Advertisement
| stochastic modeling and optimization: Stochastic Modeling and Optimization David D. Yao, Hanqin Zhang, Xun Yu Zhou, 2003-01-14 This books covers the broad range of research in stochastic models and optimization. Applications presented include networks, financial engineering, production planning, and supply chain management. Each contribution is aimed at graduate students working in operations research, probability, and statistics. |
| stochastic modeling and optimization: Optimization of Stochastic Models Georg Ch. Pflug, 1997-10-14 Stochastic models are everywhere. In manufacturing, queuing models are used for modeling production processes, realistic inventory models are stochastic in nature. Stochastic models are considered in transportation and communication. Marketing models use stochastic descriptions of the demands and buyer's behaviors. In finance, market prices and exchange rates are assumed to be certain stochastic processes, and insurance claims appear at random times with random amounts. To each decision problem, a cost function is associated. Costs may be direct or indirect, like loss of time, quality deterioration, loss in production or dissatisfaction of customers. In decision making under uncertainty, the goal is to minimize the expected costs. However, in practically all realistic models, the calculation of the expected costs is impossible due to the model complexity. Simulation is the only practicable way of getting insight into such models. Thus, the problem of optimal decisions can be seen as getting simulation and optimization effectively combined. The field is quite new and yet the number of publications is enormous. This book does not even try to touch all work done in this area. Instead, many concepts are presented and treated with mathematical rigor and necessary conditions for the correctness of various approaches are stated. Optimization of Stochastic Models: The Interface Between Simulation and Optimization is suitable as a text for a graduate level course on Stochastic Models or as a secondary text for a graduate level course in Operations Research. |
| stochastic modeling and optimization: Stochastic Modeling in Economics and Finance Jitka Dupacova, J. Hurt, J. Stepan, 2005-12-30 In Part I, the fundamentals of financial thinking and elementary mathematical methods of finance are presented. The method of presentation is simple enough to bridge the elements of financial arithmetic and complex models of financial math developed in the later parts. It covers characteristics of cash flows, yield curves, and valuation of securities. Part II is devoted to the allocation of funds and risk management: classics (Markowitz theory of portfolio), capital asset pricing model, arbitrage pricing theory, asset & liability management, value at risk. The method explanation takes into account the computational aspects. Part III explains modeling aspects of multistage stochastic programming on a relatively accessible level. It includes a survey of existing software, links to parametric, multiobjective and dynamic programming, and to probability and statistics. It focuses on scenario-based problems with the problems of scenario generation and output analysis discussed in detail and illustrated within a case study. |
| stochastic modeling and optimization: Lectures on Stochastic Programming Alexander Shapiro, Darinka Dentcheva, Andrzej Ruszczy?ski, 2009-01-01 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. |
| stochastic modeling and optimization: Modeling, Stochastic Control, Optimization, and Applications George Yin, Qing Zhang, 2019-07-16 This volume collects papers, based on invited talks given at the IMA workshop in Modeling, Stochastic Control, Optimization, and Related Applications, held at the Institute for Mathematics and Its Applications, University of Minnesota, during May and June, 2018. There were four week-long workshops during the conference. They are (1) stochastic control, computation methods, and applications, (2) queueing theory and networked systems, (3) ecological and biological applications, and (4) finance and economics applications. For broader impacts, researchers from different fields covering both theoretically oriented and application intensive areas were invited to participate in the conference. It brought together researchers from multi-disciplinary communities in applied mathematics, applied probability, engineering, biology, ecology, and networked science, to review, and substantially update most recent progress. As an archive, this volume presents some of the highlights of the workshops, and collect papers covering a broad range of topics. |
| stochastic modeling and optimization: Stochastic Optimization Models In Finance (2006 Edition) William T Ziemba, Raymond G Vickson, 2006-09-11 A reprint of one of the classic volumes on portfolio theory and investment, this book has been used by the leading professors at universities such as Stanford, Berkeley, and Carnegie-Mellon. It contains five parts, each with a review of the literature and about 150 pages of computational and review exercises and further in-depth, challenging problems.Frequently referenced and highly usable, the material remains as fresh and relevant for a portfolio theory course as ever. |
| stochastic modeling and optimization: Introduction to Stochastic Programming John R. Birge, François Louveaux, 2006-04-06 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. |
| stochastic modeling and optimization: Stochastic Modeling and Optimization David D. Yao, Hanqin Zhang, Xun Yu Zhou, 2003-01-01 |
