Other material (such as the dictionary notation) was adapted Operations Research An Introduction (9th Edition) PDF Operations Research An Introduction, 9 e is ideal for or junior senior undergraduate and first year graduate courses in Operations Research in departments of Industrial Engineering, Business Administration, Statistics, Computer Science, and Mathematics. Chapter 16. Free Operations Research An Introduction 10th Edition PDF Book Excellent Customer Service. Ohapterz x1 = ll.a..4A.o Op/;{mum Oc:<:UrJ" a.. -I- fl: x, = s- , K tr,,.,$ f'6t' ftn,,.,. ConnectPlus provides students with all the advantages of Connect, plus 24/7 access to an eBook. s Xz.. Chapter 20. Pre-View. Chapter 1. Introduction to Operations Research, 11th Edition by Frederick Hillier and Gerald Lieberman (9781259872990) Preview the textbook, purchase or get a FREE instructor-only desk copy. Chapter 10. COUPON: Rent Operations Research 10th edition by Taha eBook (9780134480190) and save up to 80% on online textbooks at Chegg.com now! Major revision is designed to meet the needs of beginning through advanced students with an emphasis placed on the formulation and applications aspects. Introduction to Operations Research 10th Edition $ 19.79. Tupili. Metaheuristics Operations Research: An Introduction, Global Edition eBook, 10th Edition : 9781292165561 Note: From time to time, not all images from hardcopy texts will be found in eBooks due to copyright restrictions. Stay current in your professional life with our handpicked selection of business books or simply relax and savor a book beyond business that spurs your curiosity. Network Optimization Models The hallmark features of this edition include new section and chapters, updated problems, clear and comprehensive coverage of fundamentals, an extensive set of interesting problems and cases, and state-of-the-practice operations research software used in conjunction with examples from the text. Chapter 29. Solutions manual for operations research an introduction 10th edition by taha ibsn 1. The Application of Queueing Theory Operations Research by H.a TAHA Solution Manual (8th Edition) Click the start the download. ; Computational issues in the revised simplex method appear in Chapter 7, including a comparison between product form and the LU decomposition used with the revised simplex method. Introduction to Operations Research 10th Edition by Frederick S. Hillier, ISBN-13: 978-0073523453 [PDF eBook eTextbook] 1390 pages Publisher: McGraw-Hill; Revised ed. Only logged in customers who have purchased this product may leave a review. Chapter 12. Register. All Rights Reserved. Book Description Paperback. Chapter 13. Hillier's Introduction to Operations Research, tenth edition, includes the power of McGraw-Hill’s LearnSmart--a proven adaptive learning system that helps students learn faster, study more efficiently, and retain more knowledge through a series of adaptive questions. Inventory Theory Appropriate for a variety of junior and senior undergraduate and first year graduate courses in operations research. Additional Special Types of Linear Programming Problems Added text mini-updates appear throughout the book. While building on the classic strengths of the text the author continues to find new ways to make the text current and relevant to students. We offer instant download for the best eBooks collection with top categories ranging from Business to Self Development, Internet, Health, Marketing and many more. Report this file. Exploring Anatomy & ... 