Download or read book A two stage stochastic integer programming approach written by and published by . This book was released on 2005 with total page 34 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book A Two stage Stochastic Integer Programming Approach written by L. F. Escudero and published by . This book was released on 2005 with total page 34 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Decision Making with Dominance Constraints in Two Stage Stochastic Integer Programming written by Uwe Gotzes and published by Springer Science & Business Media. This book was released on 2009-09-30 with total page 96 pages. Available in PDF, EPUB and Kindle. Book excerpt: Uwe Gotzes analyzes an approach to account for risk aversion in two-stage models based upon partial orders on the set of real random variables. He illustrates the superiority of the proposed decomposition method over standard solvers for example with numerical experiments with instances from energy investment.
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.
Download or read book Risk Management in Stochastic Integer Programming written by Frederike Neise and published by Springer Science & Business Media. This book was released on 2008-09-25 with total page 107 pages. Available in PDF, EPUB and Kindle. Book excerpt: The author presents two concepts to handle the classic linear mixed-integer two-stage stochastic optimization problem. She describes mean-risk modeling and stochastic programming with first order dominance constraints. Both approaches are applied to optimize the operation of a dispersed generation system.
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.
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 2011-06-15 with total page 500 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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. Review of First Edition: "The discussion on modeling issues, the large number of examples used to illustrate the material, and the breadth of the coverage make 'Introduction to Stochastic Programming' an ideal textbook for the area." (Interfaces, 1998)
Download or read book Decomposition Algorithms for Two stage Stochastic Integer Programming written by John H. Penuel and published by . This book was released on 2009 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: ABSTRACT: Stochastic programming seeks to optimize decision making in uncertain conditions. This type of work is typically amenable to decomposition into first- and second-stage decisions. First-stage decisions must be made now, while second-stage decisions are made after realizing certain future conditions and are typically constrained by first-stage decisions. This work focuses on two stochastic integer programming applications. In Chapter 2, we investigate a two-stage facility location problem with integer recourse. In Chapter 3, we investigate the graph decontamination problem with mobile agents. In both problems, we develop cutting-plane algorithms that iteratively solve the first-stage problem, then solve the second-stage problem and glean information from the second-stage solution with which we refine first-stage decisions. This process is repeated until optimality is reached. If the second-stage problems are linear programs, then duality can be exploited in order to refine first-stage decisions. If the second-stage problems are mixed-integer programs, then we resort to other methods to extract information from the second-stage problem. The applications discussed in this work have mixed-integer second-stage problems, and accordingly we develop specialized cutting-plane algorithms and demonstrate the efficacy of our solution methods.
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.
Download or read book Online Optimization of Large Scale Systems written by Martin Grötschel and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 789 pages. Available in PDF, EPUB and Kindle. Book excerpt: In its thousands of years of history, mathematics has made an extraordinary ca reer. It started from rules for bookkeeping and computation of areas to become the language of science. Its potential for decision support was fully recognized in the twentieth century only, vitally aided by the evolution of computing and communi cation technology. Mathematical optimization, in particular, has developed into a powerful machinery to help planners. Whether costs are to be reduced, profits to be maximized, or scarce resources to be used wisely, optimization methods are available to guide decision making. Opti mization is particularly strong if precise models of real phenomena and data of high quality are at hand - often yielding reliable automated control and decision proce dures. But what, if the models are soft and not all data are around? Can mathematics help as well? This book addresses such issues, e. g. , problems of the following type: - An elevator cannot know all transportation requests in advance. In which order should it serve the passengers? - Wing profiles of aircrafts influence the fuel consumption. Is it possible to con tinuously adapt the shape of a wing during the flight under rapidly changing conditions? - Robots are designed to accomplish specific tasks as efficiently as possible. But what if a robot navigates in an unknown environment? - Energy demand changes quickly and is not easily predictable over time. Some types of power plants can only react slowly.
