Stochastic Dynamic Programming With A Linear Programming Subroutine

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Stochastic Programming Problems with Probability and Quantile Functions

Author : Andreĭ Ivanovich Kibzun
Publisher : John Wiley & Sons
ISBN 13 :
Total Pages : 330 pages
Book Rating : 4.F/5 ( download)

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Book Synopsis Stochastic Programming Problems with Probability and Quantile Functions by : Andreĭ Ivanovich Kibzun

Download or read book Stochastic Programming Problems with Probability and Quantile Functions written by Andreĭ Ivanovich Kibzun and published by John Wiley & Sons. This book was released on 1996-08-06 with total page 330 pages. Available in PDF, EPUB and Kindle. Book excerpt: The concept of a system as an entity in its own right has emerged with increasing force in the past few decades in, for example, the areas of electrical and control engineering, economics, ecology, urban structures, automaton theory, operational research and industry. The more definite concept of a large-scale system is implicit in these applications, but is particularly evident in fields such as the study of communication networks, computer networks and neural networks. The Wiley-Interscience Series in Systems and Optimization has been established to serve the needs of researchers in these rapidly developing fields. It is intended for works concerned with developments in quantitative systems theory, applications of such theory in areas of interest, or associated methodology. Of related interest Stochastic Programming Peter Kall, University of Zurich, Switzerland and Stein W. Wallace, University of Trondheim, Norway Stochastic Programming is the first textbook to provide a thorough and self-contained introduction to the subject. Carefully written to cover all necessary background material from both linear and non-linear programming, as well as probability theory, the book draws together the methods and techniques previously described in disparate sources. After introducing the terms and modelling issues when randomness is introduced in a deterministic mathematical programming model, the authors cover decision trees and dynamic programming, recourse problems, probabilistic constraints, preprocessing and network problems. Exercises are provided at the end of each chapter. Throughout, the emphasis is on the appropriate use of the techniques, rather than on the underlying mathematical proofs and theories, making the book ideal for researchers and students in mathematical programming and operations research who wish to develop their skills in stochastic programming.

Approximate Dynamic Programming

Author : Warren B. Powell
Publisher : John Wiley & Sons
ISBN 13 : 0470182954
Total Pages : 487 pages
Book Rating : 4.4/5 (71 download)

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Book Synopsis Approximate Dynamic Programming by : Warren B. Powell

Download or read book Approximate Dynamic Programming written by Warren B. Powell and published by John Wiley & Sons. This book was released on 2007-10-05 with total page 487 pages. Available in PDF, EPUB and Kindle. Book excerpt: A complete and accessible introduction to the real-world applications of approximate dynamic programming With the growing levels of sophistication in modern-day operations, it is vital for practitioners to understand how to approach, model, and solve complex industrial problems. Approximate Dynamic Programming is a result of the author's decades of experience working in large industrial settings to develop practical and high-quality solutions to problems that involve making decisions in the presence of uncertainty. This groundbreaking book uniquely integrates four distinct disciplines—Markov design processes, mathematical programming, simulation, and statistics—to demonstrate how to successfully model and solve a wide range of real-life problems using the techniques of approximate dynamic programming (ADP). The reader is introduced to the three curses of dimensionality that impact complex problems and is also shown how the post-decision state variable allows for the use of classical algorithmic strategies from operations research to treat complex stochastic optimization problems. Designed as an introduction and assuming no prior training in dynamic programming of any form, Approximate Dynamic Programming contains dozens of algorithms that are intended to serve as a starting point in the design of practical solutions for real problems. The book provides detailed coverage of implementation challenges including: modeling complex sequential decision processes under uncertainty, identifying robust policies, designing and estimating value function approximations, choosing effective stepsize rules, and resolving convergence issues. With a focus on modeling and algorithms in conjunction with the language of mainstream operations research, artificial intelligence, and control theory, Approximate Dynamic Programming: Models complex, high-dimensional problems in a natural and practical way, which draws on years of industrial projects Introduces and emphasizes the power of estimating a value function around the post-decision state, allowing solution algorithms to be broken down into three fundamental steps: classical simulation, classical optimization, and classical statistics Presents a thorough discussion of recursive estimation, including fundamental theory and a number of issues that arise in the development of practical algorithms Offers a variety of methods for approximating dynamic programs that have appeared in previous literature, but that have never been presented in the coherent format of a book Motivated by examples from modern-day operations research, Approximate Dynamic Programming is an accessible introduction to dynamic modeling and is also a valuable guide for the development of high-quality solutions to problems that exist in operations research and engineering. The clear and precise presentation of the material makes this an appropriate text for advanced undergraduate and beginning graduate courses, while also serving as a reference for researchers and practitioners. A companion Web site is available for readers, which includes additional exercises, solutions to exercises, and data sets to reinforce the book's main concepts.