| stochastic modeling and optimization: Stochastic Modeling and Optimization David D. Yao, Hanqin Zhang, Xun Yu Zhou, 2012-12-06 The objective of this volume is to highlight through a collection of chap ters some of the recent research works in applied prob ability, specifically stochastic modeling and optimization. The volume is organized loosely into four parts. The first part is a col lection of several basic methodologies: singularly perturbed Markov chains (Chapter 1), and related applications in stochastic optimal control (Chapter 2); stochastic approximation, emphasizing convergence properties (Chapter 3); a performance-potential based approach to Markov decision program ming (Chapter 4); and interior-point techniques (homogeneous self-dual embedding and central path following) applied to stochastic programming (Chapter 5). The three chapters in the second part are concerned with queueing the ory. Chapters 6 and 7 both study processing networks - a general dass of queueing networks - focusing, respectively, on limit theorems in the form of strong approximation, and the issue of stability via connections to re lated fluid models. The subject of Chapter 8 is performance asymptotics via large deviations theory, when the input process to a queueing system exhibits long-range dependence, modeled as fractional Brownian motion. |
| stochastic modeling and optimization: Stochastic Simulation Optimization Chun-hung Chen, Loo Hay Lee, 2010 With the advance of new computing technology, simulation is becoming very popular for designing large, complex, and stochastic engineering systems, since closed-form analytical solutions generally do not exist for such problems. However, the added flexibility of simulation often creates models that are computationally intractable. Moreover, to obtain a sound statistical estimate at a specified level of confidence, a large number of simulation runs (or replications) is usually required for each design alternative. If the number of design alternatives is large, the total simulation cost can be very expensive. This book addresses the pertinent efficiency issue via smart allocation of computing resource in the simulation experiments for optimization, and aims to provide academic researchers and industrial practitioners a comprehensive coverage of OCBA approach for stochastic simulation optimization. Starting with an intuitive explanation of computing budget allocation and a discussion of its impact on optimization performance, a series of OCBA approaches developed for various problems are then presented, from the selection of the best design to optimization with multiple objectives.Finally, this book discusses the potential extension of OCBA notion to different applications such as data envelopment analysis, experiments of design, and rare-event simulation. |
| stochastic modeling and optimization: Modeling with Stochastic Programming Alan J. King, Stein W. Wallace, 2012-06-19 While there are several texts on how to solve and analyze stochastic programs, this is the first text to address basic questions about how to model uncertainty, and how to reformulate a deterministic model so that it can be analyzed in a stochastic setting. This text would be suitable as a stand-alone or supplement for a second course in OR/MS or in optimization-oriented engineering disciplines where the instructor wants to explain where models come from and what the fundamental issues are. The book is easy-to-read, highly illustrated with lots of examples and discussions. It will be suitable for graduate students and researchers working in operations research, mathematics, engineering and related departments where there is interest in learning how to model uncertainty. Alan King is a Research Staff Member at IBM's Thomas J. Watson Research Center in New York. Stein W. Wallace is a Professor of Operational Research at Lancaster University Management School in England. |
| stochastic modeling and optimization: Stochastic Modeling and Optimization of Manufacturing Systems and Supply Chains J. George Shanthikumar, David D. Yao, W.H.M. Zijm, 2012-12-06 This volume originates from two workshops, both focusing on themes that are reflected in the title of the volume. The first workshop took place at Eindhoven University of Technology, April 24-26, 2001, on the occasion of the University granting a doctorate honoris causa to Profes sor John A. Buzacott. The second workshop was held on June 15, 2002 at Cornell University (preceding the annual INFORMSjMSOM Confer ence), honoring John's retirement and his lifetime contributions. Each of the two workshops consisted of about a dozen technical presentations. The objective of the volume, however, is not to simply publish the proceedings of the two workshops. Rather, our objective is to put to gether a select set of articles, each organized into a well-written chapter, focusing on a timely topic. Collected into a single volume, these chapters aim to serve as a useful reference for researchers and practitioners alike, and also as reading materials for graduate courses or seminars. |
| stochastic modeling and optimization: Dynamic Optimization Karl Hinderer, Ulrich Rieder, Michael Stieglitz, 2017-01-12 This book explores discrete-time dynamic optimization and provides a detailed introduction to both deterministic and stochastic models. Covering problems with finite and infinite horizon, as well as Markov renewal programs, Bayesian control models and partially observable processes, the book focuses on the precise modelling of applications in a variety of areas, including operations research, computer science, mathematics, statistics, engineering, economics and finance. Dynamic Optimization is a carefully presented textbook which starts with discrete-time deterministic dynamic optimization problems, providing readers with the tools for sequential decision-making, before proceeding to the more complicated stochastic models. The authors present complete and simple proofs and illustrate the main results with numerous examples and exercises (without solutions). With relevant material covered in four appendices, this book is completely self-contained. |