3rd Edition eBook. Introduction to Operations Research 10th Edition by Frederick S. Hillier Rating Required Select Rating 1 star (worst) 2 stars 3 stars (average) 4 stars 5 stars (best) Name PDF | On Jan 1, 1969, Frederick S. Hillier and others published Introduction To Operations Research | Find, read and cite all the research you need on ResearchGate Project Management with PERT/CPM Dynamic Programming Added text mini-updates appear throughout the book. Dr. Hillier is especially known for his classic, award-winning text, Introduction to Operations Research, co-authored with the late Gerald J. Lieberman, which has been translated into well over a dozen languages and is currently in its 8th edition. edition (January 1, 2014) Language: English ISBN-10: 0073523453 ISBN-13: 978-0073523453. Login. While building on the classic strengths of the original text, the author continues to find new ways to make this book current and relevant to students. Other Algorithms for Linear Programming Reliability What's New in the Tenth Edition 23 Acknowiedgments 25 About the Author 27 Ttademarks 29 Chapter 1 What Is Operations Research? Markov Decision Processes One way is by incorporating a wealth of state-of-the-art, user-friendly software and more coverage of business applications than ever before. This innovative study tool pinpoints concepts the student does not understand and maps out a personalized plan for success. Integer Programming S Download pdf. Chapter 27. Chapter 26. For over four decades Introduction to Operations Research by Frederick Hillier has been the classic text on operations research. z. x.. = x, -,. This innovative and powerful system helps your students learn more efficiently and gives you the ability to customize your homework problems simply and easily. Chapter 17. A fast growing eBooks Library with great knowledge from business and beyond, right at your fingertips. Probability Theory A universe full of knowledge is just one click away. Contact us to negotiate about price. Chapter 11. Operations Research; An Introduction 10th 10E Rating Required Select Rating 1 star (worst) 2 stars 3 stars (average) 4 stars 5 stars (best) Name Buy Introduction to Operations Research - Text Only 10th edition (9780073523453) by Frederick S. Hillier for up to 90% off at Textbooks.com. The Art of Modeling with Spreadsheets Contents……Page 3 Website……Page 10 Preface……Page 14 THE ORIGINS OF OPERATIONS RESEARCH……Page 23 THE NATURE OF OPERATIONS RESEARCH……Page 24 THE RISE OF ANALYTICS TOGETHER WITH OPERATIONS RESEARCH……Page 25 THE IMPACT OF OPERATIONS RESEARCH……Page 27 ALGORITHMS AND OR COURSEWARE……Page 29 PROBLEMS……Page 31 DEFINING THE PROBLEM AND GATHERING DATA……Page 32 FORMULATING A MATHEMATICAL MODEL……Page 35 DERIVING SOLUTIONS FROM THE