{"product_id":"decision-theory-isbn-9780471976493","title":"Decision Theory","description":"Decision Theory An Introduction to Dynamic Programming and Sequential Decisions John Bather University of Sussex, UK Mathematical induction, and its use in solving optimization problems, is a topic of great interest with many applications. It enables us to study multistage decision problems by proceeding backwards in time, using a method called dynamic programming. All the techniques needed to solve the various problems are explained, and the author's fluent style will leave the reader with an avid interest in the subject.\u003cbr\u003e * Tailored to the needs of students of optimization and decision theory\u003cbr\u003e * Written in a lucid style with numerous examples and applications\u003cbr\u003e * Coverage of deterministic models: maximizing utilities, directed networks, shortest paths, critical path analysis, scheduling and convexity\u003cbr\u003e * Coverage of stochastic models: stochastic dynamic programming, optimal stopping problems and other special topics\u003cbr\u003e * Coverage of advanced topics: Markov decision processes, minimizing expected costs, policy improvements and problems with unknown statistical parameters\u003cbr\u003e * Contains exercises at the end of each chapter, with hints in an appendix\u003cbr\u003e Aimed primarily at students of mathematics and statistics, the lucid text will also appeal to engineering and science students and those working in the areas of optimization and operations research.Die Anwendung des Induktionsprinzips auf die Lösung von Optimierungsproblemen ist gegenwärtig gefragt und wird viel diskutiert. Der Autor dieses Bandes beginnt bei einem historischen Abriß und beschreibt anschließend deterministische Modelle, in denen die Wahl zwischen zwei Möglichkeiten nicht vom Zufall beeinflußt wird. Im zweiten Teil wird der Unsicherheitsfaktor einbezogen; der dritte Teil befaßt sich mit speziellen, fortgeschrittenen Anwendungen, beispielsweise Markov-Prozessen. (04\/00) \u003cp\u003ePreface xi\u003c\/p\u003e \u003cp\u003e\u003cb\u003e1 Introduction 1\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e1.1 Mathematical Induction 1\u003c\/p\u003e \u003cp\u003e1.2 Historical Background 2\u003c\/p\u003e \u003cp\u003e1.3 Dynamic Programming 5\u003c\/p\u003e \u003cp\u003e1.4 The Executioner’s Tale 8\u003c\/p\u003e \u003cp\u003e1.5 Summary 8\u003c\/p\u003e \u003cp\u003eExercises 10\u003c\/p\u003e \u003cp\u003e\u003cb\u003eI Deterministic Models 11\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003e2 Multi-Stage Decision Problems 13\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e2.1 Maximizing Utilities 13\u003c\/p\u003e \u003cp\u003e2.2 A General Model 17\u003c\/p\u003e \u003cp\u003e2.3 Applications 19\u003c\/p\u003e \u003cp\u003eExercises 25\u003c\/p\u003e \u003cp\u003e\u003cb\u003e3 Networks 27\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e3.1 Shortest Paths 27\u003c\/p\u003e \u003cp\u003e3.2 Directed Networks 29\u003c\/p\u003e \u003cp\u003e3.3 Critical Path Analysis 30\u003c\/p\u003e \u003cp\u003eExercises 37\u003c\/p\u003e \u003cp\u003e\u003cb\u003e4 Further Applications 39\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e4.1 Discrete Actions 39\u003c\/p\u003e \u003cp\u003e4.2 The Knapsack Problem 39\u003c\/p\u003e \u003cp\u003e4.3 A Simple Replacement Model 42\u003c\/p\u003e \u003cp\u003e4.4 Scheduling Problems 44\u003c\/p\u003e \u003cp\u003e4.5 Johnson’s Algorithm 45\u003c\/p\u003e \u003cp\u003eExercises 49\u003c\/p\u003e \u003cp\u003e\u003cb\u003e5 Convexity 51\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e5.1 Convex and Concave Functions 51\u003c\/p\u003e \u003cp\u003e5.2 Allocation Problems 56\u003c\/p\u003e \u003cp\u003e5.3 Concave Utility Functions 60\u003c\/p\u003e \u003cp\u003eExercises 64\u003c\/p\u003e \u003cp\u003e\u003cb\u003eII Stochastic Models 67\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003e6 Markov Systems 69\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e6.1 Introduction 69\u003c\/p\u003e \u003cp\u003e6.2 Stochastic Dynamic Programming 70\u003c\/p\u003e \u003cp\u003e6.3 Applications 72\u003c\/p\u003e \u003cp\u003eExercises 78\u003c\/p\u003e \u003cp\u003e\u003cb\u003e7 Optimal Stopping 79\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e7.1 Introduction 79\u003c\/p\u003e \u003cp\u003e7.2 Stopping Times and Stopping Sets 82\u003c\/p\u003e \u003cp\u003e7.3 Applications 90\u003c\/p\u003e \u003cp\u003eExercises 94\u003c\/p\u003e \u003cp\u003e\u003cb\u003e8 Special Problems 97\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e8.1 Introduction 97\u003c\/p\u003e \u003cp\u003e8.2 Selling an Asset 97\u003c\/p\u003e \u003cp\u003e8.3 The Marriage Problem 104\u003c\/p\u003e \u003cp\u003e8.4 Prophet Inequalities 109\u003c\/p\u003e \u003cp\u003eExercises 116\u003c\/p\u003e \u003cp\u003e\u003cb\u003eIII Markov Decision Processes 119\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003e9 General Theory 121\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e9.1 Introduction 121\u003c\/p\u003e \u003cp\u003e9.2 Minimizing Discounted Expectations 122\u003c\/p\u003e \u003cp\u003e9.3 Policy Improvements 130\u003c\/p\u003e \u003cp\u003e9.4 A Machine Replacement Model 137\u003c\/p\u003e \u003cp\u003e\u003cb\u003e10 Minimizing Average Costs 145\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e10.1 Introduction 145\u003c\/p\u003e \u003cp\u003e10.2 Long-Term Average Costs 148\u003c\/p\u003e \u003cp\u003e10.3 Extension to Infinitely Many States 153\u003c\/p\u003e \u003cp\u003e10.4 Optimal Inventory Policies 158\u003c\/p\u003e \u003cp\u003e\u003cb\u003e11 Statistical Decisions 165\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e11.1 Introduction 165\u003c\/p\u003e \u003cp\u003e11.2 Testing Statistical Hypotheses 166\u003c\/p\u003e \u003cp\u003e11.3 The Sequential Probability Ratio Test 170\u003c\/p\u003e \u003cp\u003eNotes On the Exercises 177\u003c\/p\u003e \u003cp\u003eChapter 1 177\u003c\/p\u003e \u003cp\u003eChapter 2 177\u003c\/p\u003e \u003cp\u003eChapter 3 178\u003c\/p\u003e \u003cp\u003eChapter 4 179\u003c\/p\u003e \u003cp\u003eChapter 5 179\u003c\/p\u003e \u003cp\u003eChapter 6 180\u003c\/p\u003e \u003cp\u003eChapter 7 181\u003c\/p\u003e \u003cp\u003eChapter 8 183\u003c\/p\u003e \u003cp\u003eReferences 185\u003c\/p\u003e \u003cp\u003eIndex 187\u003c\/p\u003e \"This textbook...draws on his many years of experience in teaching this topic as well as on his considerable professional expertise in the area. It is ideally suited to its stated purpose as a student text.\" (Short Book Reviews, Vol. 20. No. 3, December 2000)\u003cbr\u003e \u003cbr\u003e \"...I was impressed with this book...\" (The Statistician, Vol.51, No.2 2002)\u003cbr\u003e \u003cbr\u003e \"...excellent for the audience to whom it is addressed, and it is to be hoped that the author will write a further textbook...\" (Jnl of the Operational Research Society, Vol 54(10) 2003)  \u003cp\u003e\u003cstrong\u003eJohn Bather\u003c\/strong\u003e is the author of \u003cem\u003eDecision Theory: An Introduction to Dynamic Programming and Sequential Decisions\u003c\/em\u003e, published by Wiley.  Decision Theory An Introduction to Dynamic Programming and Sequential Decisions John Bather University of Sussex, UK Mathematical induction, and its use in solving optimization problems, is a topic of great interest with many applications. It enables us to study multistage decision problems by proceeding backwards in time, using a method called dynamic programming. All the techniques needed to solve the various problems are explained, and the author's fluent style will leave the reader with an avid interest in the subject.\u003cbr\u003e * Tailored to the needs of students of optimization and decision theory\u003cbr\u003e * Written in a lucid style with numerous examples and applications\u003cbr\u003e * Coverage of deterministic models: maximizing utilities, directed networks, shortest paths, critical path analysis, scheduling and convexity\u003cbr\u003e * Coverage of stochastic models: stochastic dynamic programming, optimal stopping problems and other special topics\u003cbr\u003e * Coverage of advanced topics: Markov decision processes, minimizing expected costs, policy improvements and problems with unknown statistical parameters\u003cbr\u003e * Contains exercises at the end of each chapter, with hints in an appendix\u003cbr\u003e Aimed primarily at students of mathematics and statistics, the lucid text will also appeal to engineering and science students and those working in the areas of optimization and operations research.\u003c\/p\u003e","brand":"Wiley","offers":[{"title":"Default Title","offer_id":47989031043301,"sku":"NP9780471976493","price":134.95,"currency_code":"USD","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/1842\/7735\/files\/9780471976493.jpg?v=1761782512","url":"https:\/\/k12savings.com\/products\/decision-theory-isbn-9780471976493","provider":"K12savings","version":"1.0","type":"link"}