Introduction to operations research

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retain important concepts, coming to class better prepared Introduction to ive sar r Frederick S Hillier • Gerald J Lieberman MD DALIM 1265980 12/23/13 CYAN MAG YELO BLACK McGraw-Hill Connect® Engineering provides online presentation, assignment, and assessment solutions A robust set of questions and activities are presented engineering and aligned with the textbook’s learning outcomes Integrate grade reports easily with Learning Management Systems (LMS), such as WebCT and Blackboard—and much more ConnectPlus® Engineering provides students with all the advantages of Connect Engineering, plus 24/7 online access to a media-rich eBook www.mcgrawhillconnect.com Introduction to • A chapter on linear programming under uncertainty that includes topics such as robust optimization, chance constraints, and stochastic programming with recourse • A section on the recent rise of analytics together with operations research • Analytic Solver Platform for Education – exciting new software that provides an all-in-one package for formulating and solving many OR models in spreadsheets Operations Research New to the Tenth Edition y For nearly fve decades, Introduction to Operations Research has been the classic text on operations research Tis edition provides more coverage of dramatic real-world applications than ever before Te hallmark features continue to be clear and comprehensive coverage of fundamentals, an extensive set of interesting problems and cases, and a wealth of state-of-the-art, user-friendly software Tenth Edition hil23453_fm_i-xxx.qxd 1/30/70 7:58 AM Page i Final PDF to printer INSTALLING ANALYTIC SOLVER PLATFORM FOR EDUCATION Instructors: A course code will enable your students to download and install Analytic Solver Platform for Education with a semester-long (140 day) license, and will enable Frontline Systems to assist students with installation, and provide technical support to you during the course To set up a course code for your course, please email 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sent to this address), course code (obtain this from your instructor), and textbook code (enter HLIOR10) If you have this textbook but you aren’t enrolled in a course, call 775-831-0300 and press for assistance with the software 3) On the download page, change 32-bit to 64-bit ONLY if you’ve confirmed that you have 64-bit Excel Click the Download Now button, and save the downloaded file (SolverSetup.exe or SolverSetup64.exe) Most users have 64-bit Windows and 32-bit Excel For Excel 2007, always download SolverSetup In Excel 2010, choose File > Help and look in the lower right In Excel 2013, choose File > Account > About Excel and look at the top of the dialog Download SolverSetup64 ONLY if you see “64-bit” displayed 4) Close any Excel windows you have open 5) Run SolverSetup/SolverSetup64 to install the software When prompted, enter the installation password and the license activation code contained in the email sent to the address you entered on the form above If you have problems downloading or installing, please email support@solver.com or call 775-831-0300 and press (tech support) Say that you have Analytic Solver Platform for Education, and have your course code and textbook code available If you have problems setting up or solving your model, or interpreting the results, please ask your instructor for assistance Frontline Systems cannot help you with homework problems hil23453_fm_i-xxx.qxd 1/30/70 7:58 AM Page ii Final PDF to printer hil23453_fm_i-xxx.qxd 1/30/70 7:58 AM Page iii Final PDF to printer INTRODUCTION TO OPERATIONS RESEARCH hil23453_fm_i-xxx.qxd 1/30/70 7:58 AM Page iv Final PDF to printer hil23453_fm_i-xxx.qxd 1/30/70 7:58 AM Final PDF to printer Page v INTRODUCTION TO OPERATIONS RESEARCH Tenth Edition FREDERICK S HILLIER Stanford University GERALD J LIEBERMAN Late of Stanford University hil23453_fm_i-xxx.qxd 1/30/70 7:58 AM Final PDF to printer Page vi INTRODUCTION TO OPERATIONS RESEARCH, TENTH EDITION Published by McGraw-Hill Education, Penn Plaza, New York, NY 10121 