MODEL……Page 37 TESTING THE MODEL……Page 40 PREPARING TO APPLY THE MODEL……Page 41 IMPLEMENTATION……Page 42 SELECTED REFERENCES……Page 43 PROBLEMS……Page 45 Intro to Linear Programming……Page 47 PROTOTYPE EXAMPLE……Page 48 THE LINEAR PROGRAMMING MODEL……Page 54 ASSUMPTIONS OF LINEAR PROGRAMMING……Page 60 ADDITIONAL EXAMPLES……Page 66 FORMULATING AND SOLVING LINEAR PROGRAMMING MODELS ON A SPREADSHEET……Page 84 FORMULATING VERY LARGE LINEAR PROGRAMMING MODELS……Page 93 SELECTED REFERENCES……Page 101 LEARNING AIDS FOR THIS CHAPTER ON OUR WEBSITE (www.mhhe.com/hillier)……Page 102 PROBLEMS……Page 103 CASES CASE 3.1 Auto Assembly……Page 112 CASE 3.4 Promoting a Breakfast Cereal……Page 114 THE ESSENCE OF THE SIMPLEX METHOD……Page 115 SETTING UP THE SIMPLEX METHOD……Page 120 THE ALGEBRA OF THE SIMPLEX METHOD……Page 123 THE SIMPLEX METHOD IN TABULAR FORM……Page 129 TIE BREAKING IN THE SIMPLEX METHOD……Page 134 ADAPTING TO OTHER MODEL FORMS……Page 137 POSTOPTIMALITY ANALYSIS……Page 155 COMPUTER IMPLEMENTATION……Page 163 THE INTERIOR-POINT APPROACH TO SOLVING LINEAR PROGRAMMING PROBLEMS……Page 165 APPENDIX 4.1 AN INTRODUCTION TO USING LINDO AND LINGO……Page 169 LEARNING AIDS FOR THIS CHAPTER ON OUR WEBSITE (www.mhhe.com/hillier)……Page 173 PROBLEMS……Page 174 CASES……Page 182 PREVIEWS OF ADDED CASES ON OUR WEBSITE (www.mhhe.com/hillier)……Page 184 FOUNDATIONS OF THE SIMPLEX METHOD……Page 185 THE SIMPLEX METHOD IN MATRIX FORM……Page 196 A FUNDAMENTAL INSIGHT……Page 205 THE REVISED SIMPLEX METHOD……Page 208 SELECTED REFERENCES……Page 211 PROBLEMS……Page 212 THE ESSENCE OF DUALITY THEORY……Page 219 ECONOMIC INTERPRETATION OF DUALITY……Page 227 PRIMAL–DUAL RELATIONSHIPS……Page 230 ADAPTING TO OTHER PRIMAL FORMS……Page 235 THE ROLE OF DUALITY THEORY IN SENSITIVITY ANALYSIS……Page 239 LEARNING AIDS FOR THIS CHAPTER ON OUR WEBSITE (www.mhhe.com/hillier)……Page 242 PROBLEMS……Page 243 Linear Programming under Uncertainty……Page 247 THE ESSENCE OF SENSITIVITY ANALYSIS……Page 248 APPLYING SENSITIVITY ANALYSIS……Page 255 PERFORMING SENSITIVITY ANALYSIS ON A SPREADSHEET……Page 272 ROBUST OPTIMIZATION……Page 286 CHANCE CONSTRAINTS……Page 290 STOCHASTIC PROGRAMMING WITH RECOURSE……Page 293 SELECTED REFERENCES……Page 298 PROBLEMS……Page 299 CASES……Page 310 PREVIEWS OF ADDED CASES ON OUR WEBSITE (www.mhhe.com/hillier)……Page 311 THE DUAL SIMPLEX METHOD……Page 312 PARAMETRIC LINEAR PROGRAMMING……Page 316 THE UPPER BOUND TECHNIQUE……Page 321 AN INTERIOR-POINT ALGORITHM……Page 323 CONCLUSIONS……Page 334 LEARNING AIDS FOR THIS CHAPTER ON OUR WEBSITE (www.mhhe.com/hillier)……Page 335 PROBLEMS……Page 336 Transportation & Assignment Problems……Page 340 THE TRANSPORTATION PROBLEM……Page 341 A STREAMLINED SIMPLEX METHOD FOR THE TRANSPORTATION PROBLEM……Page 355 THE ASSIGNMENT PROBLEM……Page 370 A SPECIAL ALGORITHM FOR THE ASSIGNMENT PROBLEM……Page 378 CONCLUSIONS……Page 382 LEARNING AIDS FOR THIS CHAPTER ON OUR WEBSITE (www.mhhe.com/hillier)……Page 383 PROBLEMS……Page 384 CASES……Page 392 PREVIEWS OF ADDED CASES ON OUR WEBSITE (www.mhhe.com/hillier)……Page 393 Network Optimization Models……Page 394 PROTOTYPE EXAMPLE……Page 395 THE TERMINOLOGY OF NETWORKS……Page 396 THE SHORTEST-PATH PROBLEM……Page 399 THE MINIMUM