional societies in his field For example, he has served as Treasurer of the Operations Research Society of America (ORSA), Vice President for Meetings of TIMS, Co-General Chairman of the 1989 TIMS International Meeting in Osaka, Japan, Chair of the TIMS Publications Committee, Chair of the ORSA Search Committee for Editor of Operations Research, Chair of the ORSA Resources Planning Committee, Chair of the ORSA/TIMS Combined Meetings Committee, and Chair of the John von Neumann Theory Prize Selection Committee for INFORMS He continues to serve as the Series Editor for Springer’s International Series in Operations Research and Management Science, a particularly prominent book series that he founded in 1993 In addition to Introduction to Operations Research and two companion volumes, Introduction to Mathematical Programming (2nd ed., 1995) and Introduction to Stochastic Models in Operations Research (1990), his books are The Evaluation of Risky Interrelated Investments (North-Holland, 1969), Queueing Tables and Graphs (Elsevier North-Holland, 1981, co-authored by O S Yu, with D M Avis, L D Fossett, F D Lo, iii hil76299_fm_i-xxiv.qxd iv 12/16/08 06:51 PM Page iv Rev.Confirming Pages ABOUT THE AUTHORS and M I Reiman), and Introduction to Management Science: A Modeling and Case Studies Approach with Spreadsheets (3rd ed., McGraw-Hill/Irwin, 2008, co-authored by M S Hillier) The late Gerald J Lieberman sadly passed away in 1999 He had been Professor Emeritus of Operations Research and Statistics at Stanford University, where he was the founding chair of the Department of Operations Research He was both an engineer (having received an undergraduate degree in mechanical engineering from Cooper Union) and an operations research statistician (with an AM from Columbia University in mathematical statistics, and a PhD from Stanford University in statistics) Dr Lieberman was one of Stanford’s most eminent leaders in recent decades After chairing the Department of Operations Research, he served as Associate Dean of the School of Humanities and Sciences, Vice Provost and Dean of Research, Vice Provost and Dean of Graduate Studies, Chair of the Faculty Senate, member of the University Advisory Board, and Chair of the Centennial Celebration Committee He also served as Provost or Acting Provost under three different Stanford presidents Throughout these years of university leadership, he also remained active professionally His research was in the stochastic areas of operations research, often at the interface of applied probability and statistics He published extensively in the areas of reliability and quality control, and in the modeling of complex systems, including their optimal design, when resources are limited Highly respected as a senior statesman of the field of operations research, Dr Lieberman served in numerous leadership roles, including as the elected president of The Institute of Management Sciences His professional honors included being elected to the National Academy of Engineering, receiving the Shewhart Medal of the American Society for Quality Control, receiving the Cuthbertson Award for exceptional service to Stanford University, and serving as a fellow at the Center for Advanced Study in the Behavioral Sciences In addition, the Institute of Operations Research and the Management Sciences (INFORMS) awarded him and Dr Hillier the honorable mention award for the 1995 Lanchester Prize for the 6th edition of this book In 1996, INFORMS also awarded him the prestigious Kimball Medal for his exceptional contributions to the field of operations research and management science In addition to Introduction to Operations Research and two companion volumes, Introduction to Mathematical Programming (2nd ed., 1995) and Introduction to Stochastic Models in Operations Research (1990), his books are Handbook of Industrial Statistics (PrenticeHall, 1955, co-authored by A H Bowker), Tables of the Non-Central t-Distribution (Stanford University Press, 1957, co-authored by G J Resnikoff), Tables of the Hypergeometric Probability Distribution (Stanford University Press, 1961, co-authored by D Owen), Engineering Statistics, Second Edition (Prentice-Hall, 1972, co-authored by A H Bowker), and Introduction to Management Science: A Modeling and Case Studies Approach with Spreadsheets (McGraw-Hill/Irwin, 2000, co-authored by F S Hillier and M S Hillier) hil76299_fm_i-xxiv.qxd 12/16/08 06:51 PM Page v Rev.Confirming Pages ABOUT THE CASE WRITERS Karl Schmedders is an associate professor in the Department of Managerial Economics and Decision Sciences at the Kellogg Graduate School of Management (Northwestern University), where he teaches quantitative methods for managerial decision making His research interests include applications of operations research in economic theory, general equilibrium theory with incomplete markets, asset pricing, and computational economics Dr Schmedders received his doctorate in operations research from Stanford University, where he taught both undergraduate and graduate classes in operations research Among the classes taught was a case studies course in operations research, and he subsequently was invited to speak at a conference sponsored by the Institute of Operations Research and the Management Sciences (INFORMS) about his successful experience with this course He received several teaching awards at Stanford, including the university’s prestigious Walter J Gores Teaching Award He also has received several teaching awards, including the L G Lavengood Professor of the Year at the Kellogg School of Management While serving as a visiting professor at WHU Koblenz (a leading German business school), he won teaching awards there as well Molly Stephens is an associate in the Los Angeles office of Quinn, Emanuel, Urquhart, Oliver & Hedges, LLP She graduated from Stanford University with a B.S degree in Industrial Engineering and an M.S degree in Operations Research Ms Stephens taught public speaking in Stanford’s School of Engineering and served as a teaching assistant for a case studies course in operations research As a teaching assistant, she analyzed operations research problems encountered in the real world and the transformation of these problems into classroom case studies Her research was rewarded when she won an undergraduate research grant from Stanford to continue her work and was invited to speak at an INFORMS conference to present her conclusions regarding successful classroom case studies Following graduation, Ms Stephens worked at Andersen Consulting as a systems integrator, experiencing real cases from the inside, before resuming her graduate studies to earn a JD degree (with honors) from the University of Texas Law School at Austin v hil76299_fm_i-xxiv.qxd 12/16/08 06:51 PM Rev.Confirming Pages Page vi DEDICATION To the memory of our parents and To the memory of my beloved mentor, Gerald J Lieberman, who was one of the true giants of our field hil76299_fm_i-xxiv.qxd 12/16/08 06:51 PM Page vii Rev.Confirming Pages TABLE OF CONTENTS PREFACE xviii CHAPTER Introduction 1.1 The Origins of Operations Research 1.2 The Nature of Operations Research 1.3 