WWW.YAZDANPRESS.COM WWW.YAZDANPRESS.COM WWW.YAZDANPRESS.COM WWW.YAZDANPRESS.COM This page intentionally left blank WWW.YAZDANPRESS.COM WWW.YAZDANPRESS.COM R E V I S E D T H I R T E E N T H E D I T I O N AN INTRODUCTION TO MANAGEMENT SCIENCE QUANTITATIVE APPROACHES TO DECISION MAKING David R Anderson University of Cincinnati Dennis J Sweeney University of Cincinnati Thomas A Williams Rochester Institute of Technology Jeffrey D Camm University of Cincinnati Kipp Martin University of Chicago Australia • Brazil • Japan • Korea • Mexico • Singapore • Spain • United Kingdom • United States WWW.YAZDANPRESS.COM WWW.YAZDANPRESS.COM This is an electronic version of the print textbook Due to electronic rights restrictions, some third party content may be suppressed Editorial review has deemed that any suppressed content does not materially affect the overall learning experience The publisher reserves the right to remove content from this title at any time if subsequent rights restrictions require it For valuable information on pricing, previous editions, changes to current editions, and alternate formats, please visit www.cengage.com/highered to search by ISBN#, author, title, or keyword for materials in your areas of interest WWW.YAZDANPRESS.COM WWW.YAZDANPRESS.COM An Introduction to Management Science: Quantitative Approaches to Decision Making, Revised Thirteenth Edition David R Anderson, Dennis J Sweeney, Thomas A Williams, Jeffrey D Camm, & Kipp Martin VP/Editorial Director: Jack W Calhoun Publisher: Joe Sabatino Senior Acquisitions Editor: Charles McCormick, Jr Developmental Editor: Maggie Kubale Editorial Assistant: Courtney Bavaro Marketing Communications Manager: Libby Shipp Marketing Manager: Adam Marsh Content Project Manager: Jacquelyn K Featherly Media Editor: Chris Valentine Manufacturing Coordinator: Miranda Klapper Production House/Compositor: MPS Limited, a Macmillan Company Senior Art Director: Stacy Jenkins Shirley Internal Designer: Michael Stratton/Chris Miller Design Cover Designer: Craig Ramsdell Cover Images: © Getty Images/GlowImages Printed in the United States of America 14 13 12 11 10 © 2012 South-Western, a part of Cengage Learning ALL RIGHTS RESERVED No part of this work covered by the copyright herein may be reproduced, transmitted, stored or used in any form or by any means graphic, electronic, or mechanical, including but not limited to photocopying, recording, scanning, digitizing, taping, Web distribution, information networks, or information storage and retrieval systems, except as permitted under Section 107 or 108 of the 1976 United States Copyright Act, without the prior written permission of the publisher For product information and technology assistance, contact us at Cengage Learning Customer & Sales Support, 1-800-354-9706 For permission to use material from this text or product, submit all requests online at www.cengage.com/permissions Further permissions questions can be emailed to permissionrequest@cengage.com ExamView® and ExamView Pro® are registered trademarks of FSCreations, Inc Windows is a registered trademark of the Microsoft Corporation used herein under license Macintosh and Power Macintosh are registered trademarks of Apple Computer, Inc used herein under license Library of Congress Control Number: 2010935955 Student Edition ISBN 13: 978-1-111-53224-6 Student Edition ISBN 10: 1-111-53224-9 Package Student Edition ISBN 13: 978-1-111-53222-2 Package Student Edition ISBN 10: 1-111-53222-2 South-Western Cengage Learning 5191 Natorp Boulevard Mason, OH 45040 USA Cengage Learning products are represented in Canada by Nelson Education, Ltd For your course and learning solutions, visit www.cengage.com Purchase any of our products at your local college store or at our preferred online store www.cengagebrain.com WWW.YAZDANPRESS.COM WWW.YAZDANPRESS.COM This page intentionally left blank WWW.YAZDANPRESS.COM WWW.YAZDANPRESS.COM Dedication To My Parents Ray and Ilene Anderson DRA To My Parents James and Gladys Sweeney DJS To My Parents Phil and Ann Williams TAW To My Wife Karen Camm JDC To My Wife Gail Honda KM WWW.YAZDANPRESS.COM WWW.YAZDANPRESS.COM This page intentionally left blank WWW.YAZDANPRESS.COM WWW.YAZDANPRESS.COM Brief Contents Preface xxv About the Authors xxix Chapter Introduction Chapter An Introduction to Linear Programming 28 Chapter Linear Programming: Sensitivity Analysis and Interpretation of Solution 92 Chapter Linear Programming Applications in Marketing, Finance, and Operations Management 153 Chapter Advanced Linear Programming Applications 214 Chapter Distribution and Network Models 255 Chapter Integer Linear Programming 317 Chapter Nonlinear Optimization Models 365 Chapter Project Scheduling: PERT/CPM 412 Chapter 10 Inventory Models 453 Chapter 11 Waiting Line Models 502 Chapter 12 Simulation 542 Chapter 13 Decision Analysis 602 Chapter 14 Multicriteria Decisions 659 Chapter 15 Time Series Analysis and Forecasting 703 Chapter 16 Markov Processes 761 Chapter 17 Linear Programming: Simplex Method On Website Chapter 18 Simplex-Based Sensitivity Analysis and Duality On Website Chapter 19 Solution Procedures for Transportation and Assignment Problems On Website Chapter 20 Minimal Spanning Tree On Website Chapter 21 Dynamic Programming On Website Appendixes 787 Appendix A Building Spreadsheet Models 788 Appendix B Areas for the Standard Normal Distribution 815 Appendix C Values of e؊λ 817 Appendix D References and Bibliography 818 Appendix E Self-Test Solutions and Answers to Even-Numbered Problems 820 Index 853 WWW.YAZDANPRESS.COM WWW.YAZDANPRESS.COM This page intentionally left blank WWW.YAZDANPRESS.COM WWW.YAZDANPRESS.COM Appendix E Chapter 16 N = (I - Q)-1 = c a 0.82 b p1 ϭ 0.5, p2 ϭ 0.5 c p1 ϭ 0.6, p2 ϭ 0.4 NR = c a 0.10 as given by the transition probability (1) b p1 ϭ 0.90p1 ϩ 0.30p2 p2 ϭ 0.10p1 ϩ 0.70p2 (2) p1 ϩ p2 ϭ (1) Using (1) and (3), 0.10p1 Ϫ 0.30p2 ϭ 0.10 p1 Ϫ 0.30 (1 Ϫ p1) ϭ 0.10 p1 Ϫ 0.30 ϩ 0.30p1 ϭ 0.40p1 ϭ 0.30 p1 ϭ 0.75 p2 ϭ (1 Ϫ p1) ϭ 0.25 a p1 ϭ 0.92, p2 ϭ 0.08 b $85 City Suburbs Suburbs 0.02 0.99 b p1 ϭ 0.333, p2 ϭ 0.667 c City will decrease from 40% to 33%; suburbs will increase from 60% to 67% a p1 ϭ 0.85p1 ϩ 0.20p2 ϭ 0.15p3 (1) p2 ϭ 0.10p1 ϩ 0.75p2 ϭ 0.10p3 (2) p3 ϭ 0.05p1 ϩ 0.05p2 ϭ 0.75p3 (3) p1 ϩ p2 ϩ p3 ϭ (4) Using (1), (2), and (4) provides three equations with three unknowns; solving provides p1 ϭ 0.548, p2 ϭ 0.286, and p3 ϭ 0.166 b 16.6% as given by p3 c Quick Stop should take 667 Ϫ 0.548(1000) ϭ 119 Murphy’s customers and 333 Ϫ 0.286(1000)ϭ 47 Ashley’s customers Total 166 Quick Stop customers It will take customers from