| stochastic modeling and optimization: Stochastic Simulation Optimization For Discrete Event Systems: Perturbation Analysis, Ordinal Optimization And Beyond Chun-hung Chen, Qing-shan Jia, Loo Hay Lee, 2013-07-03 Discrete event systems (DES) have become pervasive in our daily lives. Examples include (but are not restricted to) manufacturing and supply chains, transportation, healthcare, call centers, and financial engineering. However, due to their complexities that often involve millions or even billions of events with many variables and constraints, modeling these stochastic simulations has long been a “hard nut to crack”. The advance in available computer technology, especially of cluster and cloud computing, has paved the way for the realization of a number of stochastic simulation optimization for complex discrete event systems. This book will introduce two important techniques initially proposed and developed by Professor Y C Ho and his team; namely perturbation analysis and ordinal optimization for stochastic simulation optimization, and present the state-of-the-art technology, and their future research directions. |
| stochastic modeling and optimization: Stochastic Optimization Johannes Schneider, Scott Kirkpatrick, 2006-11-07 This book addresses stochastic optimization procedures in a broad manner. The first part offers an overview of relevant optimization philosophies; the second deals with benchmark problems in depth, by applying a selection of optimization procedures. Written primarily with scientists and students from the physical and engineering sciences in mind, this book addresses a larger community of all who wish to learn about stochastic optimization techniques and how to use them. |
| stochastic modeling and optimization: Stochastic Multi-Stage Optimization Pierre Carpentier, Jean-Philippe Chancelier, Guy Cohen, Michel De Lara, 2015-05-05 The focus of the present volume is stochastic optimization of dynamical systems in discrete time where - by concentrating on the role of information regarding optimization problems - it discusses the related discretization issues. There is a growing need to tackle uncertainty in applications of optimization. For example the massive introduction of renewable energies in power systems challenges traditional ways to manage them. This book lays out basic and advanced tools to handle and numerically solve such problems and thereby is building a bridge between Stochastic Programming and Stochastic Control. It is intended for graduates readers and scholars in optimization or stochastic control, as well as engineers with a background in applied mathematics. |
| stochastic modeling and optimization: Multistage Stochastic Optimization Georg Ch. Pflug, Alois Pichler, 2014-11-12 Multistage stochastic optimization problems appear in many ways in finance, insurance, energy production and trading, logistics and transportation, among other areas. They describe decision situations under uncertainty and with a longer planning horizon. This book contains a comprehensive treatment of today’s state of the art in multistage stochastic optimization. It covers the mathematical backgrounds of approximation theory as well as numerous practical algorithms and examples for the generation and handling of scenario trees. A special emphasis is put on estimation and bounding of the modeling error using novel distance concepts, on time consistency and the role of model ambiguity in the decision process. An extensive treatment of examples from electricity production, asset liability management and inventory control concludes the book. |
| stochastic modeling and optimization: Stochastic Optimization Methods Kurt Marti, 2015-02-21 This book examines optimization problems that in practice involve random model parameters. It details the computation of robust optimal solutions, i.e., optimal solutions that are insensitive with respect to random parameter variations, where appropriate deterministic substitute problems are needed. Based on the probability distribution of the random data and using decision theoretical concepts, optimization problems under stochastic uncertainty are converted into appropriate deterministic substitute problems. Due to the probabilities and expectations involved, the book also shows how to apply approximative solution techniques. Several deterministic and stochastic approximation methods are provided: Taylor expansion methods, regression and response surface methods (RSM), probability inequalities, multiple linearization of survival/failure domains, discretization methods, convex approximation/deterministic descent directions/efficient points, stochastic approximation and gradient procedures and differentiation formulas for probabilities and expectations. In the third edition, this book further develops stochastic optimization methods. In particular, it now shows how to apply stochastic optimization methods to the approximate solution of important concrete problems arising in engineering, economics and operations research. |