The Impact of Operations Research 1.4 Algorithms and OR Courseware Selected References Problems CHAPTER Overview of the Operations Research Modeling Approach 2.1 Defining the Problem and Gathering Data 2.2 Formulating a Mathematical Model 11 2.3 Deriving Solutions from the Model 13 2.4 Testing the Model 16 2.5 Preparing to Apply the Model 17 2.6 Implementation 18 2.7 Conclusions 19 Selected References 19 Problems 20 CHAPTER Introduction to Linear Programming 23 3.1 Prototype Example 24 3.2 The Linear Programming Model 30 3.3 Assumptions of Linear Programming 36 3.4 Additional Examples 42 3.5 Formulating and Solving Linear Programming Models on a Spreadsheet 60 3.6 Formulating Very Large Linear Programming Models 68 3.7 Conclusions 75 Selected References 75 Learning Aids for This Chapter on Our Website 76 Problems 77 Case 3.1 Auto Assembly 86 Previews of Added Cases on Our Website 88 Case 3.2 Cutting Cafeteria Costs 88 Case 3.3 Staffing a Call Center 88 Case 3.4 Promoting a Breakfast Cereal 88 vii hil76299_fm_i-xxiv.qxd viii 12/16/08 06:51 PM Page viii Rev.Confirming Pages CONTENTS CHAPTER Solving Linear Programming Problems: The Simplex Method 89 4.1 The Essence of the Simplex Method 89 4.2 Setting Up the Simplex Method 94 4.3 The Algebra of the Simplex Method 97 4.4 The Simplex Method in Tabular Form 103 4.5 Tie Breaking in the Simplex Method 108 4.6 Adapting to Other Model Forms 111 4.7 Postoptimality Analysis 129 4.8 Computer Implementation 137 4.9 The Interior-Point Approach to Solving Linear Programming Problems 140 4.10 Conclusions 145 Appendix 4.1 An Introduction to Using LINDO and LINGO 145 Selected References 149 Learning Aids for This Chapter on Our Website 149 Problems 150 Case 4.1 Fabrics and Fall Fashions 158 Previews of Added Cases on Our Website 160 Case 4.2 New Frontiers 160 Case 4.3 Assigning Students to Schools 160 CHAPTER The Theory of the Simplex Method 161 5.1 Foundations of the Simplex Method 161 5.2 The Simplex Method in Matrix Form 172 5.3 A Fundamental Insight 181 5.4 The Revised Simplex Method 184 5.5 Conclusions 187 Selected References 187 Learning Aids for This Chapter on Our Website 188 Problems 188 CHAPTER Duality Theory and Sensitivity Analysis 195 6.1 The Essence of Duality Theory 196 6.2 Economic Interpretation of Duality 203 6.3 Primal–Dual Relationships 206 6.4 Adapting to Other Primal Forms 211 6.5 The Role of Duality Theory in Sensitivity Analysis 215 6.6 The Essence of Sensitivity Analysis 217 6.7 Applying Sensitivity Analysis 225 6.8 Performing Sensitivity Analysis on a Spreadsheet 245 6.9 Conclusions 259 Selected References 260 Learning Aids for This Chapter on Our Website 260 Problems 261 Case 6.1 Controlling Air Pollution 274 Previews of Added Cases on Our Website 275 Case 6.2 Farm Management 275 Case 6.3 Assigning Students to Schools, Revisited 275 Case 6.4 Writing a Nontechnical Memo 275 hil76299_sub_idx_1029-1048.qxd 12/3/08 06:31 PM Confirming Pages Page 1035 SUBJECT INDEX Frank-Wolfe algorithm, 581–584 Franz Edelman Awards for Management Science Achievement, 13, 44, 468, 473, 766 Freddie the newsboy’s problem assumption cell, procedure for defining, 966–968 crystal ball, application of, 966 decision table tool, application of, 975 decision variable, procedure for defining, 975–979 forecast cell, procedure for defining, 968–972 simulation results, accuracy of, 972–974 spreadsheet model for, 965–966 freedom for a system of equations, degrees of, 96n free goods, 132 from plant, 69 Frontline Systems, 139 functional constraints defined, 32 in Ն form, 116–118 ordinary, number of, 138 fundamental insight in simplex method, 181–184 fundamental property, 702–703 fundamental theorem for network simplex method, 391 Furniture City, 536 G game theory extensions, 666–667 games with mixed strategies, 658–660 graphical solution procedure, 660–662 simple games, solving (prototype example), 653–658 solving by linear programming, 662–666 two-person, zero-sum games, 651–653 formulation as, 653–658 GAMS, 68 gasoline blending, 55 Gaussian elimination, proper form from, 98, 101–102, 119, 124, 223, 224 Gauss-Jordan method of elimination, 101–102 general integers, binary representation of, 478–479 generalized Erlangian distributions, 797 General Motors (GM), 804 general-purpose algorithm, 338 general-purpose programming language, 961 general-purpose simulation languages, 961 genes, 638 genetic algorithms basic concepts, 635–636 as Evolutionary Solver, 592 generating a child, procedure for, 643–644 integer version of nonlinear programming example, 637–640 outline of, 636–637 traveling salesman problem example, 640–643 geometric concepts, 89–90 geometric interpretations of simplex method, 98 geometric programming, 550 German bonds, 606 global constraint, 518 global optimization, 588 global supply chain, 470 Goferbroke Co problem, 691–693 first, how TreePlan constructs the decision tree for, 691–693 full, decision tree for, 693 full, utility theory applied to, 704–705 spreadsheet to perform sensitivity analysis, organizing, 693–696 using Senslt to create three types of sensitivity analysis graphs, 696–700 utility theory, 704–707 Good Products Company example, 479–482 government, 10 gradient algorithms, 580 gradient search procedure, 557–562, 609 1035 Grantham, Mayo, Van Otterloo and Company, 469 Graphical Method and Sensitivity Analysis, 133, 224, 254 Graphical Method demo, 27 graphical method for linear programming, 29, 45 graphical solution procedure in game theory, 660–662 in linear programming, Wyndsor Glass Co example, 27–29 Green Earth, 52 H health care applications in simulation, 950 heuristic method, 607 heuristic procedures, 14 Hewlett-Packard (HP), 767 hill-climbing procedure, 609 Hit-and-Miss Manufacturing Company, 452–454 holding cost, 830, 831 holding time, 761 Hungarian algorithm equivalent cost tables, role of, 342–344 summary of, 346 zero elements, creation of additional, 344–346 hyperexponential distribution, 797 hyperplanes, 162, 165, 167 I IBM, 17 IBM PC Company in Europe, 947 identity matrix, 173, 176, 180, 183, 185 IFORS (International Federation of Operational Research Societies), ILOG, 139, 143 ILOG CP Optimizer, 521 ILOG OPL-CPLEX Development System, 520–521 immediate predecessors, 399–400 immediate successor, 399–400 improve sales and manufacturing performance, 25 hil76299_sub_idx_1029-1048.qxd 1036 12/3/08 06:31 PM Confirming Pages Page 1036 SUBJECT INDEX increasing marginal utility for money, 700 incremental analysis, 222–223 incumbent, 494 independent demand, 841 indicating variable, 169 inequality constraints, 94 infeasible solution, 33 infinite queues, 804–805 in flow, 366 information technology (IT), 10 INFORMS (Institute for Operations Research and the Management Sciences), 3, 766 inheriting links, 642 inheriting sub-tour reversal, 642–643 initial basic solution, 130 initial basic variable, 104 initial BF solutions, 98, 111, 113 initial nonbasic variable, 104 initial tableau, 130 initial trial solution, 629, 633 in-process inventory, reducing, 826–827 input source (calling population) in queueing theory, 760–761 Institute for Operations Research and the Management Sciences (INFORMS), 3, 766 integer