Murphy’s and Ashley’s a MDA b p1 ϭ 1⁄ 3, p2 ϭ 2⁄ 10 Ϫ 1(0.59), Ϫ 1(0.52) 11 I = c d (I - Q) = c Q = c 0.75 -0.05 0.25 0.05 -0.25 d 0.75 0.25 d 0.25 1.3636 0.4545 d 0.0909 1.3636 1.3636 0.4545 0.5 dc 0.0909 1.3636 0.5 0.0 0.909 d = c 0.2 0.727 0.909 0.091 d = [7271 0.727 0.273 Estimate $1729 in bad debts BNR = [4000 5000]c 12 3580 will be sold eventually; 1420 will be lost 14 a Graduate and Drop Out b P(Drop Out) ϭ 0.15, P(Sophomore) ϭ 0.10, P(Junior) ϭ 0.75 c 0.706, 0.294 d Yes; P(Graduate) ϭ 0.54 P(Drop Out) ϭ 0.46 e 1479 (74%) will graduate Appendix A a City 0.98 0.01 851 Self-Test Solutions and Answers to Even-Numbered Problems ϭF6*$F$3 0.091 d 0.273 1729] WWW.YAZDANPRESS.COM WWW.YAZDANPRESS.COM 852 Appendix E Self-Test Solutions and Answers to Even-Numbered Problems Cell Formula D14 E14 F14 G14 H14 I14 ϭC14*$B$3 ϭC14*$B$7 ϭC14*$B$9 ϭ$B$5 ϭSUM(E14:G14) ϭD14-H14 10 Error in SUMPRODUCT range in cell B17 Cell A23 should be Lexington WWW.YAZDANPRESS.COM WWW.YAZDANPRESS.COM Index “Note: Entries accompanied by n indicate notes Chapters 17 through 21 are found on the accompanying website and are indicated by the chapter number followed by the page number (i.e., 17-5)” A Absorbing state probabilities, 781–782 Accounts receivable analysis, 771–775 Accuracy, of forecasts, 713–717 exponential smoothing and, 723–725 moving averages for, 718–720 Activity times, in project scheduling, 413 crashing, 432–433 scheduling with known times for, 413–422 scheduling with unknown times for, 422–430 time-cost tradeoffs for, 431 Additivity, 34n Advertising advertising campaign planning, 202–203 media selection application of linear programming for, 155–158 Airline industry Air New Zealand, 318–319 American Airlines, 2–3, 223, 224 Bombardier Flexjet, 366–367 preboard airport screening simulation, 573 revenue management used by, 223–230 simulation of overbooking in, 543 waiting line problems for reservations in, 539–540 Air New Zealand, 318–319 All-integer linear programs, 319–321 computer solutions of, 324–325 graphical solutions of, 322–324 Alternative optimal solutions, 57–58 American Airlines, 2–3 revenue management used by, 223, 224 Analog models, Analytic hierarchy process (AHP), 17, 679–680 consistency in, 685–686 pairwise comparisons in, 681–683, 687–688 priority rankings developed in, 688–689 software for, 689n synthesization in, 684–685 Annuities, variable, 236 Arcs, 19-8–19-9 in networks, 257 in project networks, 414 Arrival rates, 505 Arrival times, 564–565 Artificial variables, 17-21 Asset allocation, 236 Assignment problems, 263–268, 19-2 Excel for, 311–313 Hungarian method, 19-18–19-21 ASW Publishing, Inc., 357–358 AT&T, 283 @Risk (software), 557, 574 Automatic teller machines (ATMs), 503–504 simulation of, 563–574, 594–597 Automobile industry car rental industry, 224, 479–480 environmental compliance in, 374, 405–407 Ford Motor Company, 678 Porsche Shop, 443–444 Averages See Means B Backorders, 468, 471, 472n Backward passes, in project networks, 417 Banking applications, 215–216 automatic teller machines, 503–504 bank location problems, 334–337 simulation of automatic teller machines, 563–574, 594–597 Basic feasible solutions, 17-4–17-5 Basic solutions, 17-4 Basic variables, 17-4, 17-9 Bayer Pharmaceuticals, 629 Bayes' theorem, 630–633 Bellman, Richard, 21-2 Best-case scenarios, 546 Beta probability distributions, 425 Binary expansion, 340n Binary variables, 318 Blackjack (twenty-one) absorbing state probabilities in, 781–782 simulation of, 581 Blending problems, 183–188, 207–209 nonlinear optimization for, 382–387 Bombardier Flexjet (firm), 366–367 Branches adding, in TreePlan, 655 computing branch probabilities, 630–634 in decision trees, 607 Breakeven analysis, 16 Excel for, 24–27 C Call centers, 544 Calling populations, finite and infinite, 526–529 Canonical form, 18-14 WWW.YAZDANPRESS.COM WWW.YAZDANPRESS.COM 854 Index Capacitated transportation problems, 263 Capital budgeting problems, 325–329 Car rental industry, 224, 479–480 Central limit theorem, 429n Chance events, 604 Chance nodes, 605 adding, in TreePlan, 655–656 Citibank, 503–504 Clean Energy Act (U.S., 2007), 374 Communications networks, 20-5 Computer industry, call centers in, 544 Computers for all-integer linear programs, 324–325 decision analysis software for, 616, 620n for goal programming, 671–673 linear programming applications of, 50–52, 109n sensitivity analysis applications of, 103–110 Computer simulations implementation of, 574–575 random numbers generated for, 549–551 of sensitivity analysis problem, 118–122 Concave functions, 371 Conditional constraints, 342 Conditional probabilities, 632 Consequence nodes, 605 Conservative approach, in decision making, 607–608 Consistency, in analytic hierarchy process, 685–686 Consistency ratios, 685–686 Constant demand rate assumption, 454–455 Constant service times, 523 Constant supply rate assumption, 464 Constrained nonlinear optimization problems, 367–371 Constraint coefficients, 112 Constraints conditional and corequisite, 342 in goal programming, 661–663, 667n, 668n multiple-choice and mutually exclusive, 341–342 redundant constraints, 48 Continuous review inventory systems, 484 Contour lines, 370–371 Controllable inputs, 543 Convery, John, 21-21 Convex functions, 372 Corequisite constraints, 342 Corporate Average Fuel Economy (CAFE) regulations, 374, 405–407 Costs backorder costs, 471 fixed, in capital budgeting problems, 326–329 goodwill costs, 468 holding costs, 456–458 models of, 14–15 in simulations, 547 time-cost tradeoffs, in project scheduling, 431–436 in total cost models, 455n, 465–467 of waiting line channels, 519–520 Crashing, in project scheduling, 431 of activity times, 432–433 linear programming model for, 434–436 Crew scheduling problems, 318–319, 340–341 Critical activities, 416, 420 Critical Path Method (CPM), 17, 413 for project scheduling with known activity times, 413–422 Critical paths, in project scheduling with known activity times, 414–420 Microsoft Office Project for, 450–452 with unknown activity times, 425–428 Crystal Ball (software), 557n, 574, 597–601 Curling (sport), 776 Curve fitting models, 724–725 Excel Solver for, 758–759 for exponential trend equation, 733 for liner trends, 726–729 for seasonality, 737 software for, 730n Customer arrival times, 564–565 Customer service times, 565 CVS Corporation, 454 Cycle time, 461 Cyclical patterns, 713 D Dantzig, George, 2, 30, 17-3 Data, preparation of, for models, 10–11 Data envelopment analysis (DEA), 215–223 banking applications of, 215–216 Decision alternatives, 604 Decision analysis, 17, 603–604 branch probabilities