Optimal location of a single facility with circular demand areas

Chen, R.

doi:10.1016/s0898-1221(00)00339-4

Cited by 13 publications

(19 citation statements)

References 9 publications

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“…It is easy to see that formulation (18) has O(n 2 + d) variables and O(n 2 ) constraints whereas the new one written in similar terms as presented in (13) has O(n + d) variables and O(n 2 ) constraints.…”

Section: A Compact Representation Of the Convex Ordered Median Problemmentioning

confidence: 99%

“…Since then, we can find in the literature many references concerning this algorithm, as for instance the generalization to ℓ p distances with p ∈ [1,2] [38] or the analysis of its local and global convergence [4,5,6,10]. Also, these results were extended to more general problems: on Banach spaces [23,43,44], on the sphere [53], with regional demand [13,49], with sets as demand facilities and using closest Euclidean distances [7] or with radial distances [14,15,16,31,39]. In addition, one can find in the literature papers where the convergence is accelerated using alternative step sizes [17,18,25,30,42] or some related properties concerning the termination of the algorithm in any of the demand points after a finite number of iterations [6,9,8,11,12,29].…”

Section: Introductionmentioning

confidence: 99%

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Revisiting several problems and algorithms in continuous location with $$\ell _\tau $$ ℓ τ norms

2014

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This paper addresses the general continuous single facility location problems in finite dimension spaces under possibly different ℓ p norms in the demand points. We analyze the difficulty of this family of problems and revisit convergence properties of some well-known algorithms. The ultimate goal is to provide a common approach to solve the family of continuous ℓ p ordered median location problems in dimension d (including of course the ℓ p minisum or Fermat-Weber location problem for any p ≥ 1). We prove that this approach has a polynomial worse case complexity for monotone lambda weights and can be also applied to constrained and even non-convex problems.

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Section: A Compact Representation Of the Convex Ordered Median Problemmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Revisiting several problems and algorithms in continuous location with $$\ell _\tau $$ ℓ τ norms

2014

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“…Weiszfeld's scheme has also successfully been adapted to situations with area demand, in which the objective function involves an integral instead of a sum, see and Chen (2001).…”

Section: Other Single Facility Location Problemsmentioning

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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“…Another group of approaches solve a double integral representing continuous demand directly using numerical procedures. Drezner and Wesolowsky (1980), Drezner and Drezner (1997), Wang et al (1997), Chen (2001) and Franco et al (2008) extended the Weiszfeld algorithm given the differentiability of the objective function associated with continuous demand. Fekete et al (2005) proposed an exact algorithm relying on computational geometry for rectilinear distances.…”

Section: Introductionmentioning

confidence: 99%

Serving regional demand in facility location

Yao

Murray

2014

Papers in Regional Science

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Location modelling is employed in urban and regional planning to site facilities that provide services of some sort. Issues to be considered usually include the number of facilities to locate, where to site those facilities and how demand is to be served. Given the geographic nature of location problems, a key issue is how to represent facilities and demand in geographic space. Traditionally, spatial abstraction as discrete demand is assumed as it simplifies model formulation and reduces computational complexity. However, errors in derived solutions are likely not negligible, especially when demand varies continuously across a region. This paper discusses a single facility location problem that considers demand to be continuously distributed and allows a facility to be located anywhere in space, the continuous Weber problem. An approach for dealing with continuous demand is proposed that is integrated through geographical information system (GIS) functionality. Empirical results highlight the advantages of the developed approach and the importance of solution integration with GIS.

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Optimal location of a single facility with circular demand areas

Cited by 13 publications

References 9 publications

Revisiting several problems and algorithms in continuous location with $$\ell _\tau $$ ℓ τ norms

Revisiting several problems and algorithms in continuous location with $$\ell _\tau $$ ℓ τ norms

Hub Location Problems: The Location of Interacting Facilities

Serving regional demand in facility location

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