programming See IP programming integer solutions property, 311, 336, 384 integer values, 41 interactive computer-based system, 18 Interactive Operations Research Tutorial See IOR Tutorial interarrival time, 761 intercept of a line, 29 interfaces, Interfaces (journal), 3, 470, 471 interior-point algorithm (Karmarkar’s), 140–142 centering scheme for implementing concept 3, 292 gradient for concepts and 2, relevance of, 288–290 gradient to implement concepts and 2, using, 290–291 introduced, 24 summary and illustration of, 292–294 summary of, 294–298 interior-point approach barrier algorithm, 138–139 vs complementary roles of simplex method, 143–145 key solution concept, 141–142 vs simplex method, 142–143 interior points, 141 internal service systems, 765, 808 International Federation of Operational Research Societies (IFORS), international investments, 606 Interpretation of the Slack Variables, 95 inventory capacity, 69 levels, reducing, 99 reducing in-process, 826–827 throughout a supply chain, management of, 849 inventory example formulating as Markov chain, 728–730 n-step transition matrices for, in Chapman-Kolmogorov equations, 733–734 of stochastic process in Markov chains, 724–725 inventory models components of, 831–833 deterministic continuous-review, 833–843 deterministic multiechelon, for supply chain management, 848–866 deterministic periodic-review, 843–848 perishable products, stochastic single period for, 870–882 stochastic continuous-review, 866–870 See also individual headings inventory policy examples of, 829–831 revenue management (See revenue management) scientific inventory management, 828–829 inventory systems computerized, 866 future users of, 17 managing in simulation applications, 947 inverse transformation method, 955–956 summary of, 956–957 investment analysis using BIP models, 468–469 investments, international, 606 IOR Tutorial, 5, 30 Graphical Method and Sensitivity Analysis, 133, 224, 254 Solve Automatically by the InteriorPoint Algorithm, 287 Solve Automatically by the Simplex Method, 103 Solve Interactively by the Simplex Method, 103 IP programming defined, 41 explained, 464–465 nonlinear programming example, 637–640 solving, 487–491 state-of-the-art algorithms for, in CPLEX 11, 139 See also BIP models italicized letters, 173 iterative algorithm, 93 J Jackson networks, 805–807 Job Shoe Company problem, 334–339 JPMorgan Chase, 909 just-in-time (JIT) inventory management, 842–843 K Karush-Kuhn-Tucker conditions See KKT conditions KeyCorp, 779 KKT conditions for constrained optimization, 563–567 for quadratic programming, 568–569 known constant, 41 known constraints, 218 K out of N constraints, 474–475 hil76299_sub_idx_1029-1048.qxd 12/17/08 12:45 PM Page 1037 SUBJECT INDEX L Lagrangian relaxation, 500 large linear programming models, formulating LINGO modeling language, 74–75 modeling languages, 68–69 in MPL, 71–74 with no feasible solutions, 127n structure of resulting model, 70–71 Worldwide Corporation problem, 69–70 largest absolute value, 108 Las Vegas, winning in, 455–457 lead time, 832 leaving basic variable, 100 determining, 105 finding, 394–398 in tie breaking (degeneracy), 108 variables allowed to be negative, 127–128 LGO, 6, 588 limited resources, allocating among competing activities, 23 LINDO, 6, 30, 139, 140 for convex programming, 587–588 introduction to, 145–149 introduction to using, 145–149 large linear programming models formulated in, 69 for nonconvex programming, 588 for quadratic programming, 572–573 for solving BIP models, 467 student version available on Web, What’sBest! spreadsheet solver, 74 LINDO API, 69, 74, 141 LINDO Systems, Inc., 69, 74, 139 linear, defined linear complementarity problem, 552 linear functions, 23 linearly constrained optimization, 548 linear programming applications, fundamental insight on, 183–184 data needed for, 31 development of, 23 examples of, 42–68 introduction to, 23–24 to make crashing decisions, 406–409 published articles about, 23 software options, 138–140 solving games by, 662–666 terminology for, 30–31 linear programming, assumptions of additivity, 39–41 certainty, 41–42 divisibility, 41 in perspective, 42 proportionality, 36–39 linear programming, Wyndsor Glass Co example conclusions, 29 CPF solutions for, 34, 35 data for, 25, 26 estimates for, 25 formulation as problem, 26–27 graphical solution, 27–29 objectives for, 24–25 software, 138–140 linear programming in Markov decision processes formulation, 913–914 randomized policies, 912–913 solving prototype example by, 914–915 linear programming models data needed for, 31–32 defined, 11–12 formulating on a spreadsheet, 60–64 introduced, 24 large, formulating (See large linear programming models, formulating) legitimate forms of, 32–33 LINGO modeling language, 74–75 modeling languages, 68–69 standard form of, 32 terminology for solutions of, 33–36 using Excel Solver to solve, 64–68 linear programming problems computer implementation, 137–140 interior-point approach, 140–145 LINDO, 145–149 LINGO, 145–149 other model forms, adapting to, 111–129 postoptimality analysis, 129–137 reformulation as, 574–579 simplex method, 89–140 special types of, 137–138 Rev.Confirming Pages 1037 See also individual headings lines, constructing, 27–29 LINGO, 6, 30, 139, 140 for convex programming, 587–588 introduction to using, 145–149 large linear programming models formulated in, 68, 69 modeling language, 74–75 for nonconvex programming, 588, 589 for quadratic programming, 572–573 sets as fundamental concept of, 74–75 for solving BIP models, 467 student version available on Web, links, 360 Little’s formula, 764 L.L Bean, Inc., 766 local improvement procedure, 609–610 local optima multiple, nonlinear programming problems with (example), 608–611 systematic approach to finding, 590–592 using Excel Solver to find, 589–590 local search procedure, 615, 618 long-run profit maximization, long-run properties of Markov chains expected average cost per unit time, 740–741 expected average cost per unit time for complex cost functions, 741–743 steady-state probabilities, 737–740 LP relaxation, 488, 493 M macros, 73 magazines distribution channels, management of, 872 management information system computer-based, 10 providing up-to-date input for model, 17–18 management science, (See also operations research) managerial reports, 18 manufacturing systems, design and operation of, 948–949 hil76299_sub_idx_1029-1048.qxd 1038 12/3/08 06:31 PM Page 1038 Confirming Pages SUBJECT INDEX manufacturing times, reducing, 99 marginal cost analysis, 405–406 Markov chains additional examples of, 730–732 Chapman-Kolmogorov equations, 732–735 continuous time Markov chains, 748–753 explained, 725–726 first passage times, 743–745 formulating inventory example as, 728–730 formulating weather example as, 726–728 long-run properties of, 737–743 states of (See Markov chains, states of) stochastic process, 723–725 See also individual headings Markov chains, states of absorbing, 745–748 periodicity properties, 737 recurrent states and transient states, 735–737 Markov decision processes discounted cost criterion, 920–927 linear programming, 911–915 model for, 908–911 optimal policies, 