for, 630–634 at Eastman Kodak, 603 with probabilities, 610–615 problem formulation in, 604–610 risk analysis in, 615–616 with sample information, 620–630 sensitivity analysis in, 616–620 TreePlan for, 653–658 without probabilities, 607–610 Decision making multicriteria decisions, 660 problem solving and, 3–4 quantitative analysis in, 4–6 Decision nodes, 605 Decision strategies, 623–627 Decision trees, 606–607, 621–623 TreePlan for, 653–658 Decision variables, in blending problems, 188n dn, 21-7 in transportation problems, 258, 262n Decomposition methods, 366–367 Deere & Company, 489 Definitional variables, 234n Degeneracy, 110n, 17-29, 17-33–17-35 WWW.YAZDANPRESS.COM WWW.YAZDANPRESS.COM 855 Index Degenerate solutions, 19-12 Delta Airlines, 17-2 Demand See also Inventory models constant demand rate assumption for, 454–455 in order-quantity, reorder point inventory model, with probabilistic demand, 480–484 in periodic review inventory model with probabilistic demand, 484–488 quantity discounts for, 472–474 shortages and, 467–472 in simulation model, 557 single-period inventory models with probabilistic demand, 474–480 in transportation problems, 260 Dennis, Greg A., 20-5 Deterministic models, 9–10 inventory models, 474 DIRECTV (firm), 391–392 Disability claims, 612–613 Discounts, quantity discounts, 472–474 Discrete-event simulation models, 563, 573–574n Distribution models, 17 for assignment problems, 263–268 at Kellogg Company, 180 maximal flow problems, 279–283 for shortest-route problems, 276–279 for transportation problems, 256–263 for transshipment problem, 268–275 Distribution system design problems, 329–334 “Divide and conquer” solution strategy, 21-10 Divisibility, 34n Drive-through waiting line simulations, 589–590 Drug decision analysis, 629 Drugstore industry, CVS Corporation, 454 Duality, 18-14–18-20 Dual prices, 18-6, 18-18 absolute value of, 18-12n Dual problems, 18-14 Dual values, 101–102 caution regarding, 106 in computer solution, 104–105 nonintuitive, 112–114 in nonlinear optimization problems, 374 Dual variables, 18-14, 18-16–18-18 Duke Energy Corporation, 207–209, 704–705 Duke University, 634 Dummy agents, in assignment problems, 267n Dummy destinations, 19–18 Dummy origins, 19-2, 19-17, 19-19 in transportation problems, 260 Dummy variables in monthly data, 739–740 for seasonality without trends, 734–735 for seasonality with trends, 737, 739 Dynamic programming knapsack problem, 21-10–21-16 notation for, 21-6–21-10 production and inventory control problem, 21-16–21-20 shortest-route problem, 21-2–21-6 stages of, 21-6 Dynamic simulation models, 563 E Eastman Kodak, 93, 603 Economic order quantity (EOQ) formula, 459 Economic order quantity (EOQ) model, 454–459 Excel for, 462–463 optimal order quantity formula for, 500–501 order-quantity, reorder point model with probabilistic demand, 480–484 order quantity decision in, 459–460 quantity discounts in, 472–474 sensitivity analysis for, 461–462 time of order decision in, 460–461 Economic production lot size model, 464–467 optimal lot size formula for, 501 Edmonton Folk Festival, 340–341 EDS, 20-5 Efficiency data envelopment analysis to identify, 215–223 of sample information, 630 warehouse efficiency simulation, 576–577 Eisner, Mark, 18 Electricity generation, 704–705 Elementary row operations, 17-12 Energy industry, 704–705 Environmental Protection Agency (EPA, U.S.), 21-21 Environmental regulation, in automobile industry, 374, 405–407 Erlang, A K., 503 Events, in simulations, 563 Excel, 14n for assignment problems, 311–313 for breakeven analysis, 24–27 for economic order quantity model, 462–463 for financial planning problem, 210–213 for forecasting, 753–754 to generate random numbers, 549, 552 for integer linear programming, 360–364 for inventory simulation, 561–562 for linear programming, 87–91 for matrix inversions, 785–786 for nonlinear optimization problems, 409–411 for scoring models, 701–702 for sensitivity analysis, 148–150 for simulations, 554–556, 590–597 for transportation problems, 308–310 for transshipment problems, 313–315 TreePlan add-in for, 653–658 for waiting line models, 511–512 for waiting line simulation, 569–573 Excel Solver for curve fitting, 754–759 for integer linear programming, 361 WWW.YAZDANPRESS.COM WWW.YAZDANPRESS.COM 856 Index Excel Solver (continued) for linear programming, 89 for nonlinear optimization problems, 409–411 for sensitivity analysis, 148 for transshipment problem, 314 Expected times, in project scheduling, 425 Expected value approach, 610–612 Expected values (EVs), 610 of perfect information, 613–615 of sample information, 629–630 sensitivity analysis for, 617–620 Expert Choice (software), 689n Exponential probability distributions, 506 in multiple-channel waiting line model, with Poisson arrivals, 512–517 in single-channel waiting line model, with Poisson arrivals, 508–512 Exponential smoothing, 721–725 Excel for, 753–754 Excel Solver for, 754–758 spreadsheets for, 726n Exponential trend equation, 733 Extreme points, in linear programming, 48–50 F False-positive and false-negative test results, 634 Fannon, Vicki, 341 Feasible region, 38 Feasible solutions, 38–42 infeasibility and, 58–60 Financial applications of linear programming, 161 banking applications, 215–216 capital budgeting problems, 325–329 financial planning applications of, 164–172, 210–213 portfolio models, 229–235 portfolio selection, 161–164 revenue management applications, 223–229 Financial planning applications, 164–172 Excel for, 210–213 index fund construction as, 374–379 Markowitz portfolio model for, 379–382 simulation of, 585–587 Finite calling populations, 526–529 First-come, first served (FCFS) waiting lines, 507 Fixed costs, 14 in capital budgeting problems, 326–329 Fleet assignment, 17-2 Flow capacity, 279 Little's flow equations for, 517–518 simulation in, 544 Flow problems See Network flow problems Ford Motor Company, 678 Forecast errors, 713–716 Forecasting, 18, 704 accuracy of, 713–717 adoption of new products, 387–391 Excel for, 753–754 Excel Solver for, 754–759 LINGO for, 759–760 methods used for, 713 moving averages for, 717–720 in utility industry, 704–705 Forward passes, in project networks, 417 Four-stage dynamic programming procedure, 21-6 Free variables, 378n Fundamental matrices, 772–774 G Game theory, 236–247 Gantt, Henry L., 413 Gantt Charts, 413 Microsoft Office Project for, 451 General Accountability Office (GAO, U.S.), 762 General Electric Capital, 164–165 General Electric Plastics (GEP), 110 Global optima, 371–374 Goal constraints, 667n Goal equations, 661–663 for multiple goals at same priority level, 