SPANNING TREE PROBLEM……Page 404 THE MAXIMUM FLOW PROBLEM……Page 409 THE MINIMUM COST FLOW PROBLEM……Page 417 THE NETWORK SIMPLEX METHOD……Page 425 A NETWORK MODEL FOR OPTIMIZING A PROJECT’S TIME-COST TRADE-OFF……Page 435 CONCLUSIONS……Page 446 LEARNING AIDS FOR THIS CHAPTER ON OUR WEBSITE (www.mhhe.com/hillier)……Page 447 PROBLEMS……Page 448 CASES……Page 456 PREVIEWS OF ADDED CASES ON OUR WEBSITE (www.mhhe.com/hillier)……Page 459 A PROTOTYPE EXAMPLE FOR DYNAMIC PROGRAMMING……Page 460 CHARACTERISTICS OF DYNAMIC PROGRAMMING PROBLEMS……Page 465 DETERMINISTIC DYNAMIC PROGRAMMING……Page 467 PROBABILISTIC DYNAMIC PROGRAMMING……Page 484 LEARNING AIDS FOR THIS CHAPTER ON OUR WEBSITE (www.mhhe.com/hillier)……Page 490 PROBLEMS……Page 491 Integer Programming……Page 496 PROTOTYPE EXAMPLE……Page 497 SOME BIP APPLICATIONS……Page 500 INNOVATIVE USES OF BINARY VARIABLES IN MODEL FORMULATION……Page 505 SOME FORMULATION EXAMPLES……Page 511 SOME PERSPECTIVES ON SOLVING INTEGER PROGRAMMING PROBLEMS……Page 519 THE BRANCH-AND-BOUND TECHNIQUE AND ITS APPLICATION TO BINARY INTEGER PROGRAMMING……Page 523 A BRANCH-AND-BOUND ALGORITHM FOR MIXED INTEGER PROGRAMMING……Page 535 THE BRANCH-AND-CUT APPROACH TO SOLVING BIP PROBLEMS……Page 541 THE INCORPORATION OF CONSTRAINT PROGRAMMING……Page 547 CONCLUSIONS……Page 553 SELECTED REFERENCES……Page 554 LEARNING AIDS FOR THIS CHAPTER ON OUR WEBSITE (www.mhhe.com/hillier)……Page 555 PROBLEMS……Page 556 CASES……Page 565 PREVIEWS OF ADDED CASES ON OUR WEBSITE (www.mhhe.com/hillier)……Page 567 Nonlinear Programming……Page 569 SAMPLE APPLICATIONS……Page 570 GRAPHICAL ILLUSTRATION OF NONLINEAR PROGRAMMING PROBLEMS……Page 574 TYPES OF NONLINEAR PROGRAMMING PROBLEMS……Page 578 ONE-VARIABLE UNCONSTRAINED OPTIMIZATION……Page 584 MULTIVARIABLE UNCONSTRAINED OPTIMIZATION……Page 589 THE KARUSH-KUHN-TUCKER (KKT) CONDITIONS FOR CONSTRAINED OPTIMIZATION……Page 595 QUADRATIC PROGRAMMING……Page 599 SEPARABLE PROGRAMMING……Page 605 CONVEX PROGRAMMING……Page 612 NONCONVEX PROGRAMMING (WITH SPREADSHEETS)……Page 620 CONCLUSIONS……Page 624 LEARNING AIDS FOR THIS CHAPTER ON OUR WEBSITE (www.mhhe.com/hillier)……Page 625 PROBLEMS……Page 626 CASES……Page 637 PREVIEWS OF ADDED CASES ON OUR WEBSITE, (www.mhhe.com/hillier)……Page 638 Metaheuristics……Page 639 THE NATURE OF METAHEURISTICS……Page 640 TABU SEARCH……Page 647 SIMULATED ANNEALING……Page 658 GENETIC ALGORITHMS……Page 667 CONCLUSIONS……Page 677 LEARNING AIDS FOR THIS CHAPTER ON OUR WEBSITE (www.mhhe.com/hillier)……Page 678 PROBLEMS……Page 679 THE FORMULATION OF TWO-PERSON, ZERO-SUM GAMES……Page 683 SOLVING SIMPLE GAMES—A PROTOTYPE EXAMPLE……Page 685 GAMES WITH MIXED STRATEGIES……Page 690 GRAPHICAL SOLUTION PROCEDURE……Page 692 SOLVING BY LINEAR PROGRAMMING……Page 694 EXTENSIONS……Page 698 LEARNING AIDS FOR THIS CHAPTER ON OUR WEBSITE (www.mhhe.com/hillier)……Page 699 PROBLEMS……Page 700 Decision Analysis……Page 704 A PROTOTYPE EXAMPLE……Page 705 DECISION MAKING WITHOUT EXPERIMENTATION……Page 706 DECISION MAKING WITH EXPERIMENTATION……Page 712 DECISION TREES……Page 718 USING SPREADSHEETS TO PERFORM SENSITIVITY ANALYSIS ON DECISION TREES……Page 722 UTILITY THEORY……Page 730 THE PRACTICAL APPLICATION OF DECISION ANALYSIS……Page 