| stochastic modeling and optimization: Stochastic Optimization Stanislav Uryasev, Panos M. Pardalos, 2013-03-09 Stochastic programming is the study of procedures for decision making under the presence of uncertainties and risks. Stochastic programming approaches have been successfully used in a number of areas such as energy and production planning, telecommunications, and transportation. Recently, the practical experience gained in stochastic programming has been expanded to a much larger spectrum of applications including financial modeling, risk management, and probabilistic risk analysis. Major topics in this volume include: (1) advances in theory and implementation of stochastic programming algorithms; (2) sensitivity analysis of stochastic systems; (3) stochastic programming applications and other related topics. Audience: Researchers and academies working in optimization, computer modeling, operations research and financial engineering. The book is appropriate as supplementary reading in courses on optimization and financial engineering. |
| stochastic modeling and optimization: An Introduction to Stochastic Modeling Howard M. Taylor, Samuel Karlin, 2014-05-10 An Introduction to Stochastic Modeling, Revised Edition provides information pertinent to the standard concepts and methods of stochastic modeling. This book presents the rich diversity of applications of stochastic processes in the sciences. Organized into nine chapters, this book begins with an overview of diverse types of stochastic models, which predicts a set of possible outcomes weighed by their likelihoods or probabilities. This text then provides exercises in the applications of simple stochastic analysis to appropriate problems. Other chapters consider the study of general functions of independent, identically distributed, nonnegative random variables representing the successive intervals between renewals. This book discusses as well the numerous examples of Markov branching processes that arise naturally in various scientific disciplines. The final chapter deals with queueing models, which aid the design process by predicting system performance. This book is a valuable resource for students of engineering and management science. Engineers will also find this book useful. |
| stochastic modeling and optimization: Strengthening Data Science Methods for Department of Defense Personnel and Readiness Missions National Academies of Sciences, Engineering, and Medicine, Division on Engineering and Physical Sciences, Board on Mathematical Sciences and Their Applications, Committee on Applied and Theoretical Statistics, Committee on Strengthening Data Science Methods for Department of Defense Personnel and Readiness Missions, 2017-03-06 The Office of the Under Secretary of Defense (Personnel & Readiness), referred to throughout this report as P&R, is responsible for the total force management of all Department of Defense (DoD) components including the recruitment, readiness, and retention of personnel. Its work and policies are supported by a number of organizations both within DoD, including the Defense Manpower Data Center (DMDC), and externally, including the federally funded research and development centers (FFRDCs) that work for DoD. P&R must be able to answer questions for the Secretary of Defense such as how to recruit people with an aptitude for and interest in various specialties and along particular career tracks and how to assess on an ongoing basis service members' career satisfaction and their ability to meet new challenges. P&R must also address larger-scale questions, such as how the current realignment of forces to the Asia-Pacific area and other regions will affect recruitment, readiness, and retention. While DoD makes use of large-scale data and mathematical analysis in intelligence, surveillance, reconnaissance, and elsewhereâ€exploiting techniques such as complex network analysis, machine learning, streaming social media analysis, and anomaly detectionâ€these skills and capabilities have not been applied as well to the personnel and readiness enterprise. Strengthening Data Science Methods for Department of Defense Personnel and Readiness Missions offers and roadmap and implementation plan for the integration of data analysis in support of decisions within the purview of P&R. |
| stochastic modeling and optimization: Optimization in Economics and Finance Bruce D. Craven, Sardar M. N. Islam, 2005-10-24 Many optimization questions arise in economics and finance; an important example of this is the society's choice of the optimum state of the economy (the social choice problem). Optimization in Economics and Finance extends and improves the usual optimization techniques, in a form that may be adopted for modeling social choice problems. Problems discussed include: when is an optimum reached; when is it unique; relaxation of the conventional convex (or concave) assumptions on an economic model; associated mathematical concepts such as invex and quasimax; multiobjective optimal control models; and related computational methods and programs. These techniques are applied to economic growth models (including small stochastic perturbations), finance and financial investment models (and the interaction between financial and production variables), modeling sustainability over long time horizons, boundary (transversality) conditions, and models with several conflicting objectives. Although the applications are general and illustrative, the models in this book provide examples of possible models for a society's social choice for an allocation that maximizes welfare and utilization of resources. As well as using existing computer programs for optimization of models, a new computer program, named SCOM, is presented in this book for computing social choice models by optimal control. |