669–670 Goal programming, 17, 660–663 complex problems in, 668–674 graphical solution procedures for, 664–667 model used in, 667 objective functions with preemptive priorities for, 663 scoring models for, 674–678 Golf course tee time reservation simulation, 587–589 Goodwill costs, 468 Graphical solution procedures, 35–48 for all-integer linear programs, 322–324 for goal programming, 664–667 for minimization, 54–55 in sensitivity analysis, 95–103 Greedy algorithms, 20-5n H Harmonic averages, 405, 406 Harris, F W., 459 Heery International, 268 Heuristics, 19-2 Hewlett-Packard, 454 Hierarchies, in analytic hierarchy process, 679–680 Holding costs, 456–458, 464 Horizontal patterns, 705–707 Hospitals bonds issued for financing of, 422 performance of, 216–222 Human resources training versus hiring decisions, 203–204 workforce assignment applications in, 179–183, 205–207 Hungarian method, 19-18–19-21 Hypothetical composites, 216–217 WWW.YAZDANPRESS.COM WWW.YAZDANPRESS.COM 857 Index I IBM Corporation, 454 Iconic models, Immediate predecessors, in project scheduling, 413 Incoming arcs, 19-19 Incremental analysis, 476 Index funds, 374–379 Infeasibility, 58–60, 61n, 17-29–17-31, 17-35 goal programming for, 674n Infinite calling populations, 526 Influence diagrams, 605, 620–621 Inputs, to models, random, generating, 549–554 in simulations, 543 Insurance industry, portfolio models used in, 236 Integer linear programming, 16, 318 all-integer linear programs for, 321–324 for bank location problems, 334–337 for crew scheduling problem, 318–319 for distribution system design problems, 329–334 Excel, 360–364 at Kentron Management Science, 343 for product design and market share problems, 337–341 types of models for, 319–321 0-1 linear integer programs for, 325–340 Integer variables, 318, 319n binary expansion of, 340n modeling flexibility in, 341–344 Interarrival times, 564 Interior point solution procedures, 17-2n Inventory models, 17, 454 economic order quantity model, 454–463 economic production lot size model, 464–467 at Kellogg Company, 180 multistage inventory planning, 489 optimal lot size formula for, 501 optimal order quantity formula for, 500–501 order-quantity, reorder point model, with probabilistic demand, 480–484 periodic review model, with probabilistic demand, 484–488 planned shortages in, 467–472 in production and inventory applications, 283–286 quantity discounts in, 472–474 simulation in, 543, 558–562, 592–594 single-period, with probabilistic demand, 474–480 Inventory position, 460 Inversions of matrices, 785–786 Investments, 146–147 index funds for, 374–379 Markowitz portfolio model for, 379–382 portfolio models for, 229–235 portfolio optimization models, with transaction costs, 402–405 portfolio selection for, 161–164 simulation of financial planning application, 585–587 Iteration, 17-11, 17-15 J Jensen, Dale, 443 Jeppesen Sanderson, Inc., 173 Joint probabilities, 632 K Kellogg Company, 180 Kendall, D G., 520–521 Kentron Management Science (firm), 343 Knapsack problem, 21-10–21-16 Koopmans, Tjalling, 30 L Lead time, 461 Lead-time demand, 461 Lead-time demand distribution, 482 Lease structure applications, 164–165 Linear programming, 16, 29–30 See also Integer linear programming advertising campaign planning application, 202–203 applications of, 154 for assignment problems, 263–268 for blending problems, 183–188, 207–209 computer solutions in, 50–52 data envelopment analysis application of, 215–223 Excel for, 87–91 extreme points and optimal solution in, 48–50 financial planning applications of, 164–172 game theory and, 236–247 for goal programming problems with multiple priority levels, 674n graphical solution procedure in, 35–48 integer linear programming and, 318, 319n LINGO for, 85–87 make-or-buy decisions applications of, 164–172 marketing applications of, 154 marketing research application of, 158–160 for maximal flow problems, 279–283 for maximization, 30–34 media selection application of, 155–158 for minimization, 52–57 notation for, 62–64 portfolio models as, 229–235 portfolio selection applications of, 161–164 production scheduling applications of, 172–179, 204–205 for productivity strategy, 83–84 revenue management applications in, 223–229 WWW.YAZDANPRESS.COM WWW.YAZDANPRESS.COM 858 Index Linear programming (continued) sensitivity analysis and, 94 for shortest-route problems, 276 traffic control application of, 64–65 for transportation problems, 256–263 venture capital application of, 84–85 workforce assignment applications of, 179–183, 205–207 for workload balancing, 82–83 Linear programming models, 34 for crashing, 434–436 Linear trends, 726–730 LINGO, 14n for all-integer linear programs, 324–325 extra variables in, 379n for forecasting, 759–760 free variables in, 378n for linear programming, 85–87 for nonlinear optimization problems, 408–409 for sensitivity analysis, 150–152 Little, John D C., 517 Little's flow equations, 517–518 Local optima, 371–374 Location problems, 334–337 Long-term disability claims, 612–613 Lot size, 464 Lot size model, 464–467 optimal lot size formula for, 501 LP relaxation, 320, 322 Lustig, Irv, M Machine repair problems, 528–529 Make-or-buy decisions, 164–172 Management science techniques, 2, 16–18 Markov process models, 17–18 at Merrill Lynch, 13 Marathon Oil Company, 154 Marginal costs, 15 Marketing applications of linear programming, 154 advertising campaign planning, 202–203 forecasting adoption of new products, 387–391 marketing planning, 154 marketing research, 158–160 media selection, 155–158 Marketing research, 158–160 Market share analysis of, 763–770 and product design problems, 337–341 Markov chains with stationary transition probabilities, 762 Markov decision processes, 770n Markov process models, 18, 762, 17–18 for accounts receivable analysis, 771–775 blackjack application of, 781–782 curling application of, 776 for market share analysis, 763–770 matrix inversions for, 785–786 matrix notation for, 782–783 matrix operations for, 783–785 Markowitz, Harry, 379 Markowitz portfolio model, 379–382 Mathematical models, 7, 34 Mathematical programming models, 34n Matrices Excel for inversions of, 785–786 fundamental matrices, 772–774 notation for, 782–783 operations of, 783–785 Maximal flow problems, 279–283 Maximization graphical solution procedure for, 46 linear programming for, 30–34 local and global maximums, 371 in maximal flow problems, 279–283 in transportation problems, 261 in TreePlan, 658 MeadWestvao Corporation, 29 Mean absolute error (MAE), 714 for moving averages, 718–720 Mean absolute percentage error (MAPE), 715, 716 for moving averages, 