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Methods Of Solution Of Linear Programs Under Uncertainty
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Book Synopsis Methods of Solution of Linear Programs Under Uncertainty by : Albert Madansky
Download or read book Methods of Solution of Linear Programs Under Uncertainty written by Albert Madansky and published by . This book was released on 1960 with total page 30 pages. Available in PDF, EPUB and Kindle. Book excerpt: The three most usual methods of reducing the effects of uncertainty in the technology matrix, requirement vector, or cost vector of a linear programming problem are the expected-value solution, the 'fat' solution, and the 'slack' solution. These methods are explained in some detail, and the relation between these various methods is pointed out. (Author).
Book Synopsis Methods of Solution of Linear Programs Under Uncertainty. Notes on Linear Programming and Extensions by : ALBERT. MADANSKY
Download or read book Methods of Solution of Linear Programs Under Uncertainty. Notes on Linear Programming and Extensions written by ALBERT. MADANSKY and published by . This book was released on 1961 with total page 1 pages. Available in PDF, EPUB and Kindle. Book excerpt: Most applied linear-programming problems involve uncertainty in either the technology matrix, the requirement vector, or the cost. Some of the more usual methods of reducing the effects of uncertainty are (1) replacing the random elements by their expected values, (2) replacing the random elements by pessimistic estimates of their values, and (3) recasting the problem into a two-stage program so that, in the second stage, one can compensate for inaccuracies in the activities of the first stage. These methods are called the expected-value solution, the fat solution, and the slack solution, respectively. The one-stage linear program is examined under uncertainty in some detail, pointing out the relation between these various solutions. (Author).
Book Synopsis Planning Under Uncertainty by : Gerd Infanger
Download or read book Planning Under Uncertainty written by Gerd Infanger and published by Boyd & Fraser Publishing Company. This book was released on 1994 with total page 168 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Methods of Solution of Linear Programs Under Uncertainty by :
Download or read book Methods of Solution of Linear Programs Under Uncertainty written by and published by . This book was released on 1961 with total page 10 pages. Available in PDF, EPUB and Kindle. Book excerpt: The three most usual methods of reducing the effects of uncertainty in the technology matrix, requirement vector, or cost vector of a linear programming problem are the expected-value solution, the 'fat' solution, and the 'slack' solution. These methods are explained in some detail, and the relation between these various methods is pointed out. (Author).
Book Synopsis On the Solution of Two-stage Linear Programs Under Uncertainty by : George B. Dantzig
Download or read book On the Solution of Two-stage Linear Programs Under Uncertainty written by George B. Dantzig and published by . This book was released on 1961 with total page 1 pages. Available in PDF, EPUB and Kindle. Book excerpt: A possible method for compensating for uncertainty in linear-programming problems is to replace the random elements by expected values or by pessimistic estimates of these values, or to recast the problem into a two-stage program so that, in the second stage, one can compensate for inaccuracies in the first stage. The purpose of this analysis is to examine the last of these methods in detail. More precisely, it investigates the conditions under which the first-stage decisions are optimal. In addition, formulas for using various existing computational algorithms to obtain an optimal solution are given. (Author).
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".
Book Synopsis Use of the 'expected Value Solution' in Linear Programming Under Uncertainty by : Albert Madansky
Download or read book Use of the 'expected Value Solution' in Linear Programming Under Uncertainty written by Albert Madansky and published by . This book was released on 1960 with total page 16 pages. Available in PDF, EPUB and Kindle. Book excerpt: The use of two methods in the one-stage stochastic linear program is discussed: (1) replacing the random elements by their expected values (the 'expected-value solution'); and (2) replacing the random elements by pessimistic estimates of their values (the 'fat' technique). The one-stage problem and the two-stage problem are described, and the relation between the 'fat' techniques used in the one-stage problem and the so-called 'slack' techniques useful in the two-stage problem is demonstrated.
Book Synopsis Mathematical Programming The State of the Art by : A. Bachem
Download or read book Mathematical Programming The State of the Art written by A. Bachem and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 662 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the late forties, Mathematical Programming became a scientific discipline in its own right. Since then it has experienced a tremendous growth. Beginning with economic and military applications, it is now among the most important fields of applied mathematics with extensive use in engineering, natural sciences, economics, and biological sciences. The lively activity in this area is demonstrated by the fact that as early as 1949 the first "Symposium on Mathe matical Programming" took place in Chicago. Since then mathematical programmers from all over the world have gath ered at the intfrnational symposia of the Mathematical Programming Society roughly every three years to present their recent research, to exchange ideas with their colleagues and to learn about the latest developments in their own and related fields. In 1982, the XI. International Symposium on Mathematical Programming was held at the University of Bonn, W. Germany, from August 23 to 27. It was organized by the Institut fUr Okonometrie und Operations Re search of the University of Bonn in collaboration with the Sonderforschungs bereich 21 of the Deutsche Forschungsgemeinschaft. This volume constitutes part of the outgrowth of this symposium and docu ments its scientific activities. Part I of the book contains information about the symposium, welcoming addresses, lists of committees and sponsors and a brief review about the Ful kerson Prize and the Dantzig Prize which were awarded during the opening ceremony.
