Computational Techniques of the Simplex Method

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Author: István Maros

Publisher: Springer Science & Business Media

ISBN: 1461502578

Category: Mathematics

Page: 325

View: 8712

Computational Techniques of the Simplex Method is a systematic treatment focused on the computational issues of the simplex method. It provides a comprehensive coverage of the most important and successful algorithmic and implementation techniques of the simplex method. It is a unique source of essential, never discussed details of algorithmic elements and their implementation. On the basis of the book the reader will be able to create a highly advanced implementation of the simplex method which, in turn, can be used directly or as a building block in other solution algorithms.

Soft Computing for Complex Multiple Criteria Decision Making

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Author: Ignacy Kaliszewski

Publisher: Springer Science & Business Media

ISBN: 0387301771

Category: Business & Economics

Page: 172

View: 2908

This book concentrates on providing technical tools to make the user of Multiple Criteria Decision Making (MCDM) methodologies independent of bulky optimization computations. These bulky computations have been a necessary, but limiting, characteristic of interactive MCDM methodologies and algorithms. The book removes these limitations of MCDM problems by reducing a problem's computational complexity. The result is a wider and more functional general framework for presenting, teaching, implementing and applying a wide range of MCDM methodologies.

Markov Chains: Models, Algorithms and Applications

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Author: Wai-Ki Ching,Michael K. Ng

Publisher: Springer Science & Business Media

ISBN: 038729337X

Category: Mathematics

Page: 208

View: 3759

Markov chains are a particularly powerful and widely used tool for analyzing a variety of stochastic (probabilistic) systems over time. This monograph will present a series of Markov models, starting from the basic models and then building up to higher-order models. Included in the higher-order discussions are multivariate models, higher-order multivariate models, and higher-order hidden models. In each case, the focus is on the important kinds of applications that can be made with the class of models being considered in the current chapter. Special attention is given to numerical algorithms that can efficiently solve the models. Therefore, Markov Chains: Models, Algorithms and Applications outlines recent developments of Markov chain models for modeling queueing sequences, Internet, re-manufacturing systems, reverse logistics, inventory systems, bio-informatics, DNA sequences, genetic networks, data mining, and many other practical systems.

The Theory and Practice of Revenue Management

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Author: Kalyan T. Talluri,Garrett Van Ryzin,Garrett J. Ryzin

Publisher: Springer Science & Business Media

ISBN: 1402079338

Category: Business & Economics

Page: 712

View: 4015

The Theory and Practice of Revenue Management is a book that comprehensively covers theory and practice of the entire field, including quantity and price-based RM, as well as significant coverage of supporting topics such as forecasting and economics. The authors believe such a comprehensive approach is necessary to fully understand the subject. A central objective of the book is to unify the various forms of RM and to link them closely to each other and to the supporting fields of statistics and economics. Nevertheless, the topics and coverage do reflect choices about what is important to understand RM. Hence, the book's purpose is to provide a comprehensive, accessible synthesis of the state-of-the-art in Revenue Management.

Tutorials on Emerging Methodologies and Applications in Operations Research

Presented at INFORMS 2004, Denver, CO

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Author: Harvey J. Greenberg

Publisher: Springer Science & Business Media

ISBN: 0387228276

Category: Business & Economics

Page: 342

View: 919

This volume reflects the theme of the INFORMS 2004 Meeting in Denver: Back to OR Roots. Emerging as a quantitative approach to problem-solving in World War II, our founders were physicists, mathematicians, and engineers who quickly found peace-time uses. It is fair to say that Operations Research (OR) was born in the same incubator as computer science, and it has spawned many new disciplines, such as systems engineering, health care management, and transportation science. Although people from many disciplines routinely use OR methods, many scientific researchers, engineers, and others do not understand basic OR tools and how they can help them. Disciplines ranging from finance to bioengineering are the beneficiaries of what we do — we take an interdisciplinary approach to problem-solving. Our strengths are modeling, analysis, and algorithm design. We provide a quanti- tive foundation for a broad spectrum of problems, from economics to medicine, from environmental control to sports, from e-commerce to computational - ometry. We are both producers and consumers because the mainstream of OR is in the interfaces. As part of this effort to recognize and extend OR roots in future probl- solving, we organized a set of tutorials designed for people who heard of the topic and want to decide whether to learn it. The 90 minutes was spent addre- ing the questions: What is this about, in a nutshell? Why is it important? Where can I learn more? In total, we had 14 tutorials, and eight of them are published here.