915–920 See also individual headings Markov decision processes, prototype example of, 905–908 solving by exhaustive enumeration, 910–911 solving by linear programming, 914–915 solving by method of successive approximations, 926–927 solving by policy improvement algorithm, 917–920 Markovian property, 725, 748 Massachusetts Institute of Technology (MIT), 767 material requirements planning (MRP), 841–842 mathematical model, formulating, 11–13 matrix form of simplex method See simplex method, in matrix form max-flow min-cut theorem, 378 maximin likelihood criterion, 676–677 maximin payoff criterion, 675–676 maximization form, 196 maximum feasible flow, 378–379 maximum flow problem applications, 374 augmenting path algorithm, 374–379 minimum cost flow problem, 387–388 Seervada Park, 376–378 using Excel to formulate and solve, 379–380 M/D/s model, 792 measure of performance, 31, 61 M/Ek/s model, 792–794 Memorial Sloan-Kettering Cancer Center (MSKCC), 44 Merrill Lynch manage liquidity risk for revolving credit lines, 727 OR study on service charge methods, 10 pricing analysis for providing financial services, 948 Merrill Lynch (ML) Bank USA, 727 metaheuristics, 14 genetic algorithms, 635–644 nature of (See metaheuristics, nature of) simulated annealing, 626–635 tabu search, 615–626 See also individual headings metaheuristics, nature of nonlinear programming problem with multiple local optima (example), 608–611 sub-tour reversal algorithm, 613–615 traveling salesman problem example, 611–613 M/G/1 model, 791–792 midpoint rule, 553 Military Airlift Command (MAC), 433 military applications in simulation applications, 950 minimax criterion, 659 656 minimax theorem, 659 simple proof of, 664 minimization, 118–119 minimization form, 196 minimum cost flow problem, 60, 318 applications, 381–383 example of, 384–385 explained, 358–359 formulation of, 383–384 special cases, 386–389 using Excel to formulate and solve, 385–386 minimum cover of constraint, 515 minimum ratio test, 100, 178 minimum spanning tree problem algorithm for, 370–373 applications, 369–370 with constraints, 617–622 explained, 358 Seervada Park, 370–373 MIP branch-and-bound algorithm for, 503–509 defined, 464 for fixed-charge problem, 476–478 mixed congruential method, 953 mixed integer programming See MIP mixed strategies, 658–660 M/M/s/K model, 785–788 M/M/s model County Hospital example based on, 783–785 finite calling population variation of, 788–790 finite queue variation of (M/M/s/K model), 785–788 model enrichment, 12 modeling language CPLEX (See CPLEX) in large models, 68–69 LINDO (See LINDO) LINGO (See LINGO) MPL (See MPL) Optimization Programming Language (OPL), 139 software for, 68–69 model validation, 3, 12, 16, 30 modified simplex method, 570–572 money, utility functions for, 700–703 money in motion, 420–422 hil76299_sub_idx_1029-1048.qxd 12/17/08 12:45 PM Page 1039 SUBJECT INDEX move selection rule, 627 MPL, 6, 30 for convex programming, 588 large linear programming models formulated in, 71–74 for nonconvex programming, 588 OptiMax 2000 Component Library, 69, 140 for quadratic programming, 572–573 for solving BIP models, 467 student version of, 68–69, 139 Tutorial, 74 MRP (material requirements planning), 841–842 MSKCC (Memorial Sloan-Kettering Cancer Center), 44 MultiModal Applied System, 367 multiple optimal solutions, 34, 109–111 multiplicative congruential method, 954 multiplicative factors, 115 multivariable unconstrained optimization gradient search procedure, 557–562 Newton’s method, 562–563 mutations, 636 of inherited links, 643 rate, 637 mutually exclusive alternatives, 466, 476 N nation, 10 negative coefficients, 178, 278 negative right-hand sides, 116 negative variables, 127–129 neighborhood structure, 618, 629, 633 net flow constraints, 58, 366 network, connected, 362 Network Analysis Area, 398 network optimization models CPM method of time-cost tradeoffs, 359 maximum flow problem, 358, 373–380 minimum cost flow problem, 358–359, 380–389 minimum spanning tree problem, 358, 368–373 prototype example, 359–360 shortest-path problem, 358, 363–368 terminology of networks, 360–363 time-cost trade-off, for optimizing, 399–410 See also individual headings network simplex method BF solution, finding next, 394–398 BF solutions and feasible spanning trees, correspondence between, 390–392 in CPLEX, 139 entering basic variable, selecting, 392–394 fundamental theorem for, 391 leaving basic variable, finding, 394–398 upperbound technique, incorporating, 389–390 new constraints, introduction of, 239–240 newsvendor problem, 871 Newton’s methods of multivariable unconstrained optimization, 557–563 of one-variable unconstrained optimization, 552–557 quasi-, 563 new variable, introduction of, 235–236 next-event incrementing in simulation, 944–946 no backlogging, 832 node connected, 362 constraints, 383 in decision trees, 686 defined, 360 demand, 363, 382 dummy, 382 event, 686 nth nearest, 364–365 solved, 364 supply, 363 transshipment, 363, 373 no entering basic variable, 119n no feasible solutions, 126–127 Rev.Confirming Pages 1039 no leaving basic variable in tie breaking (unbounded Z), 109 nonbasic arc, 390–391 nonbasic variables changes in coefficients of, 231–235 coefficients of, changes in, 215–216 number of, 170 nonconvex programming, 550 nonconvex programming with spreadsheets evolutionary solver, 592 local optima, systematic approach to finding, 590–592 local optima, using Excel Solver to find, 589–590 solving nonconvex programming, challenge of, 588–589 nonexponential distributions involving queueing models M/D/s model, 792 M/Ek/s model, 792–794 M/G/1 model, 791–792 models without Poisson input, 795–796 other models, 796–798 nonlinear programming integer version of (example), 637–640 IP problems, example of, 637–640 portfolio selection with risky securities, 540–542 problems (See nonlinear programming problems) product-mix problem with price elasticity, 538–539 role of in OR, 537 simulated annealing example, 632–635 transportation problem with volume discounts on shipping costs, 539–540 nonlinear programming problems convex programming, 580–588 graphical illustration of, 542–546 KKT conditions for constrained optimization, 563–567 with multiple local optima (example), 608–611 multivariable unconstrained optimization, 557–563 hil76299_sub_idx_1029-1048.qxd 1040 12/3/08 06:31 PM Page 1040 Confirming Pages SUBJECT INDEX nonlinear programming problems— Cont nonconvex programming (with spreadsheets), 588–592 one-variable unconstrained optimization, 552–557 quadratic programming, 567–573 separable programming, 573–580 types of (See nonlinear programming problems, types of) See also individual headings nonlinear programming problems, types of complementarity problem, 551–552 convex programming, 549 fractional programming, 550–551 geometric programming, 550 linearly constrained optimization, 548 nonconvex programming, 550 quadratic programming, 548–549 separable programming, 549–550 unconstrained optimization, 547–548 nonnegative coefficients, 277 nonnegative right-hand sides, 89, 97, 111, 116, 203 nonnegativity constraints, 32 nonpreemptive priorities, 798–799 nonpreemptive priorities model, results