Stochastic Linear Programming

Author : Peter Kall
Publisher : Springer Science & Business Media
ISBN 13 : 1441977295
Total Pages : 439 pages
Book Rating : 4.4/5 (419 download)

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Book Synopsis Stochastic Linear Programming by : Peter Kall

Download or read book Stochastic Linear Programming written by Peter Kall and published by Springer Science & Business Media. This book was released on 2010-11-02 with total page 439 pages. Available in PDF, EPUB and Kindle. Book excerpt: This new edition of Stochastic Linear Programming: Models, Theory and Computation has been brought completely up to date, either dealing with or at least referring to new material on models and methods, including DEA with stochastic outputs modeled via constraints on special risk functions (generalizing chance constraints, ICC’s and CVaR constraints), material on Sharpe-ratio, and Asset Liability Management models involving CVaR in a multi-stage setup. To facilitate use as a text, exercises are included throughout the book, and web access is provided to a student version of the authors’ SLP-IOR software. Additionally, the authors have updated the Guide to Available Software, and they have included newer algorithms and modeling systems for SLP. The book is thus suitable as a text for advanced courses in stochastic optimization, and as a reference to the field. From Reviews of the First Edition: "The book presents a comprehensive study of stochastic linear optimization problems and their applications. ... The presentation includes geometric interpretation, linear programming duality, and the simplex method in its primal and dual forms. ... The authors have made an effort to collect ... the most useful recent ideas and algorithms in this area. ... A guide to the existing software is included as well." (Darinka Dentcheva, Mathematical Reviews, Issue 2006 c) "This is a graduate text in optimisation whose main emphasis is in stochastic programming. The book is clearly written. ... This is a good book for providing mathematicians, economists and engineers with an almost complete start up information for working in the field. I heartily welcome its publication. ... It is evident that this book will constitute an obligatory reference source for the specialists of the field." (Carlos Narciso Bouza Herrera, Zentralblatt MATH, Vol. 1104 (6), 2007)

Duality in Stochastic Linear and Dynamic Programming

Author : Willem K. Klein Haneveld
Publisher : Springer Science & Business Media
ISBN 13 : 3642516971
Total Pages : 299 pages
Book Rating : 4.6/5 (425 download)

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Book Synopsis Duality in Stochastic Linear and Dynamic Programming by : Willem K. Klein Haneveld

Download or read book Duality in Stochastic Linear and Dynamic Programming written by Willem K. Klein Haneveld and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 299 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Stochastic Linear Programming

Author : P. Kall
Publisher : Springer Science & Business Media
ISBN 13 : 3642662528
Total Pages : 103 pages
Book Rating : 4.6/5 (426 download)

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Book Synopsis Stochastic Linear Programming by : P. Kall

Download or read book Stochastic Linear Programming written by P. Kall and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 103 pages. Available in PDF, EPUB and Kindle. Book excerpt: Todaymanyeconomists, engineers and mathematicians are familiar with linear programming and are able to apply it. This is owing to the following facts: during the last 25 years efficient methods have been developed; at the same time sufficient computer capacity became available; finally, in many different fields, linear programs have turned out to be appropriate models for solving practical problems. However, to apply the theory and the methods of linear programming, it is required that the data determining a linear program be fixed known numbers. This condition is not fulfilled in many practical situations, e. g. when the data are demands, technological coefficients, available capacities, cost rates and so on. It may happen that such data are random variables. In this case, it seems to be common practice to replace these random variables by their mean values and solve the resulting linear program. By 1960 various authors had already recog nized that this approach is unsound: between 1955 and 1960 there were such papers as "Linear Programming under Uncertainty", "Stochastic Linear Pro gramming with Applications to Agricultural Economics", "Chance Constrained Programming", "Inequalities for Stochastic Linear Programming Problems" and "An Approach to Linear Programming under Uncertainty".