| stochastic modeling and optimization: Markov Models & Optimization M.H.A. Davis, 2018-02-19 This book presents a radically new approach to problems of evaluating and optimizing the performance of continuous-time stochastic systems. This approach is based on the use of a family of Markov processes called Piecewise-Deterministic Processes (PDPs) as a general class of stochastic system models. A PDP is a Markov process that follows deterministic trajectories between random jumps, the latter occurring either spontaneously, in a Poisson-like fashion, or when the process hits the boundary of its state space. This formulation includes an enormous variety of applied problems in engineering, operations research, management science and economics as special cases; examples include queueing systems, stochastic scheduling, inventory control, resource allocation problems, optimal planning of production or exploitation of renewable or non-renewable resources, insurance analysis, fault detection in process systems, and tracking of maneuvering targets, among many others. The first part of the book shows how these applications lead to the PDP as a system model, and the main properties of PDPs are derived. There is particular emphasis on the so-called extended generator of the process, which gives a general method for calculating expectations and distributions of system performance functions. The second half of the book is devoted to control theory for PDPs, with a view to controlling PDP models for optimal performance: characterizations are obtained of optimal strategies both for continuously-acting controllers and for control by intervention (impulse control). Throughout the book, modern methods of stochastic analysis are used, but all the necessary theory is developed from scratch and presented in a self-contained way. The book will be useful to engineers and scientists in the application areas as well as to mathematicians interested in applications of stochastic analysis. |
| stochastic modeling and optimization: Stochastic Modeling and Optimization , 2025 Most processes in life are prone to randomness, which can be both a challenge and an aid in mathematical modeling and optimization. In this dissertation, this randomness is studied through various modeling methods and (stochastic) optimization algorithms. It is shown how these can be developed for and applied to diverse problems in the domains of healthcare, manufacturing and search engine optimization. The key modeling methods are Markov chains and discrete-event models, and the key optimization algorithms are stochastic approximation algorithms and evolutionary algorithms. The following is addressed: • A three-step framework for capacity planning in nursing homes is developed that includes a shift scheduling algorithm and a genetic algorithm that assigns nurses to daily tasks. • A neural network metamodeler is developed that integrates biased analytical queuing features to estimate the throughput of a tandem line. This metamodeler is applied to a variety of optimization problems, such as the buffer allocation problem. • An algorithm based on pseudo-gradient methods is developed to optimize a function over the stationary distribution of a Markov chain. • The emergency response process of electric ambulances is modeled to determine the influence of transitioning from a diesel to an electric fleet on the response times. |
| stochastic modeling and optimization: Advanced Stochastic Models, Risk Assessment, and Portfolio Optimization Svetlozar T. Rachev, Stoyan V. Stoyanov, Frank J. Fabozzi, 2008-02-25 This groundbreaking book extends traditional approaches of risk measurement and portfolio optimization by combining distributional models with risk or performance measures into one framework. Throughout these pages, the expert authors explain the fundamentals of probability metrics, outline new approaches to portfolio optimization, and discuss a variety of essential risk measures. Using numerous examples, they illustrate a range of applications to optimal portfolio choice and risk theory, as well as applications to the area of computational finance that may be useful to financial engineers. |
| stochastic modeling and optimization: Stochastic Modelling of Social Processes Andreas Diekmann, Peter Mitter, 2014-05-10 Stochastic Modelling of Social Processes provides information pertinent to the development in the field of stochastic modeling and its applications in the social sciences. This book demonstrates that stochastic models can fulfill the goals of explanation and prediction. Organized into nine chapters, this book begins with an overview of stochastic models that fulfill normative, predictive, and structural–analytic roles with the aid of the theory of probability. This text then examines the study of labor market structures using analysis of job and career mobility, which is one of the approaches taken by sociologists in research on the labor market. Other chapters consider the characteristic trends and patterns from data on divorces. This book discusses as well the two approaches of stochastic modeling of social processes, namely competing risk models and semi-Markov processes. The final chapter deals with the practical application of regression models of survival data. This book is a valuable resource for social scientists and statisticians. |
| stochastic modeling and optimization: Introduction to Matrix Analytic Methods in Stochastic Modeling G. Latouche, V. Ramaswami, 1999-01-01 Presents the basic mathematical ideas and algorithms of the matrix analytic theory in a readable, up-to-date, and comprehensive manner. |
