Degeneracy Graphs And The Neighbourhood Problem

Author : H.-J. Kruse
Publisher : Springer
Page : 132 pages
File Size : 43,6 Mb
Release : 2012-04-27
Category : Business & Economics
ISBN : 3642492711

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Degeneracy Graphs and the Neighbourhood Problem by H.-J. Kruse Pdf

A few years ago nobody would have anticipated that in connection with degeneracy in Linear Programming quite a new field. could originate. In 1976 a very simple question has been posed: in the case an extreme pOint (EP) of a polytope is degenerate and the task is to find all neighbouring EP's of the degenerate EP, is it necessary to determine all basic solutions of the corresponding equalities system associated with the degenerate EP -in order to be certain to determine all neighbours of this EP? This question implied another one: Does there exists a subset of the mentioned set of basic solutions such that it suffices to find such a subset in order to determine all neighbours? The first step to solve these questions (which are motivated in the first Chapter of this book) was to define a graph (called degeneracy graph) the nodes of which correspond to the basic solutions. It turned out that such a graph has some special properties and in order to solve the above questions firstly these properties had to be investigated. Also the structure of degeneracy graphs playes hereby an important role. Because the theory of degeneracy graphs was quite new, it was necessary to elaborate first a completely new terminology and to define new notions. Dr.

Author : Hermann-Josef Kruse
Publisher : Springer
Page : 152 pages
File Size : 52,7 Mb
Release : 1986
Category : Business & Economics
ISBN : UCSD:31822002039386

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Degeneracy Graphs and the Neighbourhood Problem by Hermann-Josef Kruse Pdf

Author : H.-J. Kruse
Publisher : Springer Science & Business Media
Page : 138 pages
File Size : 43,5 Mb
Release : 2012-12-06
Category : Business & Economics
ISBN : 9783642492709

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Degeneracy Graphs and the Neighbourhood Problem by H.-J. Kruse Pdf

A few years ago nobody would have anticipated that in connection with degeneracy in Linear Programming quite a new field. could originate. In 1976 a very simple question has been posed: in the case an extreme pOint (EP) of a polytope is degenerate and the task is to find all neighbouring EP's of the degenerate EP, is it necessary to determine all basic solutions of the corresponding equalities system associated with the degenerate EP -in order to be certain to determine all neighbours of this EP? This question implied another one: Does there exists a subset of the mentioned set of basic solutions such that it suffices to find such a subset in order to determine all neighbours? The first step to solve these questions (which are motivated in the first Chapter of this book) was to define a graph (called degeneracy graph) the nodes of which correspond to the basic solutions. It turned out that such a graph has some special properties and in order to solve the above questions firstly these properties had to be investigated. Also the structure of degeneracy graphs playes hereby an important role. Because the theory of degeneracy graphs was quite new, it was necessary to elaborate first a completely new terminology and to define new notions. Dr.

Author : Hermann-Josef Kruse
Publisher : Unknown
Page : 148 pages
File Size : 51,6 Mb
Release : 1986
Category : Graph theory
ISBN : STANFORD:36105032312642

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Degeneracy Graphs and the Neighbourhood Problem by Hermann-Josef Kruse Pdf

Author : Peter Zörnig
Publisher : Springer Science & Business Media
Page : 211 pages
File Size : 54,5 Mb
Release : 2012-12-06
Category : Business & Economics
ISBN : 9783642457029

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Degeneracy Graphs and Simplex Cycling by Peter Zörnig Pdf

Many problems in economics can be formulated as linearly constrained mathematical optimization problems, where the feasible solution set X represents a convex polyhedral set. In practice, the set X frequently contains degenerate verti- ces, yielding diverse problems in the determination of an optimal solution as well as in postoptimal analysis.The so- called degeneracy graphs represent a useful tool for des- cribing and solving degeneracy problems. The study of dege- neracy graphs opens a new field of research with many theo- retical aspects and practical applications. The present pu- blication pursues two aims. On the one hand the theory of degeneracy graphs is developed generally, which will serve as a basis for further applications. On the other hand dege- neracy graphs will be used to explain simplex cycling, i.e. necessary and sufficient conditions for cycling will be de- rived.