Book Synopsis A Solution Procedure for a Class of Multi-stage Linear Programming Problems Under Uncertainty by : R. Jagannathan
Download or read book A Solution Procedure for a Class of Multi-stage Linear Programming Problems Under Uncertainty written by R. Jagannathan and published by . This book was released on 1968 with total page 36 pages. Available in PDF, EPUB and Kindle. Book excerpt: In stochastic linear programming it is necessary to distinguish two major classes of problems. First, the static models for which only one decision has to be made and second the dynamic models which involve sequential decision-making. Since more and more information will be available in succeeding periods, a dynamic model entails an adaptive policy prescription which involves a choice of decision vector for the ith period under all possible alternative realizations of the random variables observed before the ith period. A general multi-stage LP(U superscript 2) model is defined and it is proven that even under quite mild assumptions regarding the stochastic nature of the parameters of the model, it is equivalent to a convex programming problem. An algorithm is developed for solving the above convex programming problem. An approximate method is provided for solving a multi-stage capital budgeting problem under uncertainty. (Author).
Book Synopsis Linear Programming Under Uncertainty with Discrete Probability Distributions by : David P. Rutenberg
Download or read book Linear Programming Under Uncertainty with Discrete Probability Distributions written by David P. Rutenberg and published by . This book was released on 1966 with total page 32 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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.
Book Synopsis Stochastic Versus Fuzzy Approaches to Multiobjective Mathematical Programming under Uncertainty by : Shi-Yu Huang
Download or read book Stochastic Versus Fuzzy Approaches to Multiobjective Mathematical Programming under Uncertainty written by Shi-Yu Huang and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 425 pages. Available in PDF, EPUB and Kindle. Book excerpt: Operations Research is a field whose major contribution has been to propose a rigorous fonnulation of often ill-defmed problems pertaining to the organization or the design of large scale systems, such as resource allocation problems, scheduling and the like. While this effort did help a lot in understanding the nature of these problems, the mathematical models have proved only partially satisfactory due to the difficulty in gathering precise data, and in formulating objective functions that reflect the multi-faceted notion of optimal solution according to human experts. In this respect linear programming is a typical example of impressive achievement of Operations Research, that in its detenninistic fonn is not always adapted to real world decision-making : everything must be expressed in tenns of linear constraints ; yet the coefficients that appear in these constraints may not be so well-defined, either because their value depends upon other parameters (not accounted for in the model) or because they cannot be precisely assessed, and only qualitative estimates of these coefficients are available. Similarly the best solution to a linear programming problem may be more a matter of compromise between various criteria rather than just minimizing or maximizing a linear objective function. Lastly the constraints, expressed by equalities or inequalities between linear expressions, are often softer in reality that what their mathematical expression might let us believe, and infeasibility as detected by the linear programming techniques can often been coped with by making trade-offs with the real world.
Download or read book Oklahoma City written by and published by . This book was released on 19?? with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Includes newspaper clippings, maps, etc.
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 2005-06-01 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.
Book Synopsis Planning Under Uncertainty Solving Large-scale Stochastic Linear Programs by :
Download or read book Planning Under Uncertainty Solving Large-scale Stochastic Linear Programs written by and published by . This book was released on 1992 with total page 116 pages. Available in PDF, EPUB and Kindle. Book excerpt: For many practical problems, solutions obtained from deterministic models are unsatisfactory because they fail to hedge against certain contingencies that may occur in the future. Stochastic models address this shortcoming, but up to recently seemed to be intractable due to their size. Recent advances both in solution algorithms and in computer technology now allow us to solve important and general classes of practical stochastic problems. We show how large-scale stochastic linear programs can be efficiently solved by combining classical decomposition and Monte Carlo (importance) sampling techniques. We discuss the methodology for solving two-stage stochastic linear programs with recourse, present numerical results of large problems with numerous stochastic parameters, show how to efficiently implement the methodology on a parallel multi-computer and derive the theory for solving a general class of multi-stage problems with dependency of the stochastic parameters within a stage and between different stages.
Book Synopsis Systems Optimization Methodology by : V. V. Kolbin
Download or read book Systems Optimization Methodology written by V. V. Kolbin and published by World Scientific. This book was released on 1999 with total page 332 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph deals with theoretical fundamentals and numerical methods of optimizing nondetermined models of systems. The main body of this work is devoted to investigation and optimization of system models under incomplete information. Much consideration is given to one-, two- and multistage problems of stochastic programming, solution methods and problems of solution stability. Optimization problems with fuzzy variables and optimization problems in function spaces are investigated. Examples are given for implementation of specific models of optimization under incomplete information. The book is based on lectures delivered by the author since 1965 for undergraduates and postgraduates at St. Petersburg (Leningrad) State University.
Book Synopsis Stochastic Programming by : Willem K. Klein Haneveld
Download or read book Stochastic Programming written by Willem K. Klein Haneveld and published by Springer Nature. This book was released on 2019-10-24 with total page 249 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an essential introduction to Stochastic Programming, especially intended for graduate students. The book begins by exploring a linear programming problem with random parameters, representing a decision problem under uncertainty. Several models for this problem are presented, including the main ones used in Stochastic Programming: recourse models and chance constraint models. The book not only discusses the theoretical properties of these models and algorithms for solving them, but also explains the intrinsic differences between the models. In the book’s closing section, several case studies are presented, helping students apply the theory covered to practical problems. The book is based on lecture notes developed for an Econometrics and Operations Research course for master students at the University of Groningen, the Netherlands - the longest-standing Stochastic Programming course worldwide.