Linear and Multiobjective Programming with Fuzzy Stochastic Extensions

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Author: Masatoshi Sakawa,Hitoshi Yano,Ichiro Nishizaki

Publisher: Springer Science & Business Media

ISBN: 1461493994

Category: Business & Economics

Page: 339

View: 3371

Although several books or monographs on multiobjective optimization under uncertainty have been published, there seems to be no book which starts with an introductory chapter of linear programming and is designed to incorporate both fuzziness and randomness into multiobjective programming in a unified way. In this book, five major topics, linear programming, multiobjective programming, fuzzy programming, stochastic programming, and fuzzy stochastic programming, are presented in a comprehensive manner. Especially, the last four topics together comprise the main characteristics of this book, and special stress is placed on interactive decision making aspects of multiobjective programming for human-centered systems in most realistic situations under fuzziness and/or randomness. Organization of each chapter is briefly summarized as follows: Chapter 2 is a concise and condensed description of the theory of linear programming and its algorithms. Chapter 3 discusses fundamental notions and methods of multiobjective linear programming and concludes with interactive multiobjective linear programming. In Chapter 4, starting with clear explanations of fuzzy linear programming and fuzzy multiobjective linear programming, interactive fuzzy multiobjective linear programming is presented. Chapter 5 gives detailed explanations of fundamental notions and methods of stochastic programming including two-stage programming and chance constrained programming. Chapter 6 develops several interactive fuzzy programming approaches to multiobjective stochastic programming problems. Applications to purchase and transportation planning for food retailing are considered in Chapter 7. The book is self-contained because of the three appendices and answers to problems. Appendix A contains a brief summary of the topics from linear algebra. Pertinent results from nonlinear programming are summarized in Appendix B. Appendix C is a clear explanation of the Excel Solver, one of the easiest ways to solve optimization problems, through the use of simple examples of linear and nonlinear programming.

Optimization for Decision Making

Linear and Quadratic Models

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Author: Katta G. Murty

Publisher: Springer Science & Business Media

ISBN: 9781441912916

Category: Mathematics

Page: 482

View: 9605

Linear programming (LP), modeling, and optimization are very much the fundamentals of OR, and no academic program is complete without them. No matter how highly developed one’s LP skills are, however, if a fine appreciation for modeling isn’t developed to make the best use of those skills, then the truly ‘best solutions’ are often not realized, and efforts go wasted. Katta Murty studied LP with George Dantzig, the father of linear programming, and has written the graduate-level solution to that problem. While maintaining the rigorous LP instruction required, Murty's new book is unique in his focus on developing modeling skills to support valid decision making for complex real world problems. He describes the approach as 'intelligent modeling and decision making' to emphasize the importance of employing the best expression of actual problems and then applying the most computationally effective and efficient solution technique for that model.

Integrated Methods for Optimization

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Author: John Hooker

Publisher: Springer Science & Business Media

ISBN: 9780387382722

Category: Computers

Page: 486

View: 2603

This book integrates the key concepts of mathematical programming and constraint programming into a unified framework that allows them to be generalized and combined. It provides a powerful, high-level modeling solution for optimization problems.