Author : Wolfgang Bühler,Gustav Feichtinger,Richard F. Hartl,Franz Josef Radermacher,Paul Stähly
Publisher : Springer Science & Business Media
Page : 654 pages
File Size : 44,7 Mb
Release : 2012-12-06
Category : Business & Economics
ISBN : 9783642772542

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DGOR by Wolfgang Bühler,Gustav Feichtinger,Richard F. Hartl,Franz Josef Radermacher,Paul Stähly Pdf

The book presents the results of the joint annual conference of the four Operations Research Societies DGOR, GM\OR, \GOR and SVOR, held in Vienna in 1990. The main goal was to present practical experiences as well as theoretical results. Both aspects are covered in a balanced way. Papers cover topics from the fields Optimization, Stochastic Modells, Decision Theory and Multicriteria Decision Making, Control Theory, Mathematical Economics, Game Theory, Macroeconomics, Econometrics and Statistics, Supercomputing and Simulation, Non-linear Systems, Artificial Intelligence and Expert Systems, Fuzzy Sets and Systems, Production, Logistics, Inventory and Marketing among others.

Author : Rabe v. Randow
Publisher : Springer Science & Business Media
Page : 522 pages
File Size : 48,8 Mb
Release : 2012-12-06
Category : Business & Economics
ISBN : 9783642516542

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Integer Programming and Related Areas by Rabe v. Randow Pdf

The fields of integer programming and combinatorial optimization continue to be areas of great vitality, with an ever increasing number of publications and journals appearing. A classified bibliography thus continues to be necessary and useful today, even more so than it did when the project, of which this is the fifth volume, was started in 1970 in the Institut fur Okonometrie und Operations Research of the University of Bonn. The pioneering first volume was compiled by Claus Kastning during the years 1970 - 1975 and appeared in 1976 as Volume 128 of the series Lecture Notes in Economics and Mathematical Systems published by the Springer Verlag. Work on the project was continued by Dirk Hausmann, Reinhardt Euler, and Rabe von Randow, and resulted in the publication of the second, third, and fourth volumes in 1978, 1982, and 1985 (Volumes 160, 197, and 243 of the above series). The present book constitutes the fifth volume of the bibliography and covers the period from autumn 1984 to the end of 1987. It contains 5864 new publications by 4480 authors and was compiled by Rabe von Randow. Its form is practically identical to that of the first four volumes, some additions having been made to the subject list.

Author : Antonio Villar
Publisher : Springer Science & Business Media
Page : 166 pages
File Size : 46,8 Mb
Release : 2012-12-06
Category : Business & Economics
ISBN : 9783642457111

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Operator Theorems with Applications to Distributive Problems and Equilibrium Models by Antonio Villar Pdf

Presentation Many economic problems, as equilibrium models, input-output analysis, rational behaviour, etc. , are usually modelled in terms of operators in Euclidean spaces. This monograph deals with the analysis of a number of formal problems involving this kind of operators (with particular reference to complementarity problems and variational inequalities), and their applications to distributive problems and equilibrium models. Thus the purpose of this work is to provide a set of new results on the solvability of those problems, and a number of economic applications that will illustrate the interest of these results in economics. It is worth stressing from the very begining that our analysis concentrates on the existence (and in some cases optimality) of solutions. That is what is meant here by solvability (in particular, nothing will be said with respect to the uniqueness, stability, sensitivity analysis or computation of solutions). The results on the solvability of operator problems presented here, were actually arrived at as a way of solving specific economic models. Yet we are going to relate this case by somehow reversing the way it happened, that is, starting with the formal results and then presenting a number of economic models which appear as applications of VIII these formal results. The rationale for this approach is twofold. First, it provides a neat track via which to go through the whole work. Then, because I would like to emphasize the interest of complementarity and variational inequalities problems in economic modelling.