718–720 Means horizontal patterns fluctuating around, 705 moving averages, 717–720 Mean squared error (MSE), 715–716 exponential smoothing and, 724 for moving averages, 718–720 Media selection applications, 155–158 Medical applications drug decision analysis in, 629 for health care services, 762 hospital performance, 216–222 medical screening test, 634 Memoryless property, 770n Merrill Lynch, 13 Microsoft Office Project, 450–452 Middleton, Michael R., 653n Minimal spanning tree algorithm, 20-2–20-5 Minimax regret approach, 608–610 Minimization, 18-17 linear programming for, 52–57 local and global minimums, 371 in transportation problems, 261–263 in TreePlan, 658 Minimum cost method, 19-5–19-6 Minimum ratio test, 17-11 Mixed-integer linear programs, 318, 320, 340n at Kentron Management Science, 343 Mixed strategy solutions, 239–246 Model development, 7–10 Modeling (problem formulation), 31–33 flexibility in, with 0-1 linear integer programs, 341–344 Models, for assignment problems, 267 of cost, revenue, and profits, 14–16 in goal programming, 667 WWW.YAZDANPRESS.COM WWW.YAZDANPRESS.COM 859 Index for integer linear programming, 319–321 portfolio models, 229–235 scoring models, 674–678 for shortest-route problems, 279 for transportation problems, 262 for transshipment problem, 274–275 Model solutions, 11–12 Modified distribution method (MODI), 19-7 Monte Carlo simulations, 557n Monthly data, for seasonality, 739–740 Moving averages, 717–720 Excel for, 753 exponential smoothing of, 721–725 moving, 720 Multicriteria decision making, 660 analytic hierarchy process for, 679–680 establishing priorities in, using AHP, 680–688 Excel for scoring models in, 701–702 goal programming in, 660–668 for multiple goals at same priority level, 668–674 problems in, scoring models for, 674–678 Multiple-channel waiting line models, 512 with Poisson arrivals, arbitrary service times, and no waiting lines, 524–526 with Poisson arrivals and exponential service times, 512–517 Multiple-choice constraints, 341–342 Multistage inventory planning, 489 Mutual funds, 229–235 Mutually exclusive constraints, 341–342 N Naïve forecasting method, 713 National Car Rental, 224, 479–480 Net evaluation index, 19-8 Net evaluation rows, 17-3 Netherlands, 484, 576–577 Network flow problems, 256 assignment problems, 263–268 at AT&T, 283 maximal flow problems, 279–283 shortest-route problems, 276–279 transportation problems, 256–263 transshipment problem, 268–275 Network models, 17 Networks, 257 New Haven (Connecticut) Fire Department, 530 Nodes, in networks, 257 in influence diagrams, 605 in project networks, 414 in shortest-route problems, 276 transshipment nodes, 268 Non-basis variables, 17-4 Nonlinear optimization problems, 366, 392 blending problems, 382–387 Excel for, 409–411 for forecasting adoption of new products, 387–391 index fund construction as, 374–379 LINGO for, 408–409 portfolio optimization models, with transaction costs, 402–405 production application of, 367–374 for scheduling lights and crews, 366–367 Nonlinear programming, 17 Nonlinear trends, 730–733 Normal distributions, 429 Normalized pairwise comparison matrix, 684 North American Product Sourcing Study, 275 Notation for linear programming, 62–64 matrix notation, 782–783 Nutrition Coordinating Center (NCC; University of Minnesota), 116 O Objective function coefficients, 18-2–18-6 Objective functions, coefficients for, 95–100, 103n in goal programming, 663 for multiple goals at same priority level, 670–671 in nonlinear optimization problems, 366 Oglethorpe Power Corporation, 635 Ohio Edison (firm), 603 100 percent rule, 18-12n Operating characteristics, 503 in multiple-channel waiting line model, with Poisson arrivals and arbitrary service times, 524–526 in multiple-channel waiting line model, with Poisson arrivals and exponential service times, 513–517 in single-channel waiting line model, with Poisson arrivals and arbitrary service times, 521–523 in single-channel waiting line model, with Poisson arrivals and exponential service times, 508–510 for waiting line models with finite calling populations, 527–529 Operations management applications blending problems, 183–188, 207–209 make-or-buy decisions, 164–172 production scheduling, 172–179, 204–205 workforce assignments, 179–183, 205–207 Operations research, 18 Opportunity losses, 608, 614–615n, 19-23 Optimality criterion, 17-18 Optimal lease structure, 164–165 Optimal lot size formula, 501 Optimal order quantity formula, 500–501 Optimal solutions, 11, 43–44, 48–50 alternative, 57–58 infeasibility and, 58–60 local and global, in nonlinear optimization problems, 371–374 sensitivity analysis and, 93 WWW.YAZDANPRESS.COM WWW.YAZDANPRESS.COM 860 Index Optimistic approach, in decision making, 607 Ordering costs, 455, 456, 460, 464 Order-quantity, reorder point inventory model, with probabilistic demand, 480–484 Outgoing arcs, 19-8–19-9 Outputs, of simulations, 543 Overbooking, by airlines, 543 P Pairwise comparison matrix, 682–683 normalized, 684 Pairwise comparisons, in analytic hierarchy process, 681–683, 687–688 consistency in, 685–686 normalization of, 684 Parameters, 545 Paths, in networks, 416 Payoffs, in TreePlan, 656–657 Payoff tables, 605–606 Peak loads, 705 Perfect information, 613–615 Performance, operating characteristics of, 503 Performance Analysis Corporation, 102 Periodic review inventory model, with probabilistic demand, 484–488 Periodic review inventory systems, 485, 487–488 Petroleum industry, 704–705 simulation used by, 562–563 Pfizer (firm), 557 Pharmaceutical industry CVS Corporation in, 554 drug decision analysis in, 629 simulation used in, 557 Pharmacia (firm), 554 Pivot columns, 17-12 Pivot elements, 17-12 Pivot rows, 17-12 Poisson probability distributions, for waiting line problems, 505 in multiple-channel model, 512–517 in single-channel model, with arbitrary service times, 521–523 in single-channel model, with exponential service times, 508–512 Pooled components, 382 Pooling problems, 382–387 Porsche Shop, 443–444 Portfolio optimization models, 229–235 Markowitz portfolio model, 379–382 with transaction costs, 402–405 Portfolio selection, 161–164 in simulation of financial planning application, 585–587 Posterior probabilities, 620, 633 Postoptimality analysis, 93 See also Sensitivity analysis Preboard airport screening simulation, 573 Preemptive priorities, 661, 663 Primal problems, 18-14, 18-17 finding dual of, 18-18–18-20 using duals to solve, 18-18 Principle of optimality, 21-2 Priority level and goals, 661 multiple goals at same priority level, 668–674 problems with one priority level, 673n Prior