Introduction to Stochastic Programming

Author : John R. Birge
Publisher : Springer Science & Business Media
ISBN 13 : 0387226184
Total Pages : 427 pages
Book Rating : 4.3/5 (872 download)

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Book Synopsis Introduction to Stochastic Programming by : John R. Birge

Download or read book Introduction to Stochastic Programming written by John R. Birge and published by Springer Science & Business Media. This book was released on 2006-04-06 with total page 427 pages. Available in PDF, EPUB and Kindle. Book excerpt: This rapidly developing field encompasses many disciplines including operations research, mathematics, and probability. Conversely, it is 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 present a broad overview of the main themes and methods of the subject, thus helping students develop an intuition for 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. The early chapters introduce some worked examples of stochastic programming, demonstrate how a stochastic model is formally built, develop the properties of stochastic programs and the basic solution techniques used to solve them. The book then goes on to cover approximation and sampling techniques and is rounded off by an in-depth case study. A well-paced and wide-ranging introduction to this subject.

Applied Dynamic Programming

Author : Richard E. Bellman
Publisher : Princeton University Press
ISBN 13 : 1400874653
Total Pages : 389 pages
Book Rating : 4.4/5 (8 download)

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Book Synopsis Applied Dynamic Programming by : Richard E. Bellman

Download or read book Applied Dynamic Programming written by Richard E. Bellman and published by Princeton University Press. This book was released on 2015-12-08 with total page 389 pages. Available in PDF, EPUB and Kindle. Book excerpt: This comprehensive study of dynamic programming applied to numerical solution of optimization problems. It will interest aerodynamic, control, and industrial engineers, numerical analysts, and computer specialists, applied mathematicians, economists, and operations and systems analysts. Originally published in 1962. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.

Lectures on Stochastic Programming

Author : Alexander Shapiro
Publisher : SIAM
ISBN 13 : 0898718759
Total Pages : 447 pages
Book Rating : 4.8/5 (987 download)

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Book Synopsis Lectures on Stochastic Programming by : Alexander Shapiro

Download or read book Lectures on Stochastic Programming written by Alexander Shapiro and published by SIAM. This book was released on 2009-01-01 with total page 447 pages. Available in PDF, EPUB and Kindle. Book excerpt: Optimization problems involving stochastic models occur in almost all areas of science and engineering, such as telecommunications, medicine, and finance. Their existence compels a need for rigorous ways of formulating, analyzing, and solving such problems. This book focuses on optimization problems involving uncertain parameters and covers the theoretical foundations and recent advances in areas where stochastic models are available. Readers will find coverage of the basic concepts of modeling these problems, including recourse actions and the nonanticipativity principle. The book also includes the theory of two-stage and multistage stochastic programming problems; the current state of the theory on chance (probabilistic) constraints, including the structure of the problems, optimality theory, and duality; and statistical inference in and risk-averse approaches to stochastic programming.

Introduction to Stochastic Dynamic Programming

Author : Sheldon M. Ross
Publisher : Academic Press
ISBN 13 : 1483269094
Total Pages : 179 pages
Book Rating : 4.4/5 (832 download)

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Book Synopsis Introduction to Stochastic Dynamic Programming by : Sheldon M. Ross

Download or read book Introduction to Stochastic Dynamic Programming written by Sheldon M. Ross and published by Academic Press. This book was released on 2014-07-10 with total page 179 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introduction to Stochastic Dynamic Programming presents the basic theory and examines the scope of applications of stochastic dynamic programming. The book begins with a chapter on various finite-stage models, illustrating the wide range of applications of stochastic dynamic programming. Subsequent chapters study infinite-stage models: discounting future returns, minimizing nonnegative costs, maximizing nonnegative returns, and maximizing the long-run average return. Each of these chapters first considers whether an optimal policy need exist—providing counterexamples where appropriate—and then presents methods for obtaining such policies when they do. In addition, general areas of application are presented. The final two chapters are concerned with more specialized models. These include stochastic scheduling models and a type of process known as a multiproject bandit. The mathematical prerequisites for this text are relatively few. No prior knowledge of dynamic programming is assumed and only a moderate familiarity with probability— including the use of conditional expectation—is necessary.