Copyright © 2015 by McGraw-Hill Education All rights reserved Printed in the United States of America Previous editions © 2010, 2005, and 2001 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 McGraw-Hill Education, 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 QVS/QVS ISBN 978-0-07-352345-3 MHID 0-07-352345-3 Senior Vice President, Products & Markets: Kurt L Strand Vice President, General Manager, Products & Markets: Marty Lange Vice President, Content Production & Technology Services: Kimberly Meriwether David Global Publisher: Raghothaman Srinivasan Development Editor: Vincent Bradshaw Marketing Manager: Nick McFadden Director, Content Production: Terri Schiesl Content Project Manager: Mary Jane Lampe Buyer: Laura Fuller Cover Designer: Studio Montage, St Louis, MO Compositor: Laserwords Private Limited Typeface: 10/12 Times Roman Printer: Quad/Graphics All credits appearing on page or at the end of the book are considered to be an extension of the copyright page Library of Congress Cataloging-in-Publication Data Hillier, Frederick S Introduction to operations research / Frederick S Hillier, Stanford University, Gerald J Lieberman, late, of Stanford University.—Tenth edition pages cm Includes bibliographical references and indexes ISBN 978-0-07-352345-3 (alk paper) — ISBN 0-07-352345-3 (alk paper) Operations research I Lieberman, Gerald J II Title T57.6.H53 2015 658.4'032 dc23 2013035901 The Internet addresses listed in the text were accurate at the time of publication The inclusion of a website does not indicate an endorsement by the authors or McGraw-Hill Education, and McGraw-Hill Education does not guarantee the accuracy of the information presented at these sites www.mhhe.com hil23453_fm_i-xxx.qxd 1/30/70 7:58 AM Page vii Final PDF to printer 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 Stanford Symphony Orchestra, and won the Hamilton Award for combining excellence in engineering with notable achievements in the humanities and social sciences Upon his graduation with a BS 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 During his three years of graduate study, he took numerous additional courses in mathematics, statistics, and economics beyond what was required for his MS and PhD degrees while also teaching two courses (including “Introduction to Operations Research”) Upon receiving his PhD degree, he joined the faculty of Stanford University and began work on the 1st edition of this textbook two years later He subsequently 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 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 also is a Fellow of INFORMS In addition, he recently completed a 20-year tenure as the series editor for Springer’s International Series in Operations Research and Management Science, a particularly prominent book series with over 200 published books that he founded in 1993 vii hil23453_fm_i-xxx.qxd viii 1/30/70 7:58 AM Page viii Final PDF to printer ABOUT THE AUTHORS 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, and M I Reiman), and Introduction to Management Science: A Modeling and Case Studies Approach with Spreadsheets (5th ed., McGraw-Hill/Irwin, 2014, co-authored by his son Mark 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, (2nd ed., 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) hil23453_fm_i-xxx.qxd 1/30/70 7:58 AM Page ix Final PDF to printer ABOUT THE CASE WRITERS Karl Schmedders is professor of quantitative business administration at the University of Zurich in Switzerland and a visiting associate professor at the Kellogg Graduate School of Management (Northwestern University) His research interests include management science, financial economics, and computational economics and finance in 2003, a paper by Dr Schmedders received a nomination for the Smith-Breeden Prize for the best paper in Journal of Finance He received his doctorate in operations research from Stanford University, where he taught both undergraduate and graduate classes in operations research, including a case studies course in operations research He received several teaching awards at Stanford, including the