| stochastic modeling and optimization: Fundamentals of Queueing Networks Hong Chen, David D. Yao, 2013-04-17 The objective of this book is to collect in a single volume the essentials of stochastic networks, from the classical product-form theory to the more re cent developments such as diffusion and fluid limits, stochastic comparisons, stability, control (dynamic scheduling) and optimization. The selection of materials inevitably is a reflection upon our bias and preference, but it is also driven to a large extent by our desire to provide a graduate-level text that is well balanced in breadth and depth, suitable for the classroom. Given the wide-ranging applications of stochastic networks in recent years, from supply chains to telecommunications, it is also our hope that the book will serve as a useful reference for researchers and students alike in these diverse fields. The book consists of three parts. The first part, Chapters 1 through 4, covers (continuous-time) Markov-chain models, including the classical Jackson and Kelly networks, the notion of quasi-reversible queues, and stochastic comparisons. The second part, Chapters 5 through 10, focuses on Brownian models, including limit theorems for generalized Jackson net works and multiclass feedforward networks, an in-depth examination of stability in a Kumar-Seidman network, and Brownian approximations for general multiclass networks with a mixture of priority and first-in-first-out disciplines. The third part, Chapters 11 and 12, discusses scheduling in both queueing (stochastic) and fluid (deterministic) networks, along with topics such as conservation laws, polymatroid optimization, and linear pro gramming. |
| stochastic modeling and optimization: Stochastic Modelling and Analysis , 1988 |
| stochastic modeling and optimization: Stochastic and Global Optimization G. Dzemyda, V. Saltenis, A. Žilinskas, 2002-03-31 This book is dedicated to the 70th birthday of Professor J. Mockus, whose scientific interests include theory and applications of global and discrete optimization, and stochastic programming. The papers for the book were selected because they relate to these topics and also satisfy the criterion of theoretical soundness combined with practical applicability. In addition, the methods for statistical analysis of extremal problems are covered. Although statistical approach to global and discrete optimization is emphasized, applications to optimal design and to mathematical finance are also presented. The results of some subjects (e.g., statistical models based on one-dimensional global optimization) are summarized and the prospects for new developments are justified. Audience: Practitioners, graduate students in mathematics, statistics, computer science and engineering. |
| stochastic modeling and optimization: Stochastic Modeling Barry L. Nelson, 2012-10-11 Coherent introduction to techniques also offers a guide to the mathematical, numerical, and simulation tools of systems analysis. Includes formulation of models, analysis, and interpretation of results. 1995 edition. |
| stochastic modeling and optimization: Stochastic Global Optimization Gade Pandu Rangaiah, 2010 Optimization has played a key role in the design, planning and operation of chemical and related processes, for several decades. Global optimization has been receiving considerable attention in the past two decades. Of the two types of techniques for global optimization, stochastic global optimization is applicable to any type of problems having non-differentiable functions, discrete variables and/or continuous variables. It, thus, shows significant promise and potential for process optimization. So far, there are no books focusing on stochastic global optimization and its applications in chemical engineering. Stochastic Global Optimization ? a monograph with contributions by leading researchers in the area ? bridges the gap in this subject, with the aim of highlighting and popularizing stochastic global optimization techniques for chemical engineering applications. The book, with 19 chapters in all, is broadly categorized into two sections that extensively cover the techniques and the chemical engineering applications. |
| stochastic modeling and optimization: Stochastic Processes and Models in Operations Research Anbazhagan, Neelamegam, 2016-03-24 Decision-making is an important task no matter the industry. Operations research, as a discipline, helps alleviate decision-making problems through the extraction of reliable information related to the task at hand in order to come to a viable solution. Integrating stochastic processes into operations research and management can further aid in the decision-making process for industrial and management problems. Stochastic Processes and Models in Operations Research emphasizes mathematical tools and equations relevant for solving complex problems within business and industrial settings. This research-based publication aims to assist scholars, researchers, operations managers, and graduate-level students by providing comprehensive exposure to the concepts, trends, and technologies relevant to stochastic process modeling to solve operations research problems. |
| stochastic modeling and optimization: Reinforcement Learning and Stochastic Optimization Warren B. Powell, 2022-03-15 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. |
