A Maxmin Location Problem

Dasarathy, B.; White, Lee

doi:10.1287/opre.28.6.1385

Cited by 75 publications

(37 citation statements)

References 14 publications

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“…First attempts to solve location problems with such undesirable facilities appeared in the 1970's [4,6,17]. Algorithms based on a DC formulation are presented for instance in [3,9,31,40].…”

Section: Application and Numerical Resultsmentioning

confidence: 99%

Solving DC programs with a polyhedral component utilizing a multiple objective linear programming solver

Löhne¹,

Wagner²

2017

J Glob Optim

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A class of non-convex optimization problems with DC objective function is studied, where DC stands for being representable as the difference f = g − h of two convex functions g and h. In particular, we deal with the special case where one of the two convex functions g or h is polyhedral. In case g is polyhedral, we show that a solution of the DC program can be obtained from a solution of an associated polyhedral projection problem. In case h is polyhedral, we prove that a solution of the DC program can be obtained by solving a polyhedral projection problem and finitely many convex programs. Since polyhedral projection is equivalent to multiple objective linear programming (MOLP), a MOLP solver (in the second case together with a convex programming solver) can be used to solve instances of DC programs with polyhedral component. Numerical examples are provided, among them an application to locational analysis.

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“…First attempts to solve location problems with such undesirable facilities appeared in the 1970's [4,6,17]. Algorithms based on a DC formulation are presented for instance in [3,9,31,40].…”

Section: Application and Numerical Resultsmentioning

confidence: 99%

Solving DC programs with a polyhedral component utilizing a multiple objective linear programming solver

Löhne¹,

Wagner²

2017

J Glob Optim

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“…If appropriate probabilistic assumptions about underlying error distributions are made, least squares produces what is known as the maximum-likelihood estimate parameters. Even if the probabilistic assumptions are not satisfied, research in this areas has shown that least squares produces useful results [1,2,5,6,7,8,9,10,11,14,15,19,21,22,23,24,25,26] A very common source of least squares is curve fitting. Let x be the independent variable and let y  x denote an unknown function of x that we want to approximate.…”

Section: Optimal Designmentioning

confidence: 99%

“…There are numerous publications where facility location problems have been discussed [4,5,8,9,10,13,14,15,17,19,20,21,22,23].The problem has given rise to extraordinary number of generalizations, extensions and modifications. It would literally require volumes to do them justice; space only permits only a brief and somewhat arbitrarily selected summary.…”

Section: Location Theorymentioning

confidence: 99%

A Note on Convex Programming in Practical Problems

Osinuga

Agunbiade

2013

BSMaSS

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Abstract. In recent years, convex programming has become a sophisticated tool of central importance in engineering, finance, operations research, statistics etc. The goal of this paper is to emphasize modeling and present several convex programming problem formulations especially in optimal design and location theory. We build simple models to address this question, investigate their properties and apply a variant of the Weierstrass theorem to prove the existence of a solution. Our results extend and improve some other comparable results of the author [2,8,20,21,22,23,24,25].

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“…The solution is found by constructing the Voronoi diagram for the set of points. The first papers on the maximin location problem were published five years later by Dasarathy and White (1980) and .Building on their earlier work on pattern recognition, Dasarathy and White (1980) first formulated and solved the maximin problem with Euclidean distances for a feasible region, which is a convex polyhedron in k-dimensional space. They delineated their general algorithm for a 3-dimensional space.…”

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confidence: 99%

“…Although there were no apparent customers, the optimization approach-similar to the geometrical approach of Shamos and Hoey (1975)-suggests that the customers constitute an infinite set represented by the boundaries of the protected areas. The solution amounts to finding the largest (empty) circle that contains no points of the protected areas yet whose center is in S.Melachrinoudis and Smith (1995) extended the Voronoi method of Dasarathy and White (1980) and developed an O( mn 2 ) algorithm for the weighted maximin problem. For two points a k , a ℓ having weights w k , w ℓ such that w k > w ℓ , the loci of weighted equidistant points is the Apollonius circle.…”

mentioning

confidence: 99%

Hub Location Problems: The Location of Interacting Facilities

Kara

Taner

2011

International Series in Operations Research &Amp; Management Science

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), except for brief excerpts in connection with reviews or scholarly analysis. Use in connection with any form of information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed is forbidden. The use in this publication of trade names, trademarks, service marks, and similar terms, even if they are not identified as such, is not to be taken as an expression of opinion as to whether or not they are subject to proprietary rights. PrefaceThis book is the final result of a number of incidents that occurred to us while discussing location issues with colleagues at conferences. Frequently we attended presentations, in which the authors quoted the well-known references that helped to make the discipline what it is today. Upon further inquiry, though, it turned out that some of these colleagues had never actually read the original papers. We then discussed among ourselves which contributions could be credited with shaping the field. And, lo and behold, we found that we, too, had neglected to read some of the papers that form the foundation of our science. Whether it was laziness or other things that got in the way, it had become clear that something had to be done. Our first thought was to collect the original contributions (once we could agree on what they were) and reprint them. When discussing this possibility with a publisher, we immediately ran into a roadblock in the form of copyright. While this appeared to have stopped our enthusiastic effort dead in its tracks, we kept on collecting and reading what we considered original contributions.This went on until we met Camille Price, who suggested that, rather than reprinting the original contributions, we should invite some of the leaders in our field and ask them to describe the original contribution, explain and interpret it, and comment on the impact that it had to the field. This was, of course, an excellent idea, and the response by our colleagues to our pertinent requests was equally enthusiastic. What you hold in your hands is the result of this effort.In other words, the purpose of this book is to provide easy access to the main contributions to location theory. The book is organized as follows. The introductory chapter provides an overview of some of the many facets of location analysis. This is followed by contributions in the main three fields of inquiry: minisum, minimax, and covering problems. The next chapters are part of an ever-growing list of nonstandard location models: models including competitive components, those that locate undesirable facilities, those with probabilistic features, and those that allow interactions between facilities. The following chapters discuss solution techniques: after a discussion of exact and heuristic techniques, we devote an entire chapter to Weiszfeld's method, and another to Lagrangean techniques. The last chapters of this book deal with the spheres of influence that the facilities generate and that attract viii customers to them, an...

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A Maxmin Location Problem

Cited by 75 publications

References 14 publications

Solving DC programs with a polyhedral component utilizing a multiple objective linear programming solver

Solving DC programs with a polyhedral component utilizing a multiple objective linear programming solver

A Note on Convex Programming in Practical Problems

Hub Location Problems: The Location of Interacting Facilities

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