university’s prestigious Walter J Gores Teaching Award After post-doctoral research at the Hoover Institution, a think tank on the Stanford campus, he became assistant professor of managerial economics and decision sciences at the Kellogg School He was promoted to associate professor in 2001 and received tenure in 2005 In 2008, he joined the University of Zurich, where he currently teaches courses in management science, spreadsheet modeling, and computational economics and finance At Kellogg he received several teaching awards, including the L G Lavengood Professor of the Year Award More recently he won the best professor award of the Kellogg School’s European EMBA program (2008, 2009, and 2011) and its Miami EMBA program (2011) Molly Stephens is a partner in the Los Angeles office of Quinn, Emanuel, Urquhart & Sullivan, LLP She graduated from Stanford University with a BS degree in industrial engineering and an MS 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 She is a partner in the largest law firm in the United States devoted solely to business litigation, where her practice focuses on complex financial and securities litigation ix hil23453_s_idx_992-1018.qxd 1/22/70 1:00 PM Final PDF to printer Page 1005 SUBJECT INDEX priority discipline, 770–775 queueing networks explanation of, 775–776 infinite queues in series and, 776–777 Jackson networks and, 777–779 Queueing Simulator, 902–903 queueing systems classes of, 737–738 design and operation of, 738–739, 905 explanation of, 732 exponential distribution and, 739–745 queueing theory applications of, 738, 779–784 background of, 738 explanation of, 731 prototype example of, 732 terminology and notation for, 735–736 R R, Q policy (reorder-point, order-quantity policy), 839 radiation therapy, two-phase method and, 125–126 radiation therapy example illustration of, 45–47 primal-dual form and, 217 simplex method and, 123–125 RAND() function (Excel), 895, 908 random digits table, 909 random integer numbers converted to uniform random numbers, 912 explanation of, 909 generation of, 910 probability distributions and, 913 randomized policy, 884–885 random number generation computers for, 910 congruential methods for, 910–912 simulation and, 908 random number generators, 909 random numbers categories of, 909 characteristics of, 909–910 explanation of, 909 move selection rule and, 638 uniform, 895, 910, 911 random observations from probability distribution explanation of, 909 generation of, 912–917 range names, 63, 65 range of uncertainty, 265 rate in = rate out principle, 747–748 1005 recursive relationship, 444, 445 Reducing In-Process (case), 798–799 regional planning problem, 47–51 relaxation explanation of, 831 inventory and, 503, 832–833 LP, 498–500, 503, 513–518, 522–525 Reliable Construction Co problem, 413–424 See also time-cost trade-offs reoptimization in postoptimality analysis, 134 sensitivity analysis and, 233 reorder point, 806, 840–842 replicability, 20 reproducibility, 20 residual capacities, 388, 389 residual network, 388, 389 resource-allocation problems, 29, 44 results cell, 924 retrospective test, 19 revenue, 804 revenue management in airline industry, 854–855 background of, 854–856 capacity-controlled discount fares and, 856–858 considerations for models used in, 861–862 explanation of, 854 overbooking model and, 858–861 reverse arc, 403 revised simplex method applications of, 185 explanation of, 186–189 Rijkswaterstaat (Netherlands) study, 15, 17–18 risk-averse, 708 risk-neutral, 708 risk seekers, 708 robust optimization explanation of, 264–265 extension of, 267 with independent parameters, 265–267 recourse and, 275 stochastic programming and, 272 row reduction, 360 row vector, 964 Russell's approximation method, 338, 340 S saddle point, 666–667 salvage value, 804, 846 Samsung Electronics Corp., 21 Sasol, 918 hil23453_s_idx_992-1018.qxd 1006 1/22/70 1:00 PM Page 1006 Final PDF to printer SUBJECT INDEX satisficing, 16 Save-It Company problem, 53–57 Savvy Stock Selection (case), 615–616 scheduling employment levels problem, 456–462 scientific inventory management, 800 Sears, Roebuck and Company, 626 Seervada Park