Reinforcement Learning and Stochastic Optimization

Author : Warren B. Powell
Publisher : John Wiley & Sons
ISBN 13 : 1119815037
Total Pages : 1090 pages
Book Rating : 4.1/5 (198 download)

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Book Synopsis Reinforcement Learning and Stochastic Optimization by : Warren B. Powell

Download or read book Reinforcement Learning and Stochastic Optimization written by Warren B. Powell and published by John Wiley & Sons. This book was released on 2022-03-15 with total page 1090 pages. Available in PDF, EPUB and Kindle. Book excerpt: REINFORCEMENT LEARNING AND STOCHASTIC OPTIMIZATION Clearing the jungle of stochastic optimization Sequential decision problems, which consist of “decision, information, decision, information,” are ubiquitous, spanning virtually every human activity ranging from business applications, health (personal and public health, and medical decision making), energy, the sciences, all fields of engineering, finance, and e-commerce. The diversity of applications attracted the attention of at least 15 distinct fields of research, using eight distinct notational systems which produced a vast array of analytical tools. A byproduct is that powerful tools developed in one community may be unknown to other communities. Reinforcement Learning and Stochastic Optimization offers a single canonical framework that can model any sequential decision problem using five core components: state variables, decision variables, exogenous information variables, transition function, and objective function. This book highlights twelve types of uncertainty that might enter any model and pulls together the diverse set of methods for making decisions, known as policies, into four fundamental classes that span every method suggested in the academic literature or used in practice. Reinforcement Learning and Stochastic Optimization is the first book to provide a balanced treatment of the different methods for modeling and solving sequential decision problems, following the style used by most books on machine learning, optimization, and simulation. The presentation is designed for readers with a course in probability and statistics, and an interest in modeling and applications. Linear programming is occasionally used for specific problem classes. The book is designed for readers who are new to the field, as well as those with some background in optimization under uncertainty. Throughout this book, readers will find references to over 100 different applications, spanning pure learning problems, dynamic resource allocation problems, general state-dependent problems, and hybrid learning/resource allocation problems such as those that arose in the COVID pandemic. There are 370 exercises, organized into seven groups, ranging from review questions, modeling, computation, problem solving, theory, programming exercises and a “diary problem” that a reader chooses at the beginning of the book, and which is used as a basis for questions throughout the rest of the book.

Reinforcement Learning and Dynamic Programming Using Function Approximators

Author : Lucian Busoniu
Publisher : CRC Press
ISBN 13 : 1439821097
Total Pages : 280 pages
Book Rating : 4.4/5 (398 download)

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Book Synopsis Reinforcement Learning and Dynamic Programming Using Function Approximators by : Lucian Busoniu

Download or read book Reinforcement Learning and Dynamic Programming Using Function Approximators written by Lucian Busoniu and published by CRC Press. This book was released on 2017-07-28 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt: From household appliances to applications in robotics, engineered systems involving complex dynamics can only be as effective as the algorithms that control them. While Dynamic Programming (DP) has provided researchers with a way to optimally solve decision and control problems involving complex dynamic systems, its practical value was limited by algorithms that lacked the capacity to scale up to realistic problems. However, in recent years, dramatic developments in Reinforcement Learning (RL), the model-free counterpart of DP, changed our understanding of what is possible. Those developments led to the creation of reliable methods that can be applied even when a mathematical model of the system is unavailable, allowing researchers to solve challenging control problems in engineering, as well as in a variety of other disciplines, including economics, medicine, and artificial intelligence. Reinforcement Learning and Dynamic Programming Using Function Approximators provides a comprehensive and unparalleled exploration of the field of RL and DP. With a focus on continuous-variable problems, this seminal text details essential developments that have substantially altered the field over the past decade. In its pages, pioneering experts provide a concise introduction to classical RL and DP, followed by an extensive presentation of the state-of-the-art and novel methods in RL and DP with approximation. Combining algorithm development with theoretical guarantees, they elaborate on their work with illustrative examples and insightful comparisons. Three individual chapters are dedicated to representative algorithms from each of the major classes of techniques: value iteration, policy iteration, and policy search. The features and performance of these algorithms are highlighted in extensive experimental studies on a range of control applications. The recent development of applications involving complex systems has led to a surge of interest in RL and DP methods and the subsequent need for a quality resource on the subject. For graduate students and others new to the field, this book offers a thorough introduction to both the basics and emerging methods. And for those researchers and practitioners working in the fields of optimal and adaptive control, machine learning, artificial intelligence, and operations research, this resource offers a combination of practical algorithms, theoretical analysis, and comprehensive examples that they will be able to adapt and apply to their own work. Access the authors' website at www.dcsc.tudelft.nl/rlbook/ for additional material, including computer code used in the studies and information concerning new developments.