738 SELECTED REFERENCES……Page 739 LEARNING AIDS FOR THIS CHAPTER ON OUR WEBSITE (www.mhhe.com/hillier)……Page 740 PROBLEMS……Page 741 CASES……Page 751 PREVIEW OF ADDED CASES ON OUR WEBSITE (www.mhhe.com/hillier)……Page 753 Queueing Theory……Page 754 BASIC STRUCTURE OF QUEUEING MODELS……Page 755 EXAMPLES OF REAL QUEUEING SYSTEMS……Page 760 THE ROLE OF THE EXPONENTIAL DISTRIBUTION……Page 762 THE BIRTH-AND-DEATH PROCESS……Page 768 QUEUEING MODELS BASED ON THE BIRTH-AND-DEATH PROCESS……Page 773 QUEUEING MODELS INVOLVING NONEXPONENTIAL DISTRIBUTIONS……Page 785 PRIORITY-DISCIPLINE QUEUEING MODELS……Page 793 QUEUEING NETWORKS……Page 798 THE APPLICATION OF QUEUEING THEORY……Page 802 SELECTED REFERENCES……Page 807 LEARNING AIDS FOR THIS CHAPTER ON OUR WEBSITE (www.mhhe.com/hillier)……Page 808 PROBLEMS……Page 809 CASES……Page 821 PREVIEW OF AN ADDED CASE ON OUR WEBSITE (www.mhhe.com/hillier)……Page 822 Inventory Theory……Page 823 EXAMPLES……Page 824 COMPONENTS OF INVENTORY MODELS……Page 826 DETERMINISTIC CONTINUOUS-REVIEW MODELS……Page 828 A DETERMINISTIC PERIODIC-REVIEW MODEL……Page 838 DETERMINISTIC MULTIECHELON INVENTORY MODELS FOR SUPPLY CHAIN MANAGEMENT……Page 843 A STOCHASTIC CONTINUOUS-REVIEW MODEL……Page 861 A STOCHASTIC SINGLE-PERIOD MODEL FOR PERISHABLE PRODUCTS……Page 865 REVENUE MANAGEMENT……Page 877 SELECTED REFERENCES……Page 885 LEARNING AIDS FOR THIS CHAPTER ON OUR WEBSITE (www.mhhe.com/hillier)……Page 886 PROBLEMS……Page 887 CASES……Page 897 PREVIEWS OF ADDED CASES ON OUR WEBSITE (www.mhhe.com/hillier)……Page 899 Markov Decision Processes……Page 900 A PROTOTYPE EXAMPLE……Page 901 A MODEL FOR MARKOV DECISION PROCESSES……Page 903 LINEAR PROGRAMMING AND OPTIMAL POLICIES……Page 906 CONCLUSIONS……Page 910 LEARNING AIDS FOR THIS CHAPTER ON OUR WEBSITE (www.mhhe.com/hillier)……Page 911 PROBLEMS……Page 912 THE ESSENCE OF SIMULATION……Page 915 SOME COMMON TYPES OF APPLICATIONS OF SIMULATION……Page 927 GENERATION OF RANDOM NUMBERS……Page 931 GENERATION OF RANDOM OBSERVATIONS FROM A PROBABILITY DISTRIBUTION……Page 935 OUTLINE OF A MAJOR SIMULATION STUDY……Page 940 PERFORMING SIMULATIONS ON SPREADSHEETS……Page 944 CONCLUSIONS……Page 962 SELECTED REFERENCES……Page 964 LEARNING AIDS FOR THIS CHAPTER ON OUR WEBSITE (www.mhhe.com/hillier)……Page 965 PROBLEMS……Page 966 CASES……Page 973 PREVIEWS OF ADDED CASES ON OUR WEBSITE (www.mhhe.com/hillier)……Page 974 Documentation for OR Courseware……Page 975 Convexity……Page 977 Classical Optimization Methods……Page 982 Matrices & Matrix Operations……Page 985 Normal Distribution Table……Page 990 Art of Modeling with Spreadsheets……Page 1080 A CASE STUDY: THE EVERGLADE GOLDEN YEARS COMPANY CASH FLOW PROBLEM……Page 1081 OVERVIEW OF THE PROCESS OF MODELING WITH SPREADSHEETS……Page 1082 SOME GUIDELINES FOR BUILDING “GOOD” SPREADSHEET MODELS……Page 1092 DEBUGGING A SPREADSHEET MODEL……Page 1098 CONCLUSIONS……Page 1100 LEARNING AIDS FOR THIS CHAPTER ON THIS WEBSITE……Page 1101 PROBLEMS……Page 1102 CASES……Page 1104 Project Management with PERT/CPM……Page 1106 A PROTOTYPE EXAMPLE—THE RELIABLE CONSTRUCTION CO. PROJECT……Page 1107 USING A NETWORK TO VISUALLY DISPLAY A PROJECT……Page 1108 SCHEDULING A PROJECT WITH PERT/CPM……Page 1110 DEALING WITH