problem algorithm for shortest-path problem and, 378–379 maximum flow problem and, 390–392 minimum spanning tree problem and, 383–386 overview of, 373–374 sensible-odd-bizarre method (SOB), 215–217 sensitive parameters explanation of, 17, 137 sensitivity analysis to identify, 226 sensitivity analysis application of, 43, 233–250 with Bayes' decision rule, 688–689 changes in bi and, 233–239 changes in coefficients of basic variable and, 244–248 changes in coefficients of nonbasic variable and, 240–244 duality theory and, 197, 217–219 example of, 228–232 explanation of, 13, 197, 226 introduction of new constraint and, 248–250 introduction of new variable and, 244 in postoptimality analysis, 17, 18, 137–138 procedure for, 227–228, 232–233 purpose of, 226 sensitivity report to perform, 259–263 on spreadsheets, 250–263, 700–707 types of, 264 sensitivity reports, 259–263 separable programming explanation of, 559–560, 583–584 extensions of, 589–590 key property of, 586–589 reformulation as linear programming problem and, 584–586 sequences of numbers, 909 sequential-approximation algorithms, 590–591 sequential linear approximation algorithm (Frank-Wolfe), 591–594 sequential unconstrained algorithms, 590 sequential unconstrained minimization technique See SUMT serial multiechelon system assumptions for, 828–832 model for, 827–828 serial two-echelon model, 821–825 servers, 733 service industry simulation applications, 908 service level, 848, 849 service time, 733–735, 739, 741, 742 set covering problems, 496 set partitioning problems, 496 shadow price duality theory and, 185, 219 explanation of, 135–137 sensitivity analysis and, 226 shipment dispatch, 480–481 shipping costs, 549, 550 Shipping Wood to Market (case), 370 shortage cost, 804 shortest-path problem algorithm for, 378 applications for, 381–382 Excel to formulate and solve, 379–381 minimum cost flow problem and, 401 overview of, 377 Seervada Park, 378–379 simple discrete distributions, 913 simplex method See also dual simplex method; network simplex method algebra of, 101–107 basic feasible solutions in, 105–106, 172–174, 176–177 computer implementation of, 141–143 CPF solutions and, 46, 94–101, 121, 146, 147, 163, 166–174 direction of movement and, 103–104 duality and, 207–208, 219 equality constraints and, 116–120 examples in, 95–96, 123–125 explanation of, 2, 26, 93–95 extensions to augmented form of problem and, 171–174 functional constraints in ≥ form and, 120–122 geometric concepts in, 93–95 interior-point approach and, 145–147 key solution concepts in, 96–98 in matrix form, 141, 174–186 maximum flow problem and, 388 method to set up, 98–101 minimization in, 122–123 modified, 580–582 negative right-hand sides and, 120 no feasible solutions and, 130–131 optimality test and, 103, 341–342 postoptimality analysis and, 133–141 property revealed by matrix form of, 183–186 revised, 185–189 hil23453_s_idx_992-1018.qxd 1/22/70 1:00 PM Page 1007 SUBJECT INDEX summary of, 108–111 in tabular form, 107–111 terminology for, 163–166 tie breaking in, 112–115 for transportation problem, 333–347 two-phase method in, 125–130 use of, 26 with variables allowed to be negative, 131–133 simplex tableau, 108, 109, 200, 227–232, 333 simulated annealing basic concepts of, 636–638 basic simulated annealing algorithm and, 638–639 nonlinear programming and, 642–645 traveling salesman problem and, 639–642 simulated annealing algorithm, 638–639 simulation continuous, 894 discrete-event, 894 examples of, 894–900 explanation of, 892–893 fixed-time incrementing and, 900–902 next-event incrementing and, 902–904 optimization with, 924–939 in OR studies, 893–894 random number generation and, 908–912 random observation generation from probability distribution and, 912–917 software for, 893–894, 918–919 spreadsheets for, 921–939 steps in OR research studies based on applying, 917–921 simulation applications distribution system design and operation, 907 financial risk analysis, 907 health care, 907–908 innovative new, 908 inventory system management, 905 manufacturing systems design and operation, 906–907 military, 908 project completion deadline, 905–906 queuing