The Management of Uncertainty: Approaches, Methods and Applications

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Author: Luc Wilkin,A. Sutton

Publisher: Springer Science & Business Media

ISBN: 9400944586

Category: Business & Economics

Page: 285

View: 6641

For thirty years, the literature on decision-making and planning has been divided into two camps : work premised on rational models of choice and work designed to discredit such models. The sustained critic of fully rational decision-making theories has al ready a long history and a constant message to deliver : in practice, consequential decision-making hardly fulfills the canons of perfect rationality. There is also evidence that decision-making and planning are not unitary processes. Although the concept of "decision-making" connotes the idea of a single process, making a single choice involves a complex of processing tasks : structuring the problem, finding alternatives worth considering, deciding what information is relevant, assessing various consequences, and a variety of others. The aim of this volume is to bring together and try to inter relate some of the concepts and relevant knowledge from various disciplines concerned with one important aspect of this complex process : the management of uncertainty. It is hardly necessary to reiterate the case made by numerous authors about our changing and increasingly uncertain world. Suffice it to say here that it is uncertainty about the future, and in many cases about the past and the present also, which makes decision-making and planning so difficul t. The management of uncertainty may be defined as the way in which uncertainty is treated and processed in decision-making.

Linear and Nonlinear Optimization

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Author: Richard W. Cottle,Mukund N. Thapa

Publisher: Springer

ISBN: 1493970550

Category: Business & Economics

Page: 614

View: 3940

​This textbook on Linear and Nonlinear Optimization is intended for graduate and advanced undergraduate students in operations research and related fields. It is both literate and mathematically strong, yet requires no prior course in optimization. As suggested by its title, the book is divided into two parts covering in their individual chapters LP Models and Applications; Linear Equations and Inequalities; The Simplex Algorithm; Simplex Algorithm Continued; Duality and the Dual Simplex Algorithm; Postoptimality Analyses; Computational Considerations; Nonlinear (NLP) Models and Applications; Unconstrained Optimization; Descent Methods; Optimality Conditions; Problems with Linear Constraints; Problems with Nonlinear Constraints; Interior-Point Methods; and an Appendix covering Mathematical Concepts. Each chapter ends with a set of exercises. The book is based on lecture notes the authors have used in numerous optimization courses the authors have taught at Stanford University. It emphasizes modeling and numerical algorithms for optimization with continuous (not integer) variables. The discussion presents the underlying theory without always focusing on formal mathematical proofs (which can be found in cited references). Another feature of this book is its inclusion of cultural and historical matters, most often appearing among the footnotes. "This book is a real gem. The authors do a masterful job of rigorously presenting all of the relevant theory clearly and concisely while managing to avoid unnecessary tedious mathematical details. This is an ideal book for teaching a one or two semester masters-level course in optimization – it broadly covers linear and nonlinear programming effectively balancing modeling, algorithmic theory, computation, implementation, illuminating historical facts, and numerous interesting examples and exercises. Due to the clarity of the exposition, this book also serves as a valuable reference for self-study." Professor Ilan Adler, IEOR Department, UC Berkeley "A carefully crafted introduction to the main elements and applications of mathematical optimization. This volume presents the essential concepts of linear and nonlinear programming in an accessible format filled with anecdotes, examples, and exercises that bring the topic to life. The authors plumb their decades of experience in optimization to provide an enriching layer of historical context. Suitable for advanced undergraduates and masters students in management science, operations research, and related fields." Michael P. Friedlander, IBM Professor of Computer Science, Professor of Mathematics, University of British Columbia

Operations Research

Einführung

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Author: Frederick S. Hillier,Gerald J. Liebermann

Publisher: Walter de Gruyter GmbH & Co KG

ISBN: 3486792083

Category: Business & Economics

Page: 868

View: 2254

Aus dem Vorwort der Autoren: “ bereits in früheren Auflagen sind uns auch bei dieser Auflage der Motivationscharakter und die Einfachheit der Ausführungen wichtiger als exakte Beweise und technische Freiheiten. Wir glauben, dass die vorliegende Auflage für den praxisorientierten Studenten, auch ohne große mathematische Kenntnisse, attraktiver und besser lesbar geworden ist. Dennoch sind wir der Meinung, dass die Theorie der Operations Research nur von der mathematischen Seite her wirklich verstanden und gewürdigt werden kann. Es ist daher auch die fünfte Auflage nach wie vor an den gleichen Leserkreis wie die früheren Auflagen gerichtet, an die Studenten verschiedenster Fachrichtungen (Ingenieurswesen, Wirtschafts- und Sozialwissenschaften sowie mathematische Wissenschaften), die sich manchmal angesichts des riesigen Wortschwalls ihrer Studiengebiete nach einem bißchen mathematischer Klarheit sehnen. Die einzelnen Kapitel lassen sich auf vielfältige Art und Weise zu Kursen oder zum Selbststudium zusammenstellen, da das Buch sehr flexibel angelegt ist. Teil eins liefert eine Einführung in die Thematik des Operations Research. Teil zwei (über lineare Programmierung) und auch Teil drei (über mathematische Programmierung) lassen sich unabhängig von Teil vier (über stochastische Modelle) durcharbeiten.“