| stochastic modeling and optimization: Dynamic Stochastic Optimization Kurt Marti, Yuri Ermoliev, Georg Ch. Pflug, 2012-12-06 Uncertainties and changes are pervasive characteristics of modern systems involving interactions between humans, economics, nature and technology. These systems are often too complex to allow for precise evaluations and, as a result, the lack of proper management (control) may create significant risks. In order to develop robust strategies we need approaches which explic itly deal with uncertainties, risks and changing conditions. One rather general approach is to characterize (explicitly or implicitly) uncertainties by objec tive or subjective probabilities (measures of confidence or belief). This leads us to stochastic optimization problems which can rarely be solved by using the standard deterministic optimization and optimal control methods. In the stochastic optimization the accent is on problems with a large number of deci sion and random variables, and consequently the focus ofattention is directed to efficient solution procedures rather than to (analytical) closed-form solu tions. Objective and constraint functions of dynamic stochastic optimization problems have the form of multidimensional integrals of rather involved in that may have a nonsmooth and even discontinuous character - the tegrands typical situation for hit-or-miss type of decision making problems involving irreversibility ofdecisions or/and abrupt changes ofthe system. In general, the exact evaluation of such functions (as is assumed in the standard optimization and control theory) is practically impossible. Also, the problem does not often possess the separability properties that allow to derive the standard in control theory recursive (Bellman) equations. |
| stochastic modeling and optimization: Handbook of Simulation Optimization Michael C Fu, 2014-11-13 The Handbook of Simulation Optimization presents an overview of the state of the art of simulation optimization, providing a survey of the most well-established approaches for optimizing stochastic simulation models and a sampling of recent research advances in theory and methodology. Leading contributors cover such topics as discrete optimization via simulation, ranking and selection, efficient simulation budget allocation, random search methods, response surface methodology, stochastic gradient estimation, stochastic approximation, sample average approximation, stochastic constraints, variance reduction techniques, model-based stochastic search methods and Markov decision processes. This single volume should serve as a reference for those already in the field and as a means for those new to the field for understanding and applying the main approaches. The intended audience includes researchers, practitioners and graduate students in the business/engineering fields of operations research, management science, operations management and stochastic control, as well as in economics/finance and computer science. |
| stochastic modeling and optimization: Modeling, Computation and Optimization S. K. Neogy, Arup Kumar Das, R. B. Bapat, 2009 This volume provides recent developments and a state-of-the-art review in various areas of mathematical modeling, computation and optimization. It contains theory, computation as well as the applications of several mathematical models to problems in statistics, games, optimization and economics for decision making. It focuses on exciting areas like models for wireless networks, models of Nash networks, dynamic models of advertising, application of reliability models in economics, support vector machines, optimization, complementarity modeling and games. |
| stochastic modeling and optimization: Modeling, Simulation, and Optimization of Supply Chains Ciro D'Apice, Simone Gottlich, Michael Herty, Benedetto Piccoli, 2010-07-01 This book offers a state-of-the-art introduction to the mathematical theory of supply chain networks, focusing on those described by partial differential equations. The authors discuss modeling of complex supply networks as well as their mathematical theory, explore modeling, simulation, and optimization of some of the discussed models, and present analytical and numerical results on optimization problems. Real-world examples are given to demonstrate the applicability of the presented approaches. Graduate students and researchers who are interested in the theory of supply chain networks described by partial differential equations will find this book useful. It can also be used in advanced graduate-level courses on modeling of physical phenomena as well as introductory courses on supply chain theory. |
| stochastic modeling and optimization: Stochastic Discrete Event Systems Armin Zimmermann, 2009-09-02 Stochastic discrete-event systems (SDES) capture the randomness in choices due to activity delays and the probabilities of decisions. This book delivers a comprehensive overview on modeling with a quantitative evaluation of SDES. It presents an abstract model class for SDES as a pivotal unifying result and details important model classes. The book also includes nontrivial examples to explain real-world applications of SDES. |
| stochastic modeling and optimization: Stochastic Programming Horand Gassmann, W. T. Ziemba, 2013 This book shows the breadth and depth of stochastic programming applications. All the papers presented here involve optimization over the scenarios that represent possible future outcomes of the uncertainty problems. The applications, which were presented at the 12th International Conference on Stochastic Programming held in Halifax, Nova Scotia in August 2010, span the rich field of uses of these models. The finance papers discuss such diverse problems as longevity risk management of individual investors, personal financial planning, intertemporal surplus management, asset management with benchmarks, dynamic portfolio management, fixed income immunization and racetrack betting. The production and logistics papers discuss natural gas infrastructure design, farming Atlantic salmon, prevention of nuclear smuggling and sawmill planning. The energy papers involve electricity production planning, hydroelectric reservoir operations and power generation planning for liquid natural gas plants. Finally, two telecommunication papers discuss mobile network design and frequency assignment problems. |
In layman's terms: What is a stochastic process?