systems design and operation, 905 service industry, 908 simulation models checking accuracy of, 918 explanation of, 893 formulation of, 917–918 planning simulations for, 919–920 preparing recommendations based on, 921 simulation run for, 920–921 software for, 918–919 testing validity of, 919 Final PDF to printer 1007 sink, 387 site selection, 479–480 slack variables, 98, 99, 108, 227 slope-intercept form, of objective function, 31 SOB (sensible-odd-bizarre method), 215–217 social service systems, 737 soft constraints, 264, 270 software linear programming, 142–144 nonlinear programming, 582–583, 597–598 operations research background and development of, for simulation, 893–894, 918–919 for solving BIP models, 477 solid waste reclamation problem, 53–57 solutions See also basic feasible (BF) solutions; optimal solutions corner-point feasible, 36 feasible, 35 infeasible, 35 optimal, 6, 13, 36 suboptimal, 16 Solver (Excel) See also Analytic Solver Platform for Education (ASPE) application of, 65 description of, 65–69 to find local optima, 599–601 for integer programming, 477 for linear programming, 143 sensitivity analysis and, 276 source, 387 Southern Confederation of Kibbutzim problem, 47–51 Southwestern Airways example, 495–496 spanning trees explanation of, 376–377, 627 feasible, 405, 406 minimum, 627–632 spreadsheets ASPE's Solver and, 70–71 formulating linear programming models on, 62–65 sensitivity analysis on, 250–263, 700–707 software for, 918 Solver use and, 65–69 stable products, 842–843 stable solution, 667 stagecoach problem, 438–443 stages, in dynamic programming problems, 443 standard form, for linear programming model, 34 state of nature, 684 states, in dynamic programming problems, 443 stationary, deterministic policy, 883 statistic cells, 926 hil23453_s_idx_992-1018.qxd 1008 1/22/70 1:00 PM Page 1008 Final PDF to printer SUBJECT INDEX StatoilHydro, 393 steady-state condition, 736, 747, 749 steepest ascent/mildest descent approach, 625 stochastic continuous-review model assumptions of, 839 example of, 842 explanation of, 838–839 order quantity Q and, 839 reorder point R and, 840–842 stochastic inventory model, 801 stochastic process, 877 stochastic programming with recourse applications of, 274–275 example of, 272–274 explanation of, 271–272 stochastic single period model for perishable products analysis of, 847–852 application of, 849–850, 852–853 assumptions of, 846–847 example of, 844–846 explanation of, 842–843 optimal policy and, 853–854 types of perishable products and, 843–844 stock portfolios, 550–552 strong duality property, 674 structural constraints See functional constraints submatrices, 964 suboptimal solutions, 16 sub-tour reversal, 622–623 sub-tour reversal algorithm, 623–625 SULUM, SUMT example of, 596–597 explanation of, 590, 595–596 summary of, 596 superoptimal basic solution, 231 Supersuds Corporation example, 492–495 supply chain, 820 supply chain management See deterministic multiechelon inventory models for supply chain management supply node, 377 surplus variable, 121–122 Swift & Company, 27 symbols, use in linear programming models, 33–34 symmetry property, 204 system service rate, 750–751 T table lookup approach, 913 tabular form, simplex method in, 107–111 tabu list, 625 tabu search basic tabu search algorithm and, 626–627 explanation of, 625 minimum spanning tree problem with constraints and, 627–632 traveling salesman problem and, 632–636 Taco Bell Corporation, 498 tasks, 348, 350 teams, 3, 11 technological coefficients, 138 time advance methods, 900 time-cost trade-offs crashing decisions and, 418–423 critical path and, 415–417 for individual activities, 417–418 network model and, 413 project networks and, 414–415 prototype example of, 413–414 Time Inc., 844 transient condition, 736, 746 transition matrix, 877, 878 transition probabilities, 880 transportation problem basic feasible (BF) solutions and, 336–345 with dummy destination, 327–329 with dummy source, 330–332 Excel to formulate and solve, 325–327 explanation of, 318 generalizations of, 332 minimum cost flow problem and, 400 model of, 322–325 prototype example of, 319–322 streamlined