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During the Spring of 1979 one of us (Zionts) was invited to visit Erasmus University in Rotterdam, The Netherlands. It was there that Zionts met another of us (Telgen) who was then in the process of completing a dissertation on redundancy in linear programming. At that time, Telgen proposed an extended visit to Buffalo, during which time he and Zionts would do an extensive study on redundancy. Redundancy, hardly an exciting or new topic, does have numerous applications. Telgen and Zionts planned the project for the Summer of 1980, and enlisted the support of all the contributors as well as the other two members of our team (Karwan and Lotfi). Lotfi was then a Ph. D. student in Industrial Engineering searching for a thesis topic. Redundancy became his topic. Karwan and Zionts served as his thesis co-chairmen, with Telgen serving as an outside reader of the thesis. We initially had hoped to complete the study during Telgen's stay in Buffalo, but that was far too optimistic. Lotfi completed his dissertation during the late Spring-early Summer of 1981. As the project took shape, we decided that we had more than enough for an article, or even several articles. Accordingly, not wanting to produce redundant papers, we decided to produce this volume --- a state-of-the-art review of methods for handling redundancy and comprehensive tests of the various methods, together with extensions and further developments of the most promising methods.
Inequalities; Equalities; Implicit equalitites; Minimal representation; Existing theory; Implicit equalities; Redundant constraints; Minimal representation; Existing methods; Results from literature; Experimental results; Nonbinding constraints; Primal-dual relations; The simplex method; The complexity of linear programming; LP-equivalent problems; The ellipsoidal method.
With contributions by numerous experts
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.
Flexible graduate textbook that introduces the applications, theory, and algorithms of linear and nonlinear optimization in a clear succinct style, supported by numerous examples and exercises. It introduces important realistic applications and explains how optimization can address them.
This book discusses convex analysis, the basic underlying structure of argumentation in economic theory. Convex analysis is also common to the optimization of problems encountered in many applications. The text is aimed at senior undergraduate students, graduate students, and specialists of mathematical programming who are undertaking research into applied mathematics and economics. The text consists of a systematic development in eight chapters, and contains exercises. The book is appropriate as a class text or for self-study.
/homepage/sac/cam/na2000/index.html7-Volume Set now available at special set price ! In one of the papers in this collection, the remark that "nothing at all takes place in the universe in which some rule of maximum of minimum does not appear" is attributed to no less an authority than Euler. Simplifying the syntax a little, we might paraphrase this as Everything is an optimization problem. While this might be something of an overstatement, the element of exaggeration is certainly reduced if we consider the extended form: Everything is an optimization problem or a system of equations. This observation, even if only partly true, stands as a fitting testimonial to the importance of the work covered by this volume. Since the 1960s, much effort has gone into the development and application of numerical algorithms for solving problems in the two areas of optimization and systems of equations. As a result, many different ideas have been proposed for dealing efficiently with (for example) severe nonlinearities and/or very large numbers of variables. Libraries of powerful software now embody the most successful of these ideas, and one objective of this volume is to assist potential users in choosing appropriate software for the problems they need to solve. More generally, however, these collected review articles are intended to provide both researchers and practitioners with snapshots of the 'state-of-the-art' with regard to algorithms for particular classes of problem. These snapshots are meant to have the virtues of immediacy through the inclusion of very recent ideas, but they also have sufficient depth of field to show how ideas have developed and how today's research questions have grown out of previous solution attempts. The most efficient methods for local optimization, both unconstrained and constrained, are still derived from the classical Newton approach. As well as dealing in depth with the various classical, or neo-classical, approaches, the selection of papers on optimization in this volume ensures that newer ideas are also well represented. Solving nonlinear algebraic systems of equations is closely related to optimization. The two are not completely equivalent, however, and usually something is lost in the translation. Algorithms for nonlinear equations can be roughly classified as locally convergent or globally convergent. The characterization is not perfect. Locally convergent algorithms include Newton's method, modern quasi-Newton variants of Newton's method, and trust region methods. All of these approaches are well represented in this volume.
Understand common scheduling as well as other advanced operational problems with this valuable reference from a recognized leader in the field. Beginning with basic principles and an overview of linear and mixed-integer programming, this unified treatment introduces the fundamental ideas underpinning most modeling approaches, and will allow you to easily develop your own models. With more than 150 figures, the basic concepts and ideas behind the development of different approaches are clearly illustrated. Addresses a wide range of problems arising in diverse industrial sectors, from oil and gas to fine chemicals, and from commodity chemicals to food manufacturing. A perfect resource for engineering and computer science students, researchers working in the area, and industrial practitioners.
The book covers clear and crisp pedagogy in the field of decision making process, which pervades the activities of every business manager. Modest attempt has been made to discuss some of the commonly used quantitative techniques in a wide spectrum of decision-making situations. It presents the application of various techniques through a large number of examples and review illustrations. A number of problems from various examinations have also been incorporated. Simplicity in explaining complex phenomena and lucidity in style are the twin objectives of the authors' in organizing the chapters of the book so that students of Civil, Production, Mechanical, Electrical and Electronics Engineering, Commerce,Management, CA and ICWA can derive maximum benefit.