Oct 8, 2015 · A stochastic process is a way of representing the evolution of some situation that can be characterized mathematically (by numbers, points in a graph, etc.) over time. They are …
What's the difference between stochastic and random?
Feb 28, 2012 · The terms "stochastic variable" and "random variable" both occur in the literature and are synonymous. The latter is seen more often. Similarly "stochastic process" and …
「Stochastic」与「Random」有何区别？ - 知乎
知乎，中文互联网高质量的问答社区和创作者聚集的原创内容平台，于 2011 年 1 月正式上线，以「让人们更好的分享知识、经验和见解，找到自己的解答」为品牌使命。知乎凭借认真、专业 …
What are the prerequisites for stochastic calculus?
Apr 22, 2013 · -Theories of convergence of stochastic processes-Theory of continuous-time stochastic processes, Brownian motion in particular. This is all covered in volume one of …
Difference between time series and stochastic process?
Jan 30, 2011 · Basically, a stochastic process is to a time series what a random variable is to a number. The realization (the "result", the observed value) of a random variable (say, a dice …
terminology - What is the difference between stochastic calculus …
Apr 4, 2015 · Stochastic calculus is to do with mathematics that operates on stochastic processes. The best known stochastic process is the Wiener process used for modelling …
How does one interpret the meaning of a stochastic derivative?
Only the integral with respect to Brownian motion is defined in the Ito- or the Stratonovich calculus. This means that there is no "stochastic derivative", and that the notion of "velocity" is …
probability theory - What is the difference between stochastic …
Aug 1, 2020 · A stochastic process is a family of random variables indexed by some set, usually $\mathbb{Z}^{n}$ or $\mathbb{R}^{n}$. It's additional structure over random variables that let …
What is stochastic mapping? - Mathematics Stack Exchange
Stack Exchange Network. Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their …
Books recommendations on stochastic analysis - Mathematics …
Feb 21, 2023 · Stochastic Calculus for Finance I: Binomial asset pricing model and Stochastic Calculus for Finance II: tochastic Calculus for Finance II: Continuous-Time Models. These two …
In layman's terms: What is a stochastic process?
Oct 8, 2015 · A stochastic process is a way of representing the evolution of some situation that can be characterized mathematically (by numbers, points in a graph, etc.) over time. They are …
What's the difference between stochastic and random?
Feb 28, 2012 · The terms "stochastic variable" and "random variable" both occur in the literature and are synonymous. The latter is seen more often. Similarly "stochastic process" and …
「Stochastic」与「Random」有何区别？ - 知乎
知乎，中文互联网高质量的问答社区和创作者聚集的原创内容平台，于 2011 年 1 月正式上线，以「让人们更好的分享知识、经验和见解，找到自己的解答」为品牌使命。知乎凭借认真、专业 …
What are the prerequisites for stochastic calculus?
Apr 22, 2013 · -Theories of convergence of stochastic processes-Theory of continuous-time stochastic processes, Brownian motion in particular. This is all covered in volume one of …
Difference between time series and stochastic process?
Jan 30, 2011 · Basically, a stochastic process is to a time series what a random variable is to a number. The realization (the "result", the observed value) of a random variable (say, a dice …
terminology - What is the difference between stochastic calculus …
Apr 4, 2015 · Stochastic calculus is to do with mathematics that operates on stochastic processes. The best known stochastic process is the Wiener process used for modelling …
How does one interpret the meaning of a stochastic derivative?
Only the integral with respect to Brownian motion is defined in the Ito- or the Stratonovich calculus. This means that there is no "stochastic derivative", and that the notion of "velocity" is …
probability theory - What is the difference between stochastic …
Aug 1, 2020 · A stochastic process is a family of random variables indexed by some set, usually $\mathbb{Z}^{n}$ or $\mathbb{R}^{n}$. It's additional structure over random variables that let …
What is stochastic mapping? - Mathematics Stack Exchange
Stack Exchange Network. Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their …
Books recommendations on stochastic analysis - Mathematics …
Feb 21, 2023 · Stochastic Calculus for Finance I: Binomial asset pricing model and Stochastic Calculus for Finance II: tochastic Calculus for Finance II: Continuous-Time Models. These two …