simplex method for, 333–347 with volume discounts on shipping costs, 549, 550 transportation service systems, 737 transportation simplex method application of, 351–352 drawback of, 352 explanation of, 333 features of example of, 345–347 initialization of, 335–341 iteration for, 342–345 optimality test for, 341–342 set up for, 333–335 summary of, 345 transportation simplex tableau, 335, 346–347 transpose operation, 963 transshipment node, 377, 397 transshipment problem, minimum cost flow problem and, 401 hil23453_s_idx_992-1018.qxd 1/22/70 1:00 PM Final PDF to printer Page 1009 SUBJECT INDEX traveling salesman problem example of, 621–623 genetic algorithms and, 651–653 simulated annealing and, 639–642 tabu search and, 632–636 trend charts, 931 two-bin system, 838 two-person constant-sum game, 676 zero-sum games explanation of, 661–663 formulation of, 663–668 two-phase method explanation of, 125–126 use of, 126–130 U unbounded Z, 36, 113 uncertainty chance constraints and, 268–271 overview of, 225–226 robust optimization and, 264–267 sensitivity analysis and, 226–233 sensitivity analysis application and, 233–250 sensitivity analysis on spreadsheets and, 250–264 stochastic programming with recourse and, 271–275 unconstrained optimization explanation of, 557–558 multivariable, 567–573, 960 one-variable, 562–567, 959–960 undirected arcs, 374–375 undirected networks, 375, 401 undirected path, 375–376 uniform random numbers, 895, 910, 911 Union Airways problem, 57–60 United Airlines, 396 unstable solution, 667 upper bound technique example of, 300–301 explanation of, 299–300 network simplex method and, 403–404 utility function (U/M) for money M, 708–713 utility theory application of, 711–715 equivalent lottery method and, 710–711 estimating U/M and, 712–713 overview of, 707–708 utility functions for money and, 708–710 utilization factor, 735–736, 751 1009 V value of game, 665 variables artificial, 117 binary, 349, 475, 483–496 with bound on negative values allowed, 132 decision, 13, 28, 33, 74, 218 indicating, 171 negative, 131–132 in network simplex method, 406–408 with no bound on negative values allowed, 132–133 nonbasic, 100, 210, 217–218, 240 slack, 98, 99, 108, 227 surplus, 121–122 variance-reducing techniques, 920 vectors of basic variables, 176 explanation of, 964–965 Vogel's approximation method, 337–341 W waiting cost, 780 warm-up period, 902 Waste Management, Inc., 515 Welch's, Inc., 63 Westinghouse Science and Technology Center, 697 what-if analysis, 17 winning in Las Vegas problem, 466–468 Winter Simulation Conference, 908 World Health Council problem, 446–452 Worldwide Corporation problem, 73–79 Wyndor Glass Co problem additivity assumption and, 41–43 approach to, 27–28 background of, 26 certainty assumption and, 43 chance constraints and, 269, 270 complementary basic solutions for, 210 conclusions about, 31, 36, 37 constraint boundary equations for, 172–174 constraints in, 164 CPF solutions for, 165, 166, 169–170 divisibility assumption and, 43 dual simplex method and, 292–294 formulation of mathematical model for, 28–29 graphical solution to, 29–31 interior-point algorithm and, 145 LINDO and LINGO use and, 147–150 hil23453_s_idx_992-1018.qxd 1010 1/22/70 1:00 PM Final PDF to printer Page 1010 SUBJECT INDEX nonlinear programming and, 552–556, 587–588 primal and dual problems for, 199, 202 proportionality assumption and, 38–41 sensitivity analysis and, 228–232, 234–236, 238–242, 245–258 simplex method and, 94–98, 102, 108–111, 113–117, 131, 132, 183–184, 186, 188 spreadsheets for, 62–71, 251–258 stochastic programming and, 272–274 uncertainty and, 266, 267 X Xerox Corporation, 738 Y yes/no decisions, 349, 474, 483, 495 Z zero elements, 358–360 hil23453_s_idx_992-1018.qxd 1/22/70 1:00 PM Page 1011 Final PDF to printer hil23453_s_idx_992-1018.qxd 1/22/70 1:00 PM Page 1012 Final PDF to printer hil23453_s_idx_992-1018.qxd 1/22/70 1:00 PM Page 1013 Final PDF to printer hil23453_s_idx_992-1018.qxd 1/22/70 1:00 PM Page 1014 Final PDF to printer hil23453_s_idx_992-1018.qxd 1/22/70 1:00 PM Page 1015 Final PDF to printer hil23453_s_idx_992-1018.qxd 1/22/70 1:00 PM Page 1016 Final