Stochastic Linear Programming

Models, Theory, and Computation

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Author: Peter Kall,János Mayer

Publisher: Springer Science & Business Media

ISBN: 9781441977298

Category: Mathematics

Page: 426

View: 6774

This new edition of Stochastic Linear Programming: Models, Theory and Computation has been brought completely up to date, either dealing with or at least referring to new material on models and methods, including DEA with stochastic outputs modeled via constraints on special risk functions (generalizing chance constraints, ICC’s and CVaR constraints), material on Sharpe-ratio, and Asset Liability Management models involving CVaR in a multi-stage setup. To facilitate use as a text, exercises are included throughout the book, and web access is provided to a student version of the authors’ SLP-IOR software. Additionally, the authors have updated the Guide to Available Software, and they have included newer algorithms and modeling systems for SLP. The book is thus suitable as a text for advanced courses in stochastic optimization, and as a reference to the field. From Reviews of the First Edition: "The book presents a comprehensive study of stochastic linear optimization problems and their applications. ... The presentation includes geometric interpretation, linear programming duality, and the simplex method in its primal and dual forms. ... The authors have made an effort to collect ... the most useful recent ideas and algorithms in this area. ... A guide to the existing software is included as well." (Darinka Dentcheva, Mathematical Reviews, Issue 2006 c) "This is a graduate text in optimisation whose main emphasis is in stochastic programming. The book is clearly written. ... This is a good book for providing mathematicians, economists and engineers with an almost complete start up information for working in the field. I heartily welcome its publication. ... It is evident that this book will constitute an obligatory reference source for the specialists of the field." (Carlos Narciso Bouza Herrera, Zentralblatt MATH, Vol. 1104 (6), 2007)

Linear and Nonlinear Programming

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Author: David G. Luenberger,Yinyu Ye

Publisher: Springer Science & Business Media

ISBN: 0387745025

Category: Business & Economics

Page: 546

View: 4595

This third edition of the classic textbook in Optimization has been fully revised and updated. It comprehensively covers modern theoretical insights in this crucial computing area, and will be required reading for analysts and operations researchers in a variety of fields. The book connects the purely analytical character of an optimization problem, and the behavior of algorithms used to solve it. Now, the third edition has been completely updated with recent Optimization Methods. The book also has a new co-author, Yinyu Ye of California’s Stanford University, who has written lots of extra material including some on Interior Point Methods.

Linear Programming and Generalizations

A Problem-based Introduction with Spreadsheets

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Author: Eric V. Denardo

Publisher: Springer Science & Business Media

ISBN: 9781441964915

Category: Business & Economics

Page: 673

View: 5356

This book on constrained optimization is novel in that it fuses these themes: • use examples to introduce general ideas; • engage the student in spreadsheet computation; • survey the uses of constrained optimization;. • investigate game theory and nonlinear optimization, • link the subject to economic reasoning, and • present the requisite mathematics. Blending these themes makes constrained optimization more accessible and more valuable. It stimulates the student’s interest, quickens the learning process, reveals connections to several academic and professional fields, and deepens the student’s grasp of the relevant mathematics. The book is designed for use in courses that focus on the applications of constrained optimization, in courses that emphasize the theory, and in courses that link the subject to economics.