probabilities, 620 Probabilistic demand models order-quantity, reorder point inventory model, 480–484 periodic review inventory model, 484–488 single-period inventory model with, 474–480 Probabilistic inputs, 543 generating values for, 549–554 Probabilistic models, 10 Probabilities conditional, 632 in TreePlan, 656–657 Problem formulation (modeling), 31–33, 604–605 decision trees in, 606–607 influence diagrams in, 605 payoff tables in, 605–606 Process design problem, 21-26–21-27 Proctor & Gamble, 275–276 Product design and market share problems, 337–341 forecasting adoption of new products, 387–391 Product development, simulation in, 543 Production application of nonlinear optimization problems for, 367–374 blending problems in, 183–188 at Kellogg Company, 180 production and inventory applications, 283–286 scheduling problems for, 172–179, 204–205, 359–360 Production lot size model, 464–467 optimal lot size formula for, 501 Productivity, linear programming for, 83–84 Product Sourcing Heuristic (PSH), 275–276 Profits, models of, 15 Program Evaluation and Review Technique (PERT), 17, 413 for project scheduling with known activity times, 413–422 Project networks, 413 Project scheduling, 413 with known activity times, 413–422 Microsoft Office Project for, 450–452 PERT/CPM, 17 time-cost tradeoffs in, 431–436 with uncertain activity times, 422–430 Proportionality, 34n Pseudorandom numbers, 549n WWW.YAZDANPRESS.COM WWW.YAZDANPRESS.COM 861 Index Pure network flow problems, 275n Pure strategy solutions, 238–239 Q Quadratic trend equation, 731 Qualitative forecasting methods, 704 Quantitative analysis, 6–13 in decision making, 4–6 at Merrill Lynch, 13 Quantitative forecasting methods, 704 Quantities, in inventory models optimal order quantity formula, 500–501 in order-quantity, reorder point model with probabilistic demand, 481–482 Quantity discounts, 472–474 Queue discipline, 507 Queueing theory, 503 Queues, 503 Queuing models See Waiting line models R Railroads, 263 Random numbers, 549–554 Ranges of feasibility, 106, 18-9 Ranges of optimality, 95, 18-2 Redden, Emory F., 268 Reduced cost, 105 Redundant constraints, 48 Regression analysis, 730n Relevant costs, 106 Reorder points, 460 in order-quantity, inventory model with probabilistic demand, 480–484 Repair problems call centers and, 544 machine repair problems, 528–529 office equipment repairs, 540–541 Reports, generation of, 12 Reservations, by airlines simulation of overbooking in, 543 waiting line problems in, 539–540 Return function rn(xn, dn), 21-9 Revenue, models of, 15 Revenue management airline industry's use of, 224–230 National Car Rental's use of, 224 Review periods, 485–486, 488 Risk analysis, 545 in conservative portfolios, 230–232 in decision analysis, 615–616 example of, 554–556 in moderate portfolio, 232–235 in pharmaceutical industry, 557 simulation in, 547–554, 590–592 what-if analysis, 545–547 Risk profiles, 627–629 Rounding, in all-integer linear programs, 322–323 S Saaty, Thomas L., 679 Saddle points, 239 Safety stocks, 483 Sample information, 620 expected values of, 629–630 Satellite television, 391–392 Scheduling See also Project scheduling crew scheduling problem, 318–319 of flights and crews, 340–341 production scheduling, 172–179, 204–205, 359–360 project scheduling, 413 project scheduling, PERT/CPM for, 17 volunteer scheduling problem, 340–341 Scoring models, 674–678 Excel for, 701–702 at Ford Motor Company, 678 used in analytic hierarchy process, 689n Seasonality and seasonal patterns, 709–710, 733 monthly data for, 739–740 trends and, 710–712, 737–739 without trends, 734–737 Seasongood & Mayer (firm), 422 Sensitivity analysis, 93–95 cautionary note on, 344 computer solutions to, 103–110, 118–122 in decision analysis, 615–620 for economic order quantity model, 461–462 Excel for, 148–150 graphical approach to, 95–103 limitations of, 110–115 LINGO for, 150–152 Service level, 484 Service rates, 523 Service times, 523 Setup costs, 464 Shadow price See Dual values Shortages, in inventory models, 467–472 Shortest-route problems, 276–279 Short-term disability claims, 612–613 Simon, Herbert A., Simplex-based sensitivity analysis and duality duality, 18-14–18-20 sensitivity analysis with Simples tableu, 18-2–18-13 Simplex method, 2, 17-2 algebraic overview of, 17-2–17-5, 17-32–17-33 assignment problems, 19-18–19-24 basic feasible solutions, 17-4–17-5 basic solution, 17-4 criterion for removing a variable from the current basis (minimum ratio test), 17-11 degeneracy, 17-33–17-35 equality constraints, 17-24–17-25 general case tableau form, 17-20–17-27 greater-than-or-equal-to constraints, 17-20–17-24 improving the solution, 17-10–17-12 infeasibility, 17-29–17-31, 17-35n WWW.YAZDANPRESS.COM WWW.YAZDANPRESS.COM 862 Index Simplex method (continued) interpreting optimal solutions, 17-15–17-19 interpreting results of an iteration, 17-15, 17-15–17-18 phase I of, 17-23 phase II of, 17-23–17-24 simplex tableau, 17-7–17-10 unboundedness, 17-31–17-32 Simplex tableau, 17-7–17-10 calculating next, 17-12–17-14 criterion for entering a new variable into Basis, 17-11 Simulation experiments, 543 Simulations, 17, 543–544 advantages and disadvantages of use of, 575–576 computer implementation of, 574–575 Crystal Ball for, 597–601 of drive-through waiting lines, 589–590 Excel for, 590–597 of financial planning application, 585–587 of golf course tee time reservations, 587–589 inventory simulations, 558–562 preboard airport screening simulation, 573 in risk analysis, 547–556 used by petroleum industry, 562–563 verification and validation issues in, 575 of waiting line models, 563–574 warehouse efficiency simulation, 576–577 Simultaneous changes, 111–112, 18-13 Single-channel waiting lines, 504–507 with Poisson arrivals and arbitrary service times, 521–523 with Poisson arrivals and exponential service times, 508–512 Single-criterion decision problems, Single-period inventory models with probabilistic demand, 474–480 Slack variables, 47–48 Smoothing, exponential, 721–725 Sousa, Nancy L S., 603 Spanning trees, 20-2 Spreadsheets See also Excel for exponential smoothing, 726n for simulations, 574–575 Stage transformation function, 21-8 Standard form, in linear programming, 47, 48 State of the system, 763 State probabilities, 765 States of nature, 604 sample information on, 620 State variables xn and xnϪ1, 21-8 Static simulation models, 563 Steady-state operation, 507–508 Steady-state probabilities, 768 Stepping-stone method, 19-8–19-12 Stochastic (probabilistic) models, 10 See also Probabilistic demand models Stockouts (shortages), 467 Strategies mixed, 239–246 pure, 238–239 