for, 799–800 nonstandard form, converting to standard form, 211 nontechnical memo, writing, 275 nonzero entries, 72 Nori & Leets Co., 49–51, 274–275 normal distributions, 958 northwest corner rule, 323 notation in queueing theory, 763–764 N possible values, 475–476 N priority classes, 798 n-step transition matrices in Chapman-Kolmogorov equations, 733–734 for inventory example, 733–734 for weather example, 733 n-step transition probabilities, 726 nth nearest node, 364–365 null vector, 173 number of iterations, 142 O object function coefficients, analyzing simultaneous changes in, 235, 255–258 objective cells, 63 objective function, 11, 32 OMEGA, 21 100 percent rule for simultaneous changes in objective function coefficients, 235, 255–258 one-variable unconstrained optimization bisection method, 553–555 Newton’s method, 555–557 Operation Desert Storm, 433 operations research (OR) applications of, described in vignettes, approach (See operations research (OR) modeling approach) impact of, 3–4 nature of, 2–3 origins of, 1–2 simulation in, 935–936 teams, operations research (OR) courseware See OR courseware operations research (OR) modeling approach applying the model, 17–18 defining the problem and gathering data, 8–9 deriving solutions from, 13–16 implementation, 18–19 mathematical model, formulating, 11–13 testing the model, 16–17 OPL, 68, 520–521 OPL-CPLEX Development System, 139 optimal inventory policy algorithm for finding, 845–846 with I Ն and K 0, 880 with (I 0) K ϭ 0, 879 when demand has exponential distribution, approximate solution for, 881–882 optimality test for CPF solution, 91–92 for new BF solution, 99, 102, 104, 327, 397 passing, 397 in sensitivity analysis, 224 optimal policies in Markov decision processes policy improvement algorithm for, 916–920 preliminaries, 916 optimal policy for problem, 430 optimal solution, 109 defined, 3, 34 desired, finding, 29 multiple, 34, 109–111 no, 34 nonsensical, finding, 30 in OR themes, 14 resulting in algebra of simplex method, 102–103 OptiMax 2000 Component Library, 69, 140 optimization linearly constrained, 548 unconstrained, 547–548 Optimization Decision Manager, 143 Optimization Programming Language (OPL), 139 optimizing the product mix, 25 OR See operations research (OR) OR courseware additional example, 107 algorithms and, 5–6 another example, 103, 107 IOR Tutorial (See IOR Tutorial) for linear programming examples, 29–30 OR Tutor (See OR Tutor) Queueing Simulator, 944–945 simulation examples, 946 software for solving BIP models, 467 solvers available through, Worked Examples, 6, 30 ordering cost, 830 order quantity Q, choosing in stochastic continuous-review model, 867 OR Tutor, 5, 29–30 Interpretation of the Slack Variables, 95 Network Analysis Area, 398 Simplex Method—Algebraic Form, 103 hil76299_sub_idx_1029-1048.qxd 12/17/08 12:45 PM Page 1041 SUBJECT INDEX Simplex Method—Tabular Form, 107 other model forms, adapting to equality restraints, 112–116 example, solving (radiation therapy), 119–121 functional constraint in Ն form, 116–118 fundamental insight on, 183 minimization, 118–119 negative right-hand sides, 116 no feasible solutions, 126–127 two-phased method, 121–126 variables allowed to be negative, 127–129 out flow, 366 output cells, 62 overall measure of performance, 12 overbooking model, 886–888 applying, example of, 888–889 owners, 10 P Pacific Lumber Company (PALCO), 228 PALCO (Pacific Lumber Company), 228 parameters defined, 11, 32 sensitive, 15, 41–42, 133, 218 table for transportation problem, 309 See also parametric linear programming parametric linear programming postoptimality analysis, 136–137 for systemic changes in bi parameters, 282–283 summary of, 283–285 for systemic changes in cj parameters, 280–282 summary of, 280–282 systemic sensitivity analysis, 240–245 parametric programming See parametric linear programming parents, 636, 637 path, 361, 401 payoff, 674 payoff table, 652, 674 performance measures, 31, 61 periodicity properties in states of Markov chains, 737 periodic review, 833 perishable products, types of, 871–872 perishable products model See stochastic single period model for perishable products perpetual loop, cycling around, 108n personnel scheduling, 55–58 PERT, 399 petroleum exploration projects, evaluating, 675 phase-type distributions, 797 physical annealing process, 628 pivot column, 105 pivot number, 105 pivot row, 105 planned shortages, EOQ model with, 836–838 planning, 23 planning planners, 990 Poisson input, 777–778 models without, 795–796 process, 771 Poisson process, 771–773 policy decision, 429 policy improvement algorithm linear programming formulation, 924–925 for optimal policies in Markov decision processes, 915–920 summary of (discounted cost criterion), 922–924 Pollaczek-Khintchine formula, 792 polygon, 164 polyhedron, 164 polynomial time algorithm, 142 population, 636, 637 calling, (input source) in queueing theory, 760–761 posterior probabilities, 680–684 postoptimality analysis defined, 15 in parametric linear programming, 136–137 reoptimization, 130 sensitivity analysis, 133–134 using Excel to generate information, 134–136 shadow prices, 131–133 Rev.Confirming Pages 1041 posynomials, 550 preemptive priorities, 799 preemptive priorities model, results for, 801 preimplementation test, 17 Premium Solver for Education, 6, 64, 139, 140 price elasticity, product-mix problem with, 538–539 pricing under pressure, 990 primal-dual forms, 214, 215 primal-dual method, 131n primal-dual relationships, 195 complementary basic solutions, 207–209 relationships among, 209–211 See also duality theory primal-dual table, 196 primal feasible solution, 211 principle of optimality, 430 prior distribution, 674–675 priority-discipline queueing models basic, described, 798–799 County Hospital example with priorities, 801–803 nonpreemptive priorities model, results for, 799–800 preemptive priorities model, results for, 801 single-server variation of, 800 prior probabilities, 675 probabilistic dynamic programming, 451–457 determining reject allowances, 452–454 winning in Las Vegas, 455–457 probability of absorption, 745 probability tree diagram, 682 problem, defining, 8–10 Procter & Gamble, 306 product demand, different types of, 841–842 product form solution, 805 production and distribution network, designing using BIP models, 469–470 production days available, 69 production line, improving efficiency, 804 production rates, 24–25 production system, redesign of, 306 hil76299_sub_idx_1029-1048.qxd 1042 12/17/08 12:45 PM Page 1042 Rev.Confirming Pages SUBJECT INDEX product mix, 25 product-mix problem, 69–75 with price elasticity, 538–539 products assigning to plants, example of, 339–342 perishable, stochastic single period for (See stochastic single period model for perishable products) profit per batch produced, 25 program evaluation and review technique (PERT), 399 programming, 23 project deadline, 947–948 project duration, 401 project network, 400–401 project pickings, 357 proof by contradiction, 166 proper form from Gaussian elimination, 98, 101–102, 119, 124, 223, 224 proportionality, violating, 482–485 proportionality assumption, 36–39 prostate cancer, 44 PSA