Potential Function Methods for Approximately Solving Linear Programming Problems: Theory and Practice

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Author: Daniel Bienstock

Publisher: Springer Science & Business Media

ISBN: 0306476266

Category: Mathematics

Page: 111

View: 4775

Potential Function Methods For Approximately Solving Linear Programming Problems breaks new ground in linear programming theory. The book draws on the research developments in three broad areas: linear and integer programming, numerical analysis, and the computational architectures which enable speedy, high-level algorithm design. During the last ten years, a new body of research within the field of optimization research has emerged, which seeks to develop good approximation algorithms for classes of linear programming problems. This work both has roots in fundamental areas of mathematical programming and is also framed in the context of the modern theory of algorithms. The result of this work, in which Daniel Bienstock has been very much involved, has been a family of algorithms with solid theoretical foundations and with growing experimental success. This book will examine these algorithms, starting with some of the very earliest examples, and through the latest theoretical and computational developments.

Large Scale Linear and Integer Optimization: A Unified Approach

A Unified Approach

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Author: Richard Kipp Martin

Publisher: Springer Science & Business Media

ISBN: 9780792382027

Category: Business & Economics

Page: 740

View: 8704

There is a growing need in major industries such as airline, trucking, financial engineering, etc. to solve very large linear and integer linear optimization problems. Because of the dramatic increase in computing power, it is now possible to solve these problems. Along with the increase in computer power, the mathematical programming community has developed better and more powerful algorithms to solve very large problems. These algorithms are of interest to many researchers in the areas of operations research/management science, computer science, and engineering. In this book, Kipp Martin has systematically provided users with a unified treatment of the algorithms and the implementation of the algorithms that are important in solving large problems. Parts I and II of Large Scale Linear and Integer Programming provide an introduction to linear optimization using two simple but unifying ideas-projection and inverse projection. The ideas of projection and inverse projection are also extended to integer linear optimization. With the projection-inverse projection approach, theoretical results in integer linear optimization become much more analogous to their linear optimization counterparts. Hence, with an understanding of these two concepts, the reader is equipped to understand fundamental theorems in an intuitive way. Part III presents the most important algorithms that are used in commercial software for solving real-world problems. Part IV shows how to take advantage of the special structure in very large scale applications through decomposition. Part V describes how to take advantage of special structureby modifying and enhancing the algorithms developed in Part III. This section contains a discussion of the current research in linear and integer linear programming. The author also shows in Part V how to take different problem formulations and appropriately `modify' them so that the algorithms from Part III are more efficient. Again, the projection and inverse projection concepts are used in Part V to present the current research in linear and integer linear optimization in a very unified way. While the book is written for a mathematically mature audience, no prior knowledge of linear or integer linear optimization is assumed. The audience is upper-level undergraduate students and graduate students in computer science, applied mathematics, industrial engineering and operations research/management science. Course work in linear algebra and analysis is sufficient background.

Theory of linear and integer programming

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Author: A. Schrijver

Publisher: John Wiley & Sons Inc

ISBN: N.A

Category: Mathematics

Page: 471

View: 6463

Introduction and preliminaries; Problems, algorithms, and complexity. Linear algebra; Linear algebra and complexity; Notes on linear algebra; Lattices and linear diophantine equations; Theory of lattices and linear diophantine equations; Algorithms for linear diophantine equations; Diophantine approximations and basis reduction; Notes on lattices and linear diophantine equations; Polyhedra, linear inequalities, and linear programming; Fundamental concepts and results on polyhedra, linear inequalities, and linear programming; The structure of polyhedra; Polarity, and blocking and anti-blocking polyhedra; Sizes and the theoretical complexity of linear inequalities and linear programming; The simplex method; Primal-dual, elimination, and relaxation methods; Khachiyan's method for linear programming; The ellipsoid method for polyhedra more generally; Further polynomiality results in linear programming; Notes on polyhedra, linear inequalities, and linear programming; Integer linear programming; Introduction to integer linear programming; Estimates in integer linear programming; The complexity of integer linear programming; Totally unimodular matrices: fundamental properties and examples; Recognizing total unimodularity; Further theory related to total unimodularity; Integral polyhedra and total dual integrality; Cutting planes; Further methods in integer linear programming; Historical and further notes on integer linear programming; References.

Management Science

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Author: N.A

Publisher: N.A

ISBN: N.A

Category: Industrial management

Page: N.A

View: 8187

Includes special issues: The Professional series in the management sciences.