Author : Reiner Horst,Hoang Tuy
Publisher : Springer Science & Business Media
Page : 735 pages
File Size : 44,8 Mb
Release : 2013-11-11
Category : Business & Economics
ISBN : 9783662031995

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Global Optimization by Reiner Horst,Hoang Tuy Pdf

The main contents and character of the monograph did not change with respect to the first edition. However, within most chapters we incorporated quite a number of modifications which take into account the recent development of the field, the very valuable suggestions and comments that we received from numerous colleagues and students as well as our own experience while using the book. Some errors and misprints in the first edition are also corrected. Reiner Horst May 1992 Hoang Tuy PREFACE TO THE FIRST EDITION The enormous practical need for solving global optimization problems coupled with a rapidly advancing computer technology has allowed one to consider problems which a few years aga would have been considered computationally intractable. As a consequence, we are seeing the creation of a large and increasing number of diverse algorithms for solving a wide variety of multiextremal global optimization problems. The goal of this book is to systematically clarify and unify these diverse approaches in order to provide insight into the underlying concepts and their pro perties. Aside from a coherent view of the field much new material is presented.

Author : Yoshikazu Sawaragi,Koichi Inoue,Hirotaka Nakayama
Publisher : Springer Science & Business Media
Page : 462 pages
File Size : 50,8 Mb
Release : 2012-12-06
Category : Business & Economics
ISBN : 9783642466076

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Toward Interactive and Intelligent Decision Support Systems by Yoshikazu Sawaragi,Koichi Inoue,Hirotaka Nakayama Pdf

These proceedings include papers presented at the VII-th Internatio nal Conference on Multiple Criteria Decision Making which was held in Kyoto/Japan on August 18-22, 1986. Multiple Criteria Decision Making (MCDM) has been a greatly import ant subject in many practical fields, for example, in planning, design, control and management in both private and public sectors. After remark able developments of theory, methodology and pilot case studies in rec ent years, it is now facing the stage of real applications and develop ment of more sophisticated methodology as interactive intelligent decision support systems. The conference aimed to provide a significant contribu tion to the future of MCDM as one of total systems including human factors: Substantial emphasis was given to knowledge engineering and cognitive sci ence. The conference inherits the tradition and the style of the previous conferences: (1) Jouy-en-Josas/France (1975), (2) Buffalo/U.S.A. (1977), (3) Konigswinter/FRG (1978), (4) Delaware/U.S.A. (1980), (5) Mons/Belgium (1982), (6) Cleveland/U.S.A. (1984). This time a great many Japanese com panies provided grants for the conference. As a result, the total number of participants was over 120, and a computer demonstration could be reali zed on an extensive scale as well as the conference sessions. Throughout the conference, it was observed that MCDM is making steady progress not only in theory but also as a tool for decision support.

Author : Günter Fandel,Hermann Gehring
Publisher : Springer Science & Business Media
Page : 450 pages
File Size : 52,5 Mb
Release : 2012-12-06
Category : Business & Economics
ISBN : 9783642765377

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Operations Research by Günter Fandel,Hermann Gehring Pdf

Tomas Gal zum 65. Geburtstag

Author : Tomas Gal,Theodor Stewart,Thomas Hanne
Publisher : Springer Science & Business Media
Page : 549 pages
File Size : 51,8 Mb
Release : 2013-03-09
Category : Business & Economics
ISBN : 9781461550259

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Multicriteria Decision Making by Tomas Gal,Theodor Stewart,Thomas Hanne Pdf