Peugeot Citroën, 749 pseudo-random numbers, 952 P & T Company, 305 See also transportation problem pure strategies, 658 Q quadratic approximation, 556 quadratic programming KKT conditions for, 568–569 linear constraints in, 548–549 modified simplex method, 570–572 software options, 572–573 quantity discounts, with EOQ model, 838–839 quasi-Newton methods, 563 queue, 761 queue discipline, 761 queueing models birth-and death-process, 773–790 involving nonexponential distributions, 790–798 M/M/s model, 778–783 priority-discipline, 798–803 See also individual headings queueing networks described, 803–804 infinite queues in series, 804–805 Jackson networks, 805–807 Queueing Simulator, 944–945 queueing systems classes of, 765–766 design, award winning studies, 766 design and operation of, 947 exponential distribution, 767–773 queueing theory application of (See queueing theory, application of) defined, 759 prototype example, 760 structure of (See queueing theory, structure of) queueing theory, application of example of, 809–810 other issues, 810–812 servers, determining number of, 808–809 queueing theory, structure of input source (calling population), 760–761 process of, basic, 760 process of, elementary, 762–763 queue, 761 queue discipline, 761 relationships between L, W, Lq, and Wq, 764–765 service mechanism, 761–762 terminology and notation, 763–764 queuing quandary, 827 R R, Q policy (reorder-point, orderquantity policy), 866–867 radiation therapy design of, 43–45 example, applying simplex method to, 119–121 primal-dual form for, 214, 215 rail freight, plan routing of, 367 RAND() function in Excel, 937, 951 random digits, table of, 951 random integer number, 952 randomized policy, 909–910 random number, 952 random number generator, 951 random numbers in simulation applications annealing, 628 characteristics of, 951–952 generation of, 951 congruential methods for, 952–955 random observations from a probability distribution, generation of acceptance-rejection method, 958–959 Erlang distributions, 957–958 exponential distributions, 957–958 inverse transformation method, 955–956 summary of, 956–957 normal and chi-square distributions, 958 simple discrete distributions, 955 random selection of an immediate neighbor, 629, 633 random walk, 745 range name, 60–61 range of likely values, 224 raw materials, optimize use and movement of, 61 real problem, 111, 118 recipient cells, 330 recurrence time, 753 recurrent states in Markov chain, 735–737 recursive relationship, 430 redundant constraints, 57 reject allowances, determining, 452–454 relaxation Lagrangian, 500 LP, 488, 493 of a problem, 493 solving, 860–861 Reliable Construction Co problem, 399–410 See also time-cost tradeoffs reoptimization in postoptimality analysis, 130 in sensitivity analysis, 224 technique, 130 reorder point R, choosing in stochastic continuous-review model, 867–870 replicability, 18 reproducible work, 18 requirements assumption, 308, 318 hil76299_sub_idx_1029-1048.qxd 12/3/08 06:31 PM Page 1043 SUBJECT INDEX research-and-development projects, evaluating, 687 research on constraint programming, current, 520–521 residual capacities, 374 residual network, 374 restricted-entry rule, 570 retrospective test, 17 revenue, 832 revenue management capacity-controlled discount fares model, 884–885 applying, example of, 885–886 other models, 889–890 overbooking model, 886–888 applying, example of, 888–889 reverse arc, 389 revised problem, solving, 861–864 revised simplex method, 137, 180, 184–187 revision of final tableau, 221–222, 224 revision of model in sensitivity analysis, 224 revolving credit lines, manage liquidity risk for, 727 right-hand sides allowable range for, 228–229 nonnegative, 89, 97, 111, 116, 203 simultaneous changes in, analyzing, 229–230 Rijkswaterstaat of the Netherlands, 13, 15–16 risk-averse, 700 risk-neutral individual, 700 risk seekers, 700 RiskSim, 963–964 route-management system for trash collection and disposal, developing, 505 row, 104 row reduction, 343 rules of the game in simulation, 937–942 Russell’s approximation method, 324–327 Russian Federation, 422–423 S saddle point, 656 salvage value, 832 Samsung Electronics, 19, 99 San Francisco Museum of Modern Art, 535 satisficing, 14 Save-It Co problem, 51–55 scarce goods, 132 scenarios, 16 schedule disruptions occurring in airlines, 13 scheduling employment levels, 442–448 scientific inventory management, 828–829 Sears, Roebuck and Company, 471, 616 Seervada Park augmenting path algorithm, applying to, 376–378 maximum flow problem, 376–378 minimum spanning tree problem, 370–373 shortest-path problem, 364–365 sensible-odd-bizarre method (SOB), 213–215 sensitive parameters, 15, 133, 218 sensitivity analysis with Bayes’ decision rule, 678–679 in certainty assumption, 41–42 defined, 11 essence of, 217–224 in postoptimality analysis, 133–134 using Excel to generate information, 134–136 summary of procedure for, 224 sensitivity analysis, applying changes in bi, 225–231 changes in coefficients of basic variable, 236–239 changes in coefficients of nonbasic variable, 231–235 introduction of new constraints, 239–240 introduction of new variable, 235–236 systemic sensitivity analysis (parametric programming), 240–245 sensitivity analysis, in duality theory coefficients of nonbasic variable, changes in, 215–216 Confirming Pages 1043 new variable, introduction of, 216–217 other applications, 217 sensitivity analysis, performing on spreadsheet checking individual changes in model, 245–247 checking two-way changes in model, 248–251 decision trees, 690–700 (See also decision trees, performing sensitivity analysis on using spreadsheets) other types of sensitivity analysis, 258–259 using sensitivity report to perform sensitivity analysis, 134, 253–258 using solver table for two-way sensitivity analysis, 251–253 using solver table to sensitivity analysis systematically, 248 sensitivity report, using to perform sensitivity analysis, 134, 253–258 Senslt Excel add-in, 696–700 separable function, 549 separable programming in convex programming, 549–550 extensions, 579–580 key property of, 576–577 reformulation as linear programming problem, 574–579 sequence of distinct arcs, 361 sequential-approximation algorithms, 580–581 sequential linear approximation algorithm (Frank-Wolfe), 581–584 sequential unconstrained algorithms, 580 sequential unconstrained minimization technique See SUMT serial multiechelon system, model for, 855–856 assumptions for, 856–860 serial two-echelon model, 849–853 servers, 761 determining number of, 808–809 service cost, 808 service industries, simulation applications of, 950 hil76299_sub_idx_1029-1048.qxd 1044 12/3/08 06:31 PM Page 1044 Confirming Pages SUBJECT INDEX service mechanism, 761–762 service time, 761 set partitioning problems, 486 sets, stocking, 535–536 setup cost, 829 shadow prices, 131–133, 136, 147, 204 shift sizes, best mix of, 57 shipments dispatching using BIP models, 470–471 planning of, shipping cost, volume discounts on, 539–540 shortage cost, 830, 832 shortest-path problem algorithm for, 364–365 minimum cost flow problem, 387 other applications, 367–368 Seervada park, 364–365 using Excel to formulate