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Methods Of Solution Of Linear Programs Under Uncertainty Notes On Linear Programming And Extensions
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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 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 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 Linear Programming 2 by : George B. Dantzig
Download or read book Linear Programming 2 written by George B. Dantzig and published by Springer Science & Business Media. This book was released on 2006-04-28 with total page 461 pages. Available in PDF, EPUB and Kindle. Book excerpt: George Dantzig is widely regarded as the founder of this subject with his invention of the simplex algorithm in the 1940's. In this second volume, the theory of the items discussed in the first volume is expanded to include such additional advanced topics as variants of the simplex method; interior point methods, GUB, decomposition, integer programming, and game theory. Graduate students in the fields of operations research, industrial engineering and applied mathematics will thus find this volume of particular interest.
Book Synopsis Linear Programming and Extensions by : George Dantzig
Download or read book Linear Programming and Extensions written by George Dantzig and published by Princeton University Press. This book was released on 2016-08-10 with total page 651 pages. Available in PDF, EPUB and Kindle. Book excerpt: In real-world problems related to finance, business, and management, mathematicians and economists frequently encounter optimization problems. In this classic book, George Dantzig looks at a wealth of examples and develops linear programming methods for their solutions. He begins by introducing the basic theory of linear inequalities and describes the powerful simplex method used to solve them. Treatments of the price concept, the transportation problem, and matrix methods are also given, and key mathematical concepts such as the properties of convex sets and linear vector spaces are covered. George Dantzig is properly acclaimed as the "father of linear programming." Linear programming is a mathematical technique used to optimize a situation. It can be used to minimize traffic congestion or to maximize the scheduling of airline flights. He formulated its basic theoretical model and discovered its underlying computational algorithm, the "simplex method," in a pathbreaking memorandum published by the United States Air Force in early 1948. Linear Programming and Extensions provides an extraordinary account of the subsequent development of his subject, including research in mathematical theory, computation, economic analysis, and applications to industrial problems. Dantzig first achieved success as a statistics graduate student at the University of California, Berkeley. One day he arrived for a class after it had begun, and assumed the two problems on the board were assigned for homework. When he handed in the solutions, he apologized to his professor, Jerzy Neyman, for their being late but explained that he had found the problems harder than usual. About six weeks later, Neyman excitedly told Dantzig, "I've just written an introduction to one of your papers. Read it so I can send it out right away for publication." Dantzig had no idea what he was talking about. He later learned that the "homework" problems had in fact been two famous unsolved problems in statistics.
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 Linear Programs and Related Problems by : Evar D. Nering
Download or read book Linear Programs and Related Problems written by Evar D. Nering and published by Academic Press. This book was released on 1993 with total page 618 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text is concerned primarily with the theory of linear and nonlinear programming, and a number of closely-related problems, and with algorithms appropriate to those problems. In the first part of the book, the authors introduce the concept of duality which serves as a unifying concept throughout the book. The simplex algorithm is presented along with modifications and adaptations to problems with special structures. Two alternative algorithms, the ellipsoidal algorithm and Karmarker's algorithm, are also discussed, along with numerical considerations. the second part of the book looks at specific types of problems and methods for their solution. This book is designed as a textbook for mathematical programming courses, and each chapter contains numerous exercises and examples.
Book Synopsis Linear Optimization Problems with Inexact Data by : Miroslav Fiedler
Download or read book Linear Optimization Problems with Inexact Data written by Miroslav Fiedler and published by Springer Science & Business Media. This book was released on 2006-07-18 with total page 222 pages. Available in PDF, EPUB and Kindle. Book excerpt: Linear programming has attracted the interest of mathematicians since World War II when the first computers were constructed. Early attempts to apply linear programming methods practical problems failed, in part because of the inexactness of the data used to create the models. This book presents a comprehensive treatment of linear optimization with inexact data, summarizing existing results and presenting new ones within a unifying framework.
Book Synopsis Linear Programming by : Robert J Vanderbei
Download or read book Linear Programming written by Robert J Vanderbei and published by Springer Science & Business Media. This book was released on 2013-07-16 with total page 420 pages. Available in PDF, EPUB and Kindle. Book excerpt: This Fourth Edition introduces the latest theory and applications in optimization. It emphasizes constrained optimization, beginning with a substantial treatment of linear programming and then proceeding to convex analysis, network flows, integer programming, quadratic programming, and convex optimization. Readers will discover a host of practical business applications as well as non-business applications. Topics are clearly developed with many numerical examples worked out in detail. Specific examples and concrete algorithms precede more abstract topics. With its focus on solving practical problems, the book features free C programs to implement the major algorithms covered, including the two-phase simplex method, primal-dual simplex method, path-following interior-point method, and homogeneous self-dual methods. In addition, the author provides online JAVA applets that illustrate various pivot rules and variants of the simplex method, both for linear programming and for network flows. These C programs and JAVA tools can be found on the book's website. The website also includes new online instructional tools and exercises.
Book Synopsis U.S. Government Research Reports by :
Download or read book U.S. Government Research Reports written by and published by . This book was released on 1964 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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 Technical Abstract Bulletin by : Defense Documentation Center (U.S.)
Download or read book Technical Abstract Bulletin written by Defense Documentation Center (U.S.) and published by . This book was released on 1961-07 with total page 1766 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Linear Optimization and Extensions by : Dimitris Alevras
Download or read book Linear Optimization and Extensions written by Dimitris Alevras and published by Springer Science & Business Media. This book was released on 2001-06-11 with total page 466 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers a comprehensive treatment of the exercises and case studies as well as summaries of the chapters of the book "Linear Optimization and Extensions" by Manfred Padberg. It covers the areas of linear programming and the optimization of linear functions over polyhedra in finite dimensional Euclidean vector spaces. Here are the main topics treated in the book: Simplex algorithms and their derivatives including the duality theory of linear programming. Polyhedral theory, pointwise and linear descriptions of polyhedra, double description algorithms, Gaussian elimination with and without division, the complexity of simplex steps. Projective algorithms, the geometry of projective algorithms, Newtonian barrier methods. Ellipsoids algorithms in perfect and in finite precision arithmetic, the equivalence of linear optimization and polyhedral separation. The foundations of mixed-integer programming and combinatorial optimization.
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.
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 Notes on Linear Programming by : George Bernard Dantzig
Download or read book Notes on Linear Programming written by George Bernard Dantzig and published by . This book was released on 1954 with total page 36 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Mathematical Optimization and Economic Theory by : Michael D. Intriligator
Download or read book Mathematical Optimization and Economic Theory written by Michael D. Intriligator and published by SIAM. This book was released on 2002-01-01 with total page 515 pages. Available in PDF, EPUB and Kindle. Book excerpt: A classic account of mathematical programming and control techniques and their applications to static and dynamic problems in economics.