At a practical level, mathematical programming under multiple objectives has emerged as a powerful tool to assist in the process of searching for decisions which best satisfy a multitude of conflicting objectives, and there are a number of distinct methodologies for multicriteria decision-making problems that exist. These methodologies can be categorized in a variety of ways, such as form of model (e.g. linear, non-linear, stochastic), characteristics of the decision space (e.g. finite or infinite), or solution process (e.g. prior specification of preferences or interactive). Scientists from a variety of disciplines (mathematics, economics and psychology) have contributed to the development of the field of Multicriteria Decision Making (MCDM) (or Multicriteria Decision Analysis (MCDA), Multiattribute Decision Making (MADM), Multiobjective Decision Making (MODM), etc.) over the past 30 years, helping to establish MCDM as an important part of management science. MCDM has become a central component of studies in management science, economics and industrial engineering in many universities worldwide. Multicriteria Decision Making: Advances in MCDM Models, Algorithms, Theory and Applications aims to bring together `state-of-the-art' reviews and the most recent advances by leading experts on the fundamental theories, methodologies and applications of MCDM. This is aimed at graduate students and researchers in mathematics, economics, management and engineering, as well as at practicing management scientists who wish to better understand the principles of this new and fast developing field.

Author : Carsten Jordan
Publisher : Springer Science & Business Media
Page : 191 pages
File Size : 54,8 Mb
Release : 2012-12-06
Category : Business & Economics
ISBN : 9783642484032

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Batching and Scheduling by Carsten Jordan Pdf

In some manufacturing systems significant setups are required to change production from one type of products to another. The setups render the manufacturing system inflexible as for reacting to changes in demand patterns, hence inventories must be maintained to guarantee an acceptable customer service. In this environment, production scheduling faces a number of problems, and this work deals with mathematical models to support the scheduling decisions. Some more background and motivation is given in the following sections, as well as in a case description in Section 1. 3. The synopsis in Section 1. 4 outlines the topics of the work. 1. 1 Motivation of the Planning Problem Consider the production of metal sheets in a rolling mill. If the width of the next type of sheets is greater than the width of the preceding type, then the roll needs a setup: during the rolling process the edges of a sheet cause grooves on the rolls' surface, thus, the surface must be polished if a greater width is run next. Sheets with a smaller width can be run directly, without a setup. Another example in which setups are sequence dependent is a line where cars are sprayed: if the color of the paint changes, the cleaning of the tools requires a setup depending on the sequence of the colors. Only a small setup may be needed for changing from a light to a dark color, but a thorough cleaning of the tools is 2 CHAPTER 1.

Author : Günter Fandel,Manfred Grauer,Alexander Kurzhanski,Andrzej P. Wierzbicki
Publisher : Springer Science & Business Media
Page : 374 pages
File Size : 53,8 Mb
Release : 2013-06-29
Category : Business & Economics
ISBN : 9783662024737

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Large-Scale Modelling and Interactive Decision Analysis by Günter Fandel,Manfred Grauer,Alexander Kurzhanski,Andrzej P. Wierzbicki Pdf

These Proceedings report the scientific results of an International Workshop on Large-Scale Modelling and Interactive Decision Analysis organized Jointly by the System and Decision Sciences Program of the International Institute for Applied Systems Analysis (IIASA, located in Laxenburg, Austria), and the Institute for Informatics of the Academy of Sciences of the GDR (located in Berlin, GDR). The Workshop was held at a historically well-known place - the Wartburg Castl- near Eisenach (GDR). (Here Martin Luther translated the Bible into German.) More than fifty scientists representing thirteen countries participated. This Workshop is one of a series of meetings organizE!d by or In collaboration with IIASA about which two of the Lecture Notes In Economics and Mathematical Systems have already reported (Voi. 229 and Vol. 246). This time the aim of the meeting was to discuss methodological and practical problems associated with the modelling of large-scale systems and new approaches In interactive decision analysis based on advanced information processing systems.

Author : Roland Durier,Christian Michelot
Publisher : Springer Science & Business Media
Page : 369 pages
File Size : 42,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783642468230

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Recent Developments in Optimization by Roland Durier,Christian Michelot Pdf

The main objective of this volume is to provide a presentation and discussion of recent developments in optimization and related fields. Equal emphasis is given to theoretical and practical studies. All the papers in this volume contain original results except two of them which are survey contributions. They deal with a wide range of topics such as optimization and variational inequalities, sensitivity and stability analysis, control theory, convex and nonsmooth analysis, and numerical methods.