and solve, 365–367 simple discrete distributions, 955 simplex method algebra of (See simplex method, algebra of) applying to radiation therapy example, 119–121 complementary roles of, vs interior-point approach, 143–145 computer implementation, 137–138 constraint boundary, 90 corner-point solutions, 90 CPF solutions (See CPF solutions in simplex method) defined, 24 dual (See dual simplex method) duality, economic interpretation of, 205–206 example, solving, 91–92 fundamental insight, 181–184 geometric interpretations of, 98 in matrix form (See simplex method, in matrix form) minimization, 118–119 modified, 570–572 revised, 137, 180, 184–187 setting up, 94–97 solution concepts, key, 92–94 specialized versions of, 138 summary of, 104–106 in tabular form, 103–107 theory of, 161–187 tie breaking in (See simplex method, tie breaking in) See also transportation simplex method simplex method, algebra of direction of movement, determining, 99–100 initialization, 98 new BF solution, solving for, 101–102 optimality test, 99 for new BF solution, 102 optimal solution, resulting, 102–103 where to stop, determining, 100 simplex method, in matrix form, 137 BF solutions, solving for, 173–175 of current set of equations, 176–178 observations, final, 180 summary of, 178–180 simplex method, tie breaking in for entering basic variable, 108 for leaving basic variable (degeneracy), 108 multiple optimal solutions, 109–111 no leaving basic variable (unbounded Z), 109 Simplex Method—Algebraic Form, 103, 103 Simplex Method—Tabular Form, 107 simplex tableau, 103–104 simulated annealing basic concepts, 626–628 basic simulated annealing algorithm, outline of, 628–629 nonlinear programming example, 632–635 traveling salesman problem example, 629–632 simulation discrete-event vs continuous, 936 examples of, in OR courseware, 946 fixed-time incrementing, summary of, 942–944 inventory management example (performing on spreadsheets), 964–979 (See also Freddie the newsboy’s problem) next-event incrementing, summary of, 944–946 role of, in operations research studies, 935–936 rules of the game, 937–942 simulation, applications of completing a project by deadline, estimating probability of, 947–948 design and operation of distribution systems, 949 design and operation of manufacturing systems, 948–949 design and operation of queueing systems, 947 financial risk analysis, 949 health care applications, 950 managing inventory systems, 947 military applications, 950 new applications, 950–951 to other service industries, 950 random numbers (See random numbers in simulation applications) See also random observations from a probability distribution, generation of simulation, major study (outline of) step 1: formulate the problem and plan the study, 959–960 step 2: collect data and formulate stimulation model, 960 step 3: check accuracy of stimulation model, 960–961 step 4: select software and construct computer program, 961 step 5: test validity of stimulation model, 961–962 step 6: plan stimulations to be performed, 962 step 7: conduct simulation runs and analyze results, 962–963 step 8: present recommendations to management, 963 simulation model, 935 single-server variation of prioritydiscipline queueing models, 800 sink, 373–374 hil76299_sub_idx_1029-1048.qxd 12/3/08 06:31 PM Page 1045 SUBJECT INDEX site selection using BIP models, 469 slack variables, 94, 95, 104 slope of a line, 29 of the profit function, 37–38 slope-intercept form, 29 small minimization example, 467 smart steering support, 722 SOB (sensible-odd-bizarre method), 213–215 social service systems, 765 software commercial software packages, 6, 30 for convex programming, 587–588 discrete-event simulation, 944–945 general-purpose programming language, 961 for linear programming, 138–140 mathematical modeling language, 68–69 for quadratic programming, 572–573 for simulation study, 961 for solving BIP models, 467 for solving transportation problems, 311 solid waste management, 382 solid wastes, reclaiming, 51–55 solution, 33 solution tree, 493 Solve Automatically by the InteriorPoint Algorithm, 287 Solve Automatically by the InteriorPoint Algorithm, 142n Solve Automatically by the Simplex Method, 103 solved node, 364 solvers, 6, 30, 139–140 Solver Table using for two-way sensitivity analysis, 251–253 using to sensitivity analysis systematically, 248 sources, 308 Southern Confederation of Kibbutzim problem, 45–48 Southwestern Airways example, 485–486 spanning tree, 362–363 feasible, and BF solutions, 390–392 with minimum constraints, 617–622 solution, 391 See also minimum spanning tree problem SPARSEFILE produce.dat, 72 sparse format, 72 spider chart, 698 spreadsheet borders and cell shading, 60n decision trees, performing sensitivity analysis on using spreadsheets, 691–700 formulating linear programming models on, 60–64 for Goferbroke Co problem, 693–696 inventory management example for simulation, 964–979 nonconvex programming with, 588–592 solvers, 6, 30, 139–140 See also sensitivity analysis, performing on spreadsheet; individual headings Springfield School Board, 160, 275, 536 stable solution, 657 stagecoach problem, 424–429 stages of problem, 429 standard form, 97 converting to nonstandard form, 211 for general linear programming, 180 for linear programming problem, 45, 169 for primal linear programming problem, 195 using matrices, 173 start-up cost, 50 state of nature, 674 states and transient states in Markov chain, recurrent, 735–737 states of stages, 429 stationary policy, 909 stationary probabilities, 738 stationary transition probabilities, 725–726, 748 steady-state condition, 764 steady-state equations, 751 steady-state probabilities, 738 in continuous time Markov chains, 751–753 Confirming Pages 1045 in long-run properties of Markov chains, 737–740 steepest ascent/mildest descent approach, 615 stochastic continuous-review model assumptions of, 867 example of, 870 order quantity Q, choosing, 867 reorder point R, choosing, 867–870 stochastic process in Markov chains defined, 723–724 inventory example, 724–725 weather example, 724 stochastic single period model for perishable products analysis of (See stochastic single period model for perishable products, analysis of) assumptions of, 874–875 example of, 872–874 application to, 877–878, 880–881 optimal inventory policy (See optimal inventory policy) types of perishable products, 871–872 stochastic single period model for perishable products, analysis of with initial inventory (I 0) and no setup cost (K ϭ 0), 878 with no initial inventory (I ϭ 0) and no setup cost (K ϭ 0), 875–877 with setup cost (K 0), 879–880 stopping rule, 614, 616, 618, 623 strategy, 652 dominated, 655 mixed, 658–660 pure, 658 streamlined algorithms, 304 strong duality property, 201, 202 structural constraints See functional constraints students, assigning to schools, 160, 275, 536 suboptimal solution, 14 sub-tour reversal, 613 algorithm, 613–615 inheriting, 642–643 success, steps to, 423 successive approximations, method of finite-period Markov decision processes, 925–926 hil76299_sub_idx_1029-1048.qxd 1046 12/3/08 06:31 PM Page 1046 Confirming Pages SUBJECT INDEX successive approximations, method of—Cont