UNCERTAIN ACTIVITY DURATIONS……Page 1120 CONSIDERING TIME-COST TRADE-OFFS……Page 1126 SCHEDULING AND CONTROLLING PROJECT COSTS……Page 1135 AN EVALUATION OF PERT/CPM……Page 1142 CONCLUSIONS……Page 1146 CASE……Page 1155 Additional Special Types of Linear Programming Problems……Page 1159 THE TRANSSHIPMENT PROBLEM……Page 1160 MULTIDIVISIONAL PROBLEMS……Page 1165 THE DECOMPOSITION PRINCIPLE FOR MULTIDIVISIONAL PROBLEMS……Page 1169 MULTITIME PERIOD PROBLEMS……Page 1177 MULTIDIVISIONAL MULTITIME PERIOD PROBLEMS……Page 1180 SELECTED REFERENCES PROBLEMS……Page 1182 Probability Theory……Page 1186 RANDOM VARIABLES……Page 1188 PROBABILITY AND PROBABILITY DISTRIBUTIONS……Page 1189 CONDITIONAL PROBABILITY AND INDEPENDENT EVENTS……Page 1193 DISCRETE PROBABILITY DISTRIBUTIONS……Page 1195 CONTINUOUS PROBABILITY DISTRIBUTIONS……Page 1199 EXPECTATION……Page 1205 MOMENTS……Page 1207 BIVARIATE PROBABILITY DISTRIBUTION……Page 1208 MARGINAL AND CONDITIONAL PROBABILITY DISTRIBUTIONS……Page 1212 EXPECTATIONS FOR BIVARIATE DISTRIBUTIONS……Page 1215 INDEPENDENT RANDOM VARIABLES AND RANDOM SAMPLES……Page 1217 CENTRAL LIMIT THEOREM……Page 1219 FUNCTIONS OF RANDOM VARIABLES……Page 1220 SELECTED REFERENCES……Page 1223 PROBLEMS……Page 1224 STRUCTURE FUNCTION OF A SYSTEM……Page 1227 SYSTEM RELIABILITY……Page 1229 CALCULATION OF EXACT SYSTEM RELIABILITY……Page 1231 BOUNDS ON SYSTEM RELIABILITY……Page 1235 BOUNDS ON RELIABILITY BASED UPON FAILURE TIMES……Page 1236 SELECTED REFERENCES……Page 1239 PROBLEMS……Page 1240 EXAMPLES……Page 1242 DECISION MAKING……Page 1244 FORMULATION OF WAITING-COST FUNCTIONS……Page 1247 DECISION MODELS……Page 1251 THE EVALUATION OF TRAVEL TIME……Page 1256 CONCLUSIONS……Page 1261 SELECTED REFERENCES LEARNING AIDS FOR THIS CHAPTER ON THIS WEBSITE PROBLEMS……Page 1262 Forecasting……Page 1267 SOME APPLICATIONS OF FORECASTING……Page 1268 JUDGMENTAL FORECASTING METHODS……Page 1270 TIME SERIES……Page 1271 FORECASTING METHODS FOR A CONSTANT-LEVEL MODEL……Page 1272 INCORPORATING SEASONAL EFFECTS INTO FORECASTING METHODS……Page 1275 AN EXPONENTIAL SMOOTHING METHOD FOR A LINEAR TREND MODEL……Page 1278 FORECASTING ERRORS……Page 1281 BOX-JENKINS METHOD……Page 1282 CAUSAL FORECASTING WITH LINEAR REGRESSION……Page 1284 FORECASTING IN PRACTICE……Page 1292 CONCLUSIONS SELECTED REFERENCES……Page 1294 LEARNING AIDS FOR THIS CHAPTER ON THIS WEBSITE PROBLEMS……Page 1295 CASE……Page 1304 BIDDING FOR A CONSTRUCTION PROJECT……Page 1308 PROJECT MANAGEMENT……Page 1313 CASH FLOW MANAGEMENT……Page 1319 FINANCIAL RISK ANALYSIS……Page 1325 REVENUE MANAGEMENT IN THE TRAVEL INDUSTRY……Page 1329 CHOOSING THE RIGHT DISTRIBUTION……Page 1335 DECISION MAKING WITH PARAMETER ANALYSIS REPORTS AND TREND CHARTS……Page 1348 SUMMARY……Page 1351 PROBLEMS……Page 1352 ACKNOWLEDGMENT……Page 1354 STOCHASTIC PROCESSES……Page 1355 MARKOV CHAINS……Page 1357 CHAPMAN-KOLMOGOROV EQUATIONS……Page 1363 CLASSIFICATION OF STATES OF A MARKOV CHAIN……Page 1366 LONG-RUN PROPERTIES OF MARKOV CHAINS……Page 1369 FIRST PASSAGE TIMES……Page 1375 ABSORBING STATES……Page 1377 CONTINUOUS TIME MARKOV CHAINS……Page 1380 LEARNING AIDS FOR THIS CHAPTER ON THIS WEBSITE……Page 1385 PROBLEMS……Page 1386. 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