Applications of Stochastic Programming

Author : Stein W. Wallace
Publisher : SIAM
ISBN 13 : 9780898718799
Total Pages : 724 pages
Book Rating : 4.7/5 (187 download)

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Book Synopsis Applications of Stochastic Programming by : Stein W. Wallace

Download or read book Applications of Stochastic Programming written by Stein W. Wallace and published by SIAM. This book was released on 2005-01-01 with total page 724 pages. Available in PDF, EPUB and Kindle. Book excerpt: Consisting of two parts, this book presents papers describing publicly available stochastic programming systems that are operational. It presents a diverse collection of application papers in areas such as production, supply chain and scheduling, gaming, environmental and pollution control, financial modeling, telecommunications, and electricity.

Stochastic Decomposition

Author : Julia L. Higle
Publisher : Springer Science & Business Media
ISBN 13 : 1461541158
Total Pages : 237 pages
Book Rating : 4.4/5 (615 download)

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Book Synopsis Stochastic Decomposition by : Julia L. Higle

Download or read book Stochastic Decomposition written by Julia L. Higle and published by Springer Science & Business Media. This book was released on 2013-11-27 with total page 237 pages. Available in PDF, EPUB and Kindle. Book excerpt: Motivation Stochastic Linear Programming with recourse represents one of the more widely applicable models for incorporating uncertainty within in which the SLP optimization models. There are several arenas model is appropriate, and such models have found applications in air line yield management, capacity planning, electric power generation planning, financial planning, logistics, telecommunications network planning, and many more. In some of these applications, modelers represent uncertainty in terms of only a few seenarios and formulate a large scale linear program which is then solved using LP software. However, there are many applications, such as the telecommunications planning problem discussed in this book, where a handful of seenarios do not capture variability well enough to provide a reasonable model of the actual decision-making problem. Problems of this type easily exceed the capabilities of LP software by several orders of magnitude. Their solution requires the use of algorithmic methods that exploit the structure of the SLP model in a manner that will accommodate large scale applications.

Encyclopedia of Optimization

Author : Christodoulos A. Floudas
Publisher : Springer Science & Business Media
ISBN 13 : 0387747583
Total Pages : 4646 pages
Book Rating : 4.3/5 (877 download)

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Book Synopsis Encyclopedia of Optimization by : Christodoulos A. Floudas

Download or read book Encyclopedia of Optimization written by Christodoulos A. Floudas and published by Springer Science & Business Media. This book was released on 2008-09-04 with total page 4646 pages. Available in PDF, EPUB and Kindle. Book excerpt: The goal of the Encyclopedia of Optimization is to introduce the reader to a complete set of topics that show the spectrum of research, the richness of ideas, and the breadth of applications that has come from this field. The second edition builds on the success of the former edition with more than 150 completely new entries, designed to ensure that the reference addresses recent areas where optimization theories and techniques have advanced. Particularly heavy attention resulted in health science and transportation, with entries such as "Algorithms for Genomics", "Optimization and Radiotherapy Treatment Design", and "Crew Scheduling".

Markov Decision Processes

Author : Martin L. Puterman
Publisher : John Wiley & Sons
ISBN 13 : 1118625870
Total Pages : 544 pages
Book Rating : 4.1/5 (186 download)

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Book Synopsis Markov Decision Processes by : Martin L. Puterman

Download or read book Markov Decision Processes written by Martin L. Puterman and published by John Wiley & Sons. This book was released on 2014-08-28 with total page 544 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Wiley-Interscience Paperback Series consists of selected books that have been made more accessible to consumers in an effort to increase global appeal and general circulation. With these new unabridged softcover volumes, Wiley hopes to extend the lives of these works by making them available to future generations of statisticians, mathematicians, and scientists. "This text is unique in bringing together so many results hitherto found only in part in other texts and papers. . . . The text is fairly self-contained, inclusive of some basic mathematical results needed, and provides a rich diet of examples, applications, and exercises. The bibliographical material at the end of each chapter is excellent, not only from a historical perspective, but because it is valuable for researchers in acquiring a good perspective of the MDP research potential." —Zentralblatt fur Mathematik ". . . it is of great value to advanced-level students, researchers, and professional practitioners of this field to have now a complete volume (with more than 600 pages) devoted to this topic. . . . Markov Decision Processes: Discrete Stochastic Dynamic Programming represents an up-to-date, unified, and rigorous treatment of theoretical and computational aspects of discrete-time Markov decision processes." —Journal of the American Statistical Association