solving prototype example by, 926–927 SUM keyword, 73 SUM operator, 73–74, 75 SUMPRODUCT, 62–63 SUMT, 580, 585–587 Super Grain Corporation, 88, 606 superoptimal basic solution, 223 Supersuds Corporation example, 482–485 suppliers, 10 supply, 308 supply chain, 848 managing inventories throughout, 849 supply chain management See deterministic multiechelon inventory models for supply chain management supply node, 363 surplus variable, 117–118 Swift & Company, 25 symmetry property, 202 SYSNET, 21–22 systemic sensitivity analysis (parametric programming), 240–245 system service rate, 77 T tabular form of simplex method, 103–107 tabu list, 615, 618, 623 tabu moves, 615, 618, 623 tabu search algorithm, outline of, 616–617 basic concepts, 615 minimum spanning tree problem with constraints, 617–622 questions and answers, 618–619, 623 traveling salesman problem example, 622–625 Taco Bell, 488 target cells, 63 tasks, 334 team approach, technological coefficients, 134 temperature schedule, 628, 629–630, 633–634 tentative initial decision, 131 terminology for linear programming, 30–31 in network optimization models, 360–363 in queueing theory, 763–764 in simplex method, foundations of, 161–164 for solutions of linear programming models, 33–36 Texago Corp., 357 time-cost trade-offs CPM method of, 359, 399, 403 critical path, 401–403 for individual activities, 403–404 project networks, 400–401 prototype example, 399–400 See also crashing decisions Time Inc., 872 toplant, 69 tornado chart, 699–700 total profit, maximizing, 24–25 tractable model transient condition, 764 transient states in Markov chain, recurrent, 735–737 transition intensities, 750 transition probabilities, 726, 748 transportation problem example with dummy destination, 313–315 example with dummy source, 316–318 generalizations of, 318 minimum cost flow problem, 385–386 model, 308–311 prototype example, 305–308 streamlined simplex method for (See transportation simplex method) using Excel to formulate and solve, 311–313 with volume discounts on shipping costs, 539–540 transportation service systems, 765 transportation simplex method initialization, 321–327 iteration, 328–331 optimality test, 327–328 setting up, 319–321 special features of example, 331–333 summary of, 331 transportation simplex tableau, 321 transshipment node, 363, 373 transshipment problem, 318, 387 traveling salesman problem example genetic algorithms, 640–643 nature of metaheuristics, 611–613 simulated annealing, 629–632 tabu search, 622–625 TreePlan Excel add-in, 690–693 TrendLines, 158–160 trial-and-error procedure for constructing lines, 27–29 two-bin system, 866 two demonstration examples, 946 two-person, zero-sum games, 651–653 formulation as, 653–658 two-phased method, 121–126 two-way changes, checking in spreadsheet model, 248–251 two-way sensitivity analysis, using solver table for, 251–253 U U/M (utility functions for money), 700–703 estimating using utility theory, 705–706 unbounded objective, 34, 109 unbounded Z, 34, 109 unconditional state probabilities in Chapman-Kolmogorov equations, 734–735 unconstrained optimization, 547–548 undirected arc, 360 undirected network, 361 undirected path, 361 uniform random number, 952 Union Airways problem, 55–58 United Airlines plan employee work schedules at airports and reservations offices, 56 reassign airplanes to flights when disruptions occur, 13, 382 U.S Military Logistical planning of Operations Desert Storm, 433 unit production cost, 829 hil76299_sub_idx_1029-1048.qxd 12/3/08 06:31 PM Page 1047 Confirming Pages SUBJECT INDEX University Toys and Engineering Professor Action Figures, 722 unstable solution, 657 upper-bound constraints, 58 upper bound technique, 74 incorporating, 389–390 in linear programming problems, 285–287 user team, 17 utility functions for money (U/M), 700–703 utility theory applying to full Goferbroke Co problem, 704–705 equivalent lottery method, 703–704 estimating U(M), 705–706 Goferbroke Co problem with utilities, using decision tree to analyze, 706–707 utility functions for money, 700–703 utilization factor, 763–764 V value of the game, 655 variables basic (See basic variables) binary, 44, 465 complementary, 569 indicating, 169 initial basic, 104 initial nonbasic, 104 negative, 127–129 new, introduction of, 216–217, 235–236 nonbasic (See nonbasic variables) vectors, 173 of basic variables, 174 vehicle routing and scheduling for home services and deliveries, 616 vehicle-routing problem with time windows (VRPTW), 615 Vogel’s approximation method, 323–324, 326–327 volume discounts on shipping costs, 539–540 VRPTW (vehicle-routing problem with time windows), 615 W waiting cost, 808 warm-up period, 944 Waste Management Inc., 505 weak duality property, 201, 202 weather example formulating as Markov chain, 726–728 n-step transition matrices for Chapman-Kolmogorov equations, 733 1047 of stochastic process in Markov chains, 724 weighted average, 109 Welch’s, Inc., 61 Westinghouse, 687 what-if analysis, 15 What’sBest! spreadsheet solver, 74 “Who Wants to be a Millionaire?”, 722 Workers’ Compensation Board (WCB), 681 World Bank, 471 World Health Council problem, 432–440 Worldwide Corporation problem, 69–75 worst-case performance, 142 Wyndsor Glass Co example See dynamic programming; linear programming, Wyndsor Glass Co example X Xerox Corporation, 766 Z zero elements, creation of additional, 344–346 hil76299_sub_idx_1029-1048.qxd 12/3/08 06:31 PM Page 1048 Confirming Pages Errata for First Printing of 9th Edition Page Line Was Should be 3.6 3.5 77, Prob 3.1-7(d) 92 139 160 Welch’s line of Table 1.1 16 13 & 20 Case 4-3 $60 another example Sec 3.6 It should refer to the website itself for the problem data 169 13 60 another example Sec 3.7 The website refers to the CD-ROM for the problem data = b1 179 261, Prob 6.1-7 343 418, Prob 9.7-4 24 14 [-3, —, —] 10 if D,I 9.7-4 429 550 554 698 698 739 770 Fig 10.2 T 32-33 now called posynomials Fig 12.13 12–3x4–2x6 15 15.16 15 15.17 16 eαn from Stop if Specified bottom Precision is Reached 3.7 968 992, LINGO/LINDO Files (should be moved left to align with = b2) [-3, —] -10 is 9.7-4 (Do not use OR Tutorial for this problem) J (twice) (now called posynomials) 12x–3x4–2x6 15.15 15.16 e-αn Stop when precision control limits are reached 3.6 A software alert regarding TreePlan: The original version of TreePlan (part of the Decision ToolKit that now is called TreePlan ToolKit) posted on the book’s website had some problems when using Excel 2010 This version now has been replaced by an updated version that is fully compatible with Excel 2010 ... over four decades, Introduction to Operations Research has been the classic text on operations research Ninth Edition Introduction to Operations Research and the Institute for research for further... to Introduction to Operations Research and two companion volumes, Introduction to Mathematical Programming (2nd ed., 1995) and Introduction to Stochastic Models in Operations Research (1990),... exceptional contributions to the field of operations research and management science In addition to Introduction to Operations Research and two companion volumes, Introduction to Mathematical Programming