Sunk costs, 106 Supply constant supply rate assumption for, 464 quantity discounts in, 472–474 in transportation problems, 260 Surplus variables, 55–56 Synthesization, 684–685 System constraints, 667n T Tableau form, 17-5–17-7 eliminating negative right-hand-side values, 17-25–17-26 equality constrains, 17-24–17-25 general case, 17-20–17-27 steps to create, 17-26–17-27 Target values, 661 Taylor, Frederic W., Tea production, 122–123 Telecommunications AT&T, 283 satellite television, 391–392 Time series analysis, 704 exponential smoothing in, 721–725 moving averages for, 717–720 spreadsheets for, 726n Time series patterns, 705 cyclical patterns, 713 horizontal patterns, 705–707 linear trend patterns, 726–730 nonlinear trend patterns, 730–733 seasonal patterns, 709–710, 733–740 trend patterns, 707–709 trend patterns, seasonal patterns and, 710–712 Timing See Activity times; Project scheduling Tornado diagrams, 620n Total balance method, for accounts receivable, 771 Total cost models, 455n, 465–467 Traffic control, 64–65 simulation in, 544 Transaction costs, 402–405 Transient periods, 507–508 Transition probabilities, 763–764 Transportation problems, 256–263, 19-2 assignment problem as special case of, 267n Excel for, 308–310 shortest-route problems, 276–279 transshipment problem and, 268–275 for Union Pacific Railroad, 263 Transportation simplex method, 19-17 phase I: finding initial feasible solution, 19-2–19-6 phase II: iterating to optimal solution, 19-7–19-16 problem variations, 19-17–19-18 WWW.YAZDANPRESS.COM WWW.YAZDANPRESS.COM 863 Index Transportation tableaux, 19-2 Transshipment problems, 268–275 Excel for, 313–315 production and inventory applications of, 283–286 TreePlan (software), 653–658 Trend patterns, 707–709 Excel for projection of, 754 linear, 726–730 nonlinear, 730–733 seasonality and, 734–737 seasonal patterns and, 710–712 Trials of the process, 763 Truck leasing, 147–148 Two-person, zero-sum games, 236, 247n U Unbounded feasible region, 17-31–17-32, 17-35n Unbounded solutions, 60–61, 61n Unconstrained nonlinear optimization problems, 367–378 Union Pacific Railroad, 263 Unit columns, 17-8 Unit vectors, 17-8 Upjohn (firm), 554 Utility industry, 704–705 V Validation issues, in simulations, 575 Valley Metal Container (VMC), 320–321 Values expected values, 610 random, generating, 549–554 in simulation experiments, 543 Vancouver International Airport, 573 Vanguard Index Funds, 375 Variable annuities, 236 Variable costs, 14 Variables binary variables, 318 decision variables, definitional variables, 234n free variables, 378n integer variables, 318 slack variables, 47–48 surplus variables, 55–56 Venture capital, 84–85 Verification issues, in simulations, 575 Volume, models of, 14–15 Volunteer scheduling problem, 340–341 W Waiting line (queueing) models, 17, 503 for airline reservations, 539–540 for automatic teller machines, 503–504 drive-through line simulation of, 589–590 economic analysis of, 519–520 Excel for, 511–512 with finite calling populations, 526–529 Little's flow equations for, 517–518 multiple-channel, with Poisson arrivals, arbitrary service times and no waiting line, 524–526 multiple-channel, with Poisson arrivals and exponential service times, 512–517 office equipment repairs, 540–541 other models, 520–521 preboard airport screening simulation, 573 simulation in, 544, 563–574 single-channel, with Poisson arrivals and arbitrary service times, 521–523 single-channel, with Poisson arrivals and exponential service times, 508–512 structures of, 504–508 Warehouse efficiency, 576–577 Water quality management problem, 21-21 Weighted moving averages, 720 exponential smoothing of, 721–725 Welte Mutual Funds, Inc., 161–164 What-if analysis, 545–547 Whole Foods Markets, 507 Workers' Compensation Board of British Columbia, 612–613 Workforce assignment applications, 179–183, 205–207 Workload balancing, 82–83 Worst-case scenarios, 546 Z 0-1 linear integer programs, 318, 320, 325–340 for bank location problems, 334–337 binary expansion of integer variables for, 340n for capital budgeting problems, 325–329 for crew scheduling problem, 318–319 for distribution system design problems, 329–334 at Kentron Management Science, 343 multiple-choice and mutually-exclusive constraints in, 341–342 for product design and market share problems, 337–341 for volunteer scheduling problem, 340–341 Zero-sum games, 236, 247n WWW.YAZDANPRESS.COM WWW.YAZDANPRESS.COM David R Anderson Dennis J Sweeney Thomas A Williams Jeffrey D Camm Kipp Martin Dear Colleague: to Management Science the 13th Edition of An Introduction of sion revi the ent pres to sed plea We are ld like to share some of the meet your teaching needs, and we wou will on editi new the that in certa We are changes in the new edition are adding a new member to ges, we want to announce that we Prior to getting into the content chan University He has been at the received his Ph.D from Clemson the author team: Jeffrey Camm Jeff ford University and a visiting Stan a visiting scholar at been has and , 1984 e sinc ti inna Cinc University of th College Jeff has published Tuck School of Business at Dartmou the at n ratio inist adm ness busi of r professo in operations management At of optimization applied to problems area ral gene the in rs pape 30 than more Excellence and in 2006 received named the Dornoff Fellow of Teaching was he ti, inna Cinc of y ersit Univ the currently serves as editor-in-chief of Operations Research Practice He the INFORMS Prize for the Teaching Education We welcome Jeff to the board of INFORMS Transactions on of Interfaces, and is on the editorial years to come s will make the text even better in the author team and expect his new idea kplace Because it is a ® inant analysis software used in the wor dom the me beco has el Exc that r It is clea and engineering graduates must be l decision models, today’s business ytica anal ding buil for tool l erfu pow basics and modeling to this edition e added an appendix on spreadsheet efor ther have We el Exc in t cien profi el, and how to audit the model how to build a reliable spreadsheet mod Appendix A covers basic Excel skills, once it is constructed lysis and Interpretation (Linear Programming: Sensitivity Ana pter Cha sed revi ly cant ifi sign We have focus of this chapter, but we ysis and its interpretation are still the anal ty itivi sens al ition Trad ) tion of Solu example, difficulty with multiple of traditional sensitivity analysis (for ns tatio limi the on rial mate d adde have to explore models by actually ficients) and we encourage students changes and changes in constraint coef ents