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The aim of stochastic programming is to find optimal decisions in problems which involve uncertain data. This field is currently developing rapidly with contributions from many disciplines including operations research, mathematics, and probability. At the same time, it is now being applied in a wide variety of subjects ranging from agriculture to financial planning and from industrial engineering to computer networks. This textbook provides a first course in stochastic programming suitable for students with a basic knowledge of linear programming, elementary analysis, and probability. The authors aim to present a broad overview of the main themes and methods of the subject. Its prime goal is to help students develop an intuition on how to model uncertainty into mathematical problems, what uncertainty changes bring to the decision process, and what techniques help to manage uncertainty in solving the problems.In this extensively updated new edition there is more material on methods and examples including several new approaches for discrete variables, new results on risk measures in modeling and Monte Carlo sampling methods, a new chapter on relationships to other methods including approximate dynamic programming, robust optimization and online methods. The book is highly illustrated with chapter summaries and many examples and exercises. Students, researchers and practitioners in operations research and the optimization area will find it particularly of interest.

Stochastic programming --- Stochastic programming. --- Mathematical statistics. --- Mathematical optimization. --- Statistique mathématique. --- Optimisation mathématique.

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Optimization problems involving uncertain data arise in many areas of industrial and economic applications. Stochastic programming provides a useful framework for modeling and solving optimization problems for which a probability distribution of the unknown parameters is available. Motivated by practical optimization problems occurring in energy systems with regenerative energy supply, Debora Mahlke formulates and analyzes multistage stochastic mixed-integer models. For their solution, the author proposes a novel decomposition approach which relies on the concept of splitting the underlying scenario tree into subtrees. Based on the formulated models from energy production, the algorithm is computationally investigated and the numerical results are discussed.

Mathematical optimization. --- Stochastic approximation. --- Stochastic processes. --- Engineering & Applied Sciences --- Mathematics --- Physical Sciences & Mathematics --- Applied Mathematics --- Mathematical Statistics --- Stochastic programming. --- Mathematics. --- Probabilities. --- Probability Theory and Stochastic Processes. --- Mathematics, general. --- Linear programming --- Distribution (Probability theory. --- Math --- Science --- Distribution functions --- Frequency distribution --- Characteristic functions --- Probabilities --- Probability --- Statistical inference --- Combinations --- Chance --- Least squares --- Mathematical statistics --- Risk

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Although studies on multiobjective mathematical programming under uncertainty have been accumulated and several books on multiobjective mathematical programming under uncertainty have been published (e.g., Stancu-Minasian (1984); Slowinski and Teghem (1990); Sakawa (1993); Lai and Hwang (1994); Sakawa (2000)), there seems to be no book which concerns both randomness of events related to environments and fuzziness of human judgments simultaneously in multiobjective decision making problems. In this book, the authors are concerned with introducing the latest advances in the field of multiobjective optimization under both fuzziness and randomness on the basis of the authors’ continuing research works. Special stress is placed on interactive decision making aspects of fuzzy stochastic multiobjective programming for human-centered systems under uncertainty in most realistic situations when dealing with both fuzziness and randomness. Organization of each chapter is briefly summarized as follows: Chapter 2 is devoted to mathematical preliminaries, which will be used throughout the remainder of the book. Starting with basic notions and methods of multiobjective programming, interactive fuzzy multiobjective programming as well as fuzzy multiobjective programming is outlined. In Chapter 3, by considering the imprecision of decision maker’s (DM’s) judgment for stochastic objective functions and/or constraints in multiobjective problems, fuzzy multiobjective stochastic programming is developed. In Chapter 4, through the consideration of not only the randomness of parameters involved in objective functions and/or constraints but also the experts’ ambiguous understanding of the realized values of the random parameters, multiobjective programming problems with fuzzy random variables are formulated. In Chapter 5, for resolving conflict of decision making problems in hierarchical managerial or public organizations where there exist two DMs who have different priorities in making decisions, two-level programming problems are discussed. Finally, Chapter 6 outlines some future research directions.

Fuzzy logic. --- Multiple criteria decision making. --- Stochastic programming. --- Programming (Mathematics) --- Fuzzy systems --- Stochastic processes --- Management --- Engineering & Applied Sciences --- Civil & Environmental Engineering --- Business & Economics --- Operations Research --- Computer Science --- Management Theory --- Fuzzy systems. --- Stochastic processes. --- Random processes --- Systems, Fuzzy --- Mathematical programming --- Goal programming --- Business. --- Operations research. --- Decision making. --- Management science. --- Probabilities. --- Business and Management. --- Operation Research/Decision Theory. --- Operations Research, Management Science. --- Probability Theory and Stochastic Processes. --- Probabilities --- System analysis --- Fuzzy logic --- Algorithms --- Functional equations --- Mathematical optimization --- Operations research --- Distribution (Probability theory. --- Operations Research/Decision Theory. --- Distribution functions --- Frequency distribution --- Characteristic functions --- Operational analysis --- Operational research --- Industrial engineering --- Management science --- Research --- System theory --- Probability --- Statistical inference --- Combinations --- Mathematics --- Chance --- Least squares --- Mathematical statistics --- Risk --- Quantitative business analysis --- Problem solving --- Statistical decision --- Deciding --- Decision (Psychology) --- Decision analysis --- Decision processes --- Making decisions --- Management decisions --- Choice (Psychology) --- Decision making