PDF to printer hil23453_s_idx_992-1018.qxd 1/22/70 1:00 PM Page 1017 Final PDF to printer hil23453_s_idx_992-1018.qxd 1/22/70 1:00 PM Page 1018 Final PDF to printer Additional Features Te text website (www.mhhe.com/hillier) contains many other software options, including: • Student versions of the MPL Modeling System and its elite solvers, as well as an MPL tutorial and formulation examples from the text • Student versions of LINGO and LINDO with many formulation examples from the text • OR Tutor and IOR Tutorial for efciently learning various algorithms • Excel spreadsheet formulations and solutions, using either the standard Excel Solver or the Analytic Solver Platform for Education, for the examples in the text • Many Excel templates for automatically solving a variety of models Digital supplements ConnectPlus (125917400X) and LearnSmart (1259173992) have been added to this textbook package to make it convenient for students to learn the material and easier for instructors to assign and grade their work See below for more on these products McGraw-Hill LearnSmart® is available as a standalone product or an integrated feature of McGraw-Hill Connect Engineering It is an adaptive learning system designed to help students learn faster, study more efciently, and retain more knowledge for greater success LearnSmart assesses a student’s knowledge of course content through a series of adaptive questions It pinpoints concepts the student does not understand and maps out a personalized study plan for success Tis innovative study tool also has features that allow instructors to see exactly what students have accomplished www.mhlearnsmart.com Tenth Edition Operations Research Ann Hillier Lieberman Powered by the intelligent and adaptive LearnSmart engine, SmartBook™ is the frst and only continuously adaptive reading experience available today Distinguishing what students know from what they don’t, and honing in on concepts they are most likely to forget, SmartBook personalizes content for each student Reading is no longer a passive and linear experience but an engaging and dynamic one, where students are more likely to master and retain important concepts, coming to class better prepared Introduction to ive sar r Frederick S Hillier • Gerald J Lieberman MD DALIM 1265980 12/23/13 CYAN MAG YELO BLACK McGraw-Hill Connect® Engineering provides online presentation, assignment, and assessment solutions A robust set of questions and activities are presented engineering and aligned with the textbook’s learning outcomes Integrate grade reports easily with Learning Management Systems (LMS), such as WebCT and Blackboard—and much more ConnectPlus® Engineering provides students with all the advantages of Connect Engineering, plus 24/7 online access to a media-rich eBook www.mcgrawhillconnect.com Introduction to • A chapter on linear programming under uncertainty that includes topics such as robust optimization, chance constraints, and stochastic programming with recourse • A section on the recent rise of analytics together with operations research • Analytic Solver Platform for Education – exciting new software that provides an all-in-one package for formulating and solving many OR models in spreadsheets Operations Research New to the Tenth Edition y For nearly fve decades, Introduction to Operations Research has been the classic text on operations research Tis edition provides more coverage of dramatic real-world applications than ever before Te hallmark features continue to be clear and comprehensive coverage of fundamentals, an extensive set of interesting problems and cases, and a wealth of state-of-the-art, user-friendly software Tenth Edition ... PDF to printer ABOUT THE AUTHORS In addition to Introduction to Operations Research and two companion volumes, Introduction to Mathematical Programming (2nd ed., 1995) and Introduction to Stochastic... 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... CHAPTER Introduction 1.1 The Origins of Operations Research 1.2 The Nature of Operations Research 1.3 The Rise of Analytics Together with Operations Research 1.4 The Impact of Operations Research