that a model should be viewed problems Indeed, we teach our stud changing the data and re-solving the the data for multiple scenarios of experimentation; this means running as a laboratory It should be used for the input data e major revisions and updates and Forecasting) has also undergon lysis Ana es Seri e (Tim 15 pter Cha to select an appropriate forecasting on using the pattern in a time series s focu d ease incr has now 15 pter Cha moving averages and exponential sure forecast accuracy, we show how method After discussing how to mea We show how to use optimization time series with a horizontal pattern smoothing can be used to forecast a ng Then, for time series that othing constant in exponential smoothi to find the best-fitting value of the smo to set up and solve the least a curve-fitting approach, showing how have only a long-term trend, we take inear trend We continue the nonl parameter values for both linear and squares problem to find the best-fitting s can be used to forecast a able vari show how the use of dummy and , data onal seas for oach appr curve-fitting forces the material presented ve taking a curve-fitting approach rein belie We cts effe onal seas with s time serie in optimization chapters many of you have used The ge in terms of software We know that Finally, we have made a major chan y years With this edition, we have has accompanied the text for so man Management Scientist software that continued WWW.YAZDANPRESS.COM WWW.YAZDANPRESS.COM decided to discontinue use of The Man agement Scientist We suggest that past users of The Management Scientist move to either Excel Solv er or LINGO as a replacement App endices describing the use of Excel Solver and LINGO are provided This edition marks our transition from Excel 2007 to Excel 2010 In particular, you will find the screen shot s of Excel Solver in the appendices base d on the Solver that ships with 2010 Fortunately, there is no chan ge in how you build models using the 2010 version of Excel Solver developed by Frontline Systems How ever, those familiar with the 2007 vers ion of Exc el Solver will notice changes in the Dialog Boxes The scre en shots and corresponding discussi on we provide in the appendices will equip students to use the 2010 vers ion Considerable deliberation went into the decision to discontinue the use of The Management Scientist and there are three reasons why we are mak ing this move First, The Management Scientist software is no longer being developed and supported by its authors We not think it is beneficial to our readers to expend effort learning and using software that is no longer supported Second, students are far more likely to encounter Excel-based software in the workpla ce Finally, for optimization problems , The Management Scientist often required a fair amount of algebraic manipulation of the model to get all variables on the left-hand side of the constraints and a single constant on the right-hand side Modern softw are packages, such as LINGO and Excel Solver, not require this and allow the user to enter a model in its more natu ral formulation Users who liked the simple input format of The Management Scientist and not wan t to switch to Excel Solver may wish to use LINGO This allows for directly entering the objective function and constraints It is possible to use LINGO as your calculator and avoi d any arithmetic or algebraic simplifi cations We believe this strengthens our model-focused approach, as it eliminates the distraction of having to manipulate the model before solving At the publication Website we provide a documented LINGO model for every optimization example developed in the text We also provide an Excel Solver model for all of thes e problems For project management, a trial version of Microsoft Proj ect Professional 2010 is packaged with each new copy of the text and we include an appendix on how to use it in Chapter For these reasons, The Management Scientist software is no longer discussed in the text For those of you wishing to continue to use The Management Scientist, it is available at no extra charge on the Website for this book To access addi tional course materials, please visit www.cengagebrain.com At the Cen gageBrain.com home page, fill in the ISBN of your title (from the back cover of your book) using the search box at the top of the page This will take you to the product page where these resources can be found The focus of the text has always been on modeling and the applications of thes e models As such, the book has always been software-independent With the decision to discontinue The Management Science software, we were faced with the decision of how to present optimization output Rather than choose LINGO or Excel Solver output (which present sensitivi ty analysis in slightly different ways), we decided to present a generic output for optimization problems in the body of the chapters This removes any dependence on a single piece of software In this edition, we use the dual value rather than the dual price The dual value is defined as the change in the optimal objective func tion value resulting from an increase of one unit in the right-hand side of a constraint Using the dual valu e eliminates the need to discuss diffe rences in interpretation between maximization problem and a minimiz ation problem The dual value and its sign are interpreted the same, regardless of whether the problem is a minimization or a maximization In this generic output, we of course also present the allowable changes to the right-hand sides for which the dual value holds The new edition continues our long tradition of writing a text that is appl icati ons oriented and pragmatic We thank you for your interest in our text Our ultimate goal is to prov ide you with material that truly helps your students learn and also mak es your job as their instructor easier We wish you and your students the very best Sincerely, David R Anderson Dennis J Sweeney Thomas A Williams Jeffrey D Camm Kipp Martin ... 255 6.1 Transportation Problem 256 Problem Variations 260 A General Linear Programming Model 262 6.2 Assignment Problem 263 Problem Variations 266 A General Linear Programming Model 267 6.3 Transshipment... Variations 274 A General Linear Programming Model 274 6.4 Shortest-Route Problem 276 A General Linear Programming Model 279 6.5 Maximal Flow Problem 279 6.6 A Production and Inventory Application 283... Solver 754 Appendix 15.3 Forecasting with LINGO 759 Chapter 16 Markov Processes 761 16.1 Market Share Analysis 763 16.2 Accounts Receivable Analysis 771 Fundamental Matrix and Associated Calculations