The gravity p-median model

Drezner, Tammy; Drezner, Zvi

doi:10.1016/j.ejor.2005.04.054

Cited by 95 publications

(51 citation statements)

References 15 publications

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“…However, the question is important, since there are indeed some other problems for which the same property does not hold. Typical examples include the center point problem, addressed in the same Hakimi (1964) paper, the general absolute median problem of Minieka (1977), and the gravity p-median of Drezner and Drezner (2007). In these cases, location restricted to nodes could lead to sub-optimal solutions, while in the case of the p-median, the property proved by Hakimi (sometimes referred to as "Hakimi property") of existence of optimal solutions on vertices allowed looking for the optimal solution of the problem over a finite set (the nodes), instead of having to search over an infinite and continuous set (anywhere on the network).…”

Section: Hakimi (1965): Multiple Facilities and Vertex Optimalitymentioning

confidence: 99%

“…Colome et al (2003) made an amendment to the Maximum Capture Model (MAX-CAP) by ReVelle (1986) to calculate the capture of market share with the gravity model instead of just proximity. Finally, Drezner and Drezner (2007) introduced the "gravity p-median model," where customers have different probabilities for competing facilities that differ from standard p-median problems where customers are assigned to the closet facility.…”

Section: New Approaches and Outlookmentioning

confidence: 99%

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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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Section: Hakimi (1965): Multiple Facilities and Vertex Optimalitymentioning

confidence: 99%

Section: New Approaches and Outlookmentioning

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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“…Gravity p-Median: Drezner and Drezner [30] analyzed the p-median model with the stipulation that consumers at each demand point do not necessarily patronize the closest facility. Planar Gravity p-Median and Minimum Variance: Drezner and Drezner [29] considered the p-median in the plane and minimized the variance of loads using the gravity approach.…”

Section: Applying the Gravity Approach To Other Location Modelsmentioning

confidence: 99%

A review of competitive facility location in the plane

Drezner

2014

Logist. Res.

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In this paper, we review competitive location models. Retail facilities operate in a competitive environment with an objective of profit and market share maximization. These facilities are different from each other in their overall attractiveness to consumers. The basic problem is the optimal location of one or more new facilities in a market where competition already exists or will exist in the future. Extensions to the models include an analysis of the optimal allocation of a budget among new facilities and their best locations, modeling location under conditions of uncertainty and future competition, incorporating the concept of a threshold in competitive location, modeling lost demand, and minimizing cannibalization.

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“…Although the p-median objective is not a competitive one, the p-median objective is still applicable to many situations. The p-median problem in a network environment where customers select the facility to use according to the gravity model rather than use the closest facility is analyzed in Drezner and Drezner [37]. The solution to the standard p-median problem is always on nodes leading to tractable solution procedures (Current et al [18]).…”

mentioning

confidence: 99%

“…The optimal facilities' location can be anywhere on the network. In Drezner and Drezner [37], heuristic solution procedures were proposed assuming that facilities' locations are on nodes. Steepest descent and tabu search algorithms were proposed with good computational results on a set of test problems.…”

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confidence: 99%

Modeling Competitive Facility Location Problems: New Approaches and Results

Berman¹,

Drezner²,

Drezner³

et al. 2009

Decision Technologies and Applications

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The gravity model as applied to competitive facility location is described in this tutorial. The gravity model is used mainly by marketers to estimate the market share attracted by competing retail facilities. A demand area consists of potential customers who spend their discretionary buying power at competing retail facilities. We discuss the gravity model and issues related to the determination of the parameters of the models. The basic model is to find the best locations for new facilities that would attract the maximum buying power from customers in the area. Extensions to this basic model include modeling uncertainty about future market conditions, minimizing the probability that the attracted market share falls short of a certain target, demand generated by intercepting a flow of customers, market expansion and lost demand, and allocation of a given budget among one's facilities to improve their attractiveness. We describe special tools that are utilized in the solution procedures. These are the generalized Weiszfeld procedure, the big triangle small triangle global optimization approach, and the tangent line approximation.

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The gravity p-median model

Cited by 95 publications

References 15 publications

Hub Location Problems: The Location of Interacting Facilities

Hub Location Problems: The Location of Interacting Facilities

A review of competitive facility location in the plane

Modeling Competitive Facility Location Problems: New Approaches and Results

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