Advances in Stochastic Dynamic Programming for Operations Management

Author : Frank Schneider
Publisher : Logos Verlag Berlin GmbH
ISBN 13 : 3832536337
Total Pages : 172 pages
Book Rating : 4.8/5 (325 download)

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Book Synopsis Advances in Stochastic Dynamic Programming for Operations Management by : Frank Schneider

Download or read book Advances in Stochastic Dynamic Programming for Operations Management written by Frank Schneider and published by Logos Verlag Berlin GmbH. This book was released on 2014 with total page 172 pages. Available in PDF, EPUB and Kindle. Book excerpt: Many tasks in operations management require the solution of complex optimization problems. Problems in which decisions are taken sequentially over time can be modeled and solved by dynamic programming. Real-world dynamic programming problems, however, exhibit complexity that cannot be handled by conventional solution techniques. This complexity may stem from large state and solution spaces, huge sets of possible actions, non-convexities in the objective function, and uncertainty. In this book, three highly complex real-world problems from the domain of operations management are modeled and solved by newly developed solution techniques based on stochastic dynamic programming. First, the problem of optimally scheduling participating demand units in an energy transmission network is considered. These units are scheduled such that total cost of supplying demand for electric energy is minimized under uncertainty in demand and generation. Second, the integrated problem of investment in and optimal operations of a network of battery swap stations under uncertain demand and energy prices is modeled and solved. Third, the inventory control problem of a multi-channel retailer selling through independent sales channels is modeled and optimality conditions for replenishment policies of simple structure are proven. This book introduces efficient approximation techniques based on approximate dynamic programming (ADP) and extends existing proximal point algorithms to the stochastic case. The methods are applicable to a wide variety of dynamic programming problems of high dimension.

An Introduction to Linear Programming and Game Theory

Author : Paul R. Thie
Publisher : John Wiley & Sons
ISBN 13 : 1118165454
Total Pages : 476 pages
Book Rating : 4.1/5 (181 download)

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Book Synopsis An Introduction to Linear Programming and Game Theory by : Paul R. Thie

Download or read book An Introduction to Linear Programming and Game Theory written by Paul R. Thie and published by John Wiley & Sons. This book was released on 2011-09-15 with total page 476 pages. Available in PDF, EPUB and Kindle. Book excerpt: Praise for the Second Edition: "This is quite a well-done book: very tightly organized, better-than-average exposition, and numerous examples, illustrations, and applications." —Mathematical Reviews of the American Mathematical Society An Introduction to Linear Programming and Game Theory, Third Edition presents a rigorous, yet accessible, introduction to the theoretical concepts and computational techniques of linear programming and game theory. Now with more extensive modeling exercises and detailed integer programming examples, this book uniquely illustrates how mathematics can be used in real-world applications in the social, life, and managerial sciences, providing readers with the opportunity to develop and apply their analytical abilities when solving realistic problems. This Third Edition addresses various new topics and improvements in the field of mathematical programming, and it also presents two software programs, LP Assistant and the Solver add-in for Microsoft Office Excel, for solving linear programming problems. LP Assistant, developed by coauthor Gerard Keough, allows readers to perform the basic steps of the algorithms provided in the book and is freely available via the book's related Web site. The use of the sensitivity analysis report and integer programming algorithm from the Solver add-in for Microsoft Office Excel is introduced so readers can solve the book's linear and integer programming problems. A detailed appendix contains instructions for the use of both applications. Additional features of the Third Edition include: A discussion of sensitivity analysis for the two-variable problem, along with new examples demonstrating integer programming, non-linear programming, and make vs. buy models Revised proofs and a discussion on the relevance and solution of the dual problem A section on developing an example in Data Envelopment Analysis An outline of the proof of John Nash's theorem on the existence of equilibrium strategy pairs for non-cooperative, non-zero-sum games Providing a complete mathematical development of all presented concepts and examples, Introduction to Linear Programming and Game Theory, Third Edition is an ideal text for linear programming and mathematical modeling courses at the upper-undergraduate and graduate levels. It also serves as a valuable reference for professionals who use game theory in business, economics, and management science.