Download or read book Integer Programming Approaches for Semicontinuous and Stochastic Optimization written by Gustavo Angulo Olivares (I.) and published by . This book was released on 2014 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: This thesis concerns the application of mixed-integer programming techniques to solve special classes of network flow problems and stochastic integer programs. We draw tools from complexity and polyhedral theory to analyze these problems and propose improved solution methods. In the first part, we consider semi-continuous network flow problems, that is, a class of network flow problems where some of the variables are required to take values above a prespecified minimum threshold whenever they are not zero. These problems find applications in management and supply chain models where orders in small quantities are undesirable. We introduce the semi-continuous inflow set with variable upper bounds as a relaxation of general semi-continuous network flow problems. Two particular cases of this set are considered, for which we present complete descriptions of the convex hull in terms of linear inequalities and extended formulations. We also consider a class of semi-continuous transportation problems where inflow systems arise as substructures, for which we investigate complexity questions. Finally, we study the computational efficacy of the developed polyhedral results in solving randomly generated instances of semi-continuous transportation problems. In the second part, we introduce and study the forbidden-vertices problem. Given a polytope P and a subset X of its vertices, we study the complexity of optimizing a linear function on the subset of vertices of P that are not contained in X. This problem is closely related to finding the k-best basic solutions to a linear problem and finds applications in stochastic integer programming. We observe that the complexity of the problem depends on how P and X are specified. For instance, P can be explicitly given by its linear description, or implicitly by an oracle. Similarly, X can be explicitly given as a list of vectors, or implicitly as a face of P. While removing vertices turns to be hard in general, it is tractable for tractable 0-1 polytopes, and compact extended formulations can be obtained. Some extensions to integral polytopes are also presented. The third part is devoted to the integer L-shaped method for two-stage stochastic integer programs. A widely used model assumes that decisions are made in a two-step fashion, where first-stage decisions are followed by second-stage recourse actions after the uncertain parameters are observed, and we seek to minimize the expected overall cost. In the case of finitely many possible outcomes or scenarios, the integer L-shaped method proposes a decomposition scheme akin to Benders' decomposition for linear problems, but where a series of mixed-integer subproblems have to be solved at each iteration. To improve the performance of the method, we devise a simple modification that alternates between linear and mixed-integer subproblems, yielding significant time savings in instances from the literature. We also present a general framework to generate optimality cuts via a cut-generating problem. Using an extended formulation of the forbidden-vertices problem, we recast our cut-generating problem as a linear problem and embed it within the integer L-shaped method. Our numerical experiments suggest that this approach can prove beneficial when the first-stage set is relatively complicated.
Download or read book A Multi stage Stochastic Integer Programming Approach for Capacity Expansion Under Uncertainty written by Shabbir Ahmed and published by . This book was released on 2001 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Stochastic Linear Programming Algorithms written by Janos Mayer and published by Taylor & Francis. This book was released on 2022-04-19 with total page 164 pages. Available in PDF, EPUB and Kindle. Book excerpt: A computationally oriented comparison of solution algorithms for two stage and jointly chance constrained stochastic linear programming problems, this is the first book to present comparative computational results with several major stochastic programming solution approaches. The following methods are considered: regularized decomposition, stochastic decomposition and successive discrete approximation methods for two stage problems; cutting plane methods, and a reduced gradient method for jointly chance constrained problems. The first part of the book introduces the algorithms, including a unified approach to decomposition methods and their regularized counterparts. The second part addresses computer implementation of the methods, describes a testing environment based on a model management system, and presents comparative computational results with the various algorithms. Emphasis is on the computational behavior of the algorithms.
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.
Download or read book Two stage Stochastic Integer Programming written by Rüdiger Schultz and published by . This book was released on 1994 with total page 14 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Applications of Stochastic Programming written by Stein W. Wallace and published by SIAM. This book was released on 2005-06-01 with total page 701 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.
Download or read book Stochastic Linear Programming Algorithms written by Janos Mayer and published by CRC Press. This book was released on 1998-02-25 with total page 174 pages. Available in PDF, EPUB and Kindle. Book excerpt: A computationally oriented comparison of solution algorithms for two stage and jointly chance constrained stochastic linear programming problems, this is the first book to present comparative computational results with several major stochastic programming solution approaches. The following methods are considered: regularized decomposition, stochastic decomposition and successive discrete approximation methods for two stage problems; cutting plane methods, and a reduced gradient method for jointly chance constrained problems. The first part of the book introduces the algorithms, including a unified approach to decomposition methods and their regularized counterparts. The second part addresses computer implementation of the methods, describes a testing environment based on a model management system, and presents comparative computational results with the various algorithms. Emphasis is on the computational behavior of the algorithms.
