Double bound method for solving the p-center location problem

Çalık, Hatice; Tansel, Barbaros Ç.

doi:10.1016/j.cor.2013.07.011

Cited by 49 publications

(50 citation statements)

References 22 publications

(45 reference statements)

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“…Their algorithm uses the two-phase idea and a binary search strategy similar to the algorithm by Ilhan and Pınar (2001), but restricts the set of radius values to solve the set covering problems with the finite radius set R as in Minieka (1970). Calik and Tansel (2013) developed new IP formulations and a new exact algorithm based on the decomposition of their models for solving the p-center problem. They associated a binary variable u k with r k , for each k 2 f1; : : : ; Kg.…”

Section: Exact Methods For P-center Problemsmentioning

confidence: 99%

“…In this formulation, constraints (4.14) are replaced with constraints (4.17) given below: The semi relaxations of these formulations, in which the binary restriction of the y-variables are removed, provide the tight lower bound obtained by Elloumi et al (2004). The algorithm developed by Calik and Tansel (2013) solves their formulations for restricted sets of radius values iteratively to converge to an optimal solution. They proposed several selection strategies for a two-element specialization of their algorithm.…”

Section: Exact Methods For P-center Problemsmentioning

confidence: 99%

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p-Center Problems

2015

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A p-center is a minimax solution that consists in a set of p points that minimizes the maximum distance between a demand point and a closest point belonging to that set. We present different variants of that problem. We review special polynomial cases, determine the complexity of the problems and present mixed integer linear programming formulations, exact algorithms and heuristics. Several extensions are also reviewed.

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Section: Exact Methods For P-center Problemsmentioning

confidence: 99%

Section: Exact Methods For P-center Problemsmentioning

confidence: 99%

p-Center Problems

2015

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“…Basically, this model is combination of k-median model (Rahman and Smith, 2000) and k-center model (Calik and Tansel, 2013).The objective function in Eq. (2) represents minimization of Centdian.…”

Section: K-centdian Modelmentioning

confidence: 99%

“…However, if the accessibility in such area improves, the accessibility in low population density area deteriorates, because of not considering few people living in a remote area (Rahman and Smith, 2000). By contrast, there is a maximum distance that is the maximum of all distance from each demand point to its nearest facility (Calik and Tansel, 2013). This measurement can consider the distance from the farthest demand point to facility.…”

Section: Introductionmentioning

confidence: 99%

Method of Determining Future Facility Location with Maintaining Present Accessibility

Takahagi¹,

Sumitani²,

Takahashi³

et al. 2016

Industrial Engineering and Management Systems

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The public services closely related to the daily lives of the Japanese people, such as firefighting, police or primary school education, are largely financed by the local governments. As the population as a whole in Japan declines, the population in local regions are forecasted to experience particularly rapid decline in the future, and it is inevitable to reduce the cost of public services provided by the local governments to keep their financial basis sustainable. In order to provide public services to the people properly and fairly, the local governments own and utilize their public facilities, such as fire stations, police stations or primary schools. On the other hand, we have to secure the accessibility, which is the condition of accessing a facility easily in a whole local city including the high population density area and low population density area. In this paper, we propose a method of determining the number of future facilities and its facility locations in which we maintain the present accessibility. In our proposed method, we determine them comparing the accessibility measurement calculated by facility location model using the present and future population. We adopted k-centdian model as the facility location model, which can secure the accessibility in a whole local city determining the weights of both areas. We applied our proposed method to fire station in Iwaki city, Japan. The results suggested that 7 facilities would be reduced in 2064, after 50 years from 2014. Additionally, we confirmed that the future facility location had securedaccessibility in both high and low population density area.

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“…The latter algorithm solved the vertex location problems with sizes up to 4,461 points in space. Calik and Tansel [20] proposed a new integer programming formulation for the p-center problem, in which the optimal p-center solution is obtained by solving a series of simple structured integer programs. The algorithm successfully solved problems with sizes up to 3,038 points in space.…”

Section: A Literature Reviewmentioning

confidence: 99%

A particle swarm optimization algorithm for the continuous absolute p-center location problem with Euclidean distance

Rabie¹,

El-Khodary²,

Tharwat³

2013

IJACSA

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Abstract-The p-center location problem is concerned with determining the location of p centers in a plane/space to serve n demand points having fixed locations. The continuous absolute pcenter location problem attempts to locate facilities anywhere in a space/plane with Euclidean distance. The continuous Euclidean p-center location problem seeks to locate p facilities so that the maximum Euclidean distance to a set of n demand points is minimized. A particle swarm optimization (PSO) algorithm previously advised for the solution of the absolute p-center problem on a network has been extended to solve the absolute pcenter problem on space/plan with Euclidean distance. In this paper we develop a PSO algorithm for the continuous absolute pcenter location problem to minimize the maximum Euclidean distance from each customer to his/her nearest facility, called "PSO-ED". This problem is proven to be NP-hard. We tested the proposed algorithm "PSO-ED" on a set of 2D and 3D problems and compared the results with a branch and bound algorithm. The numerical experiments show that PSO-ED algorithm can solve optimally location problems with Euclidean distance including up to 1,904,711 points.

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Double bound method for solving the p-center location problem

Cited by 49 publications

References 22 publications

p-Center Problems

p-Center Problems

Method of Determining Future Facility Location with Maintaining Present Accessibility

A particle swarm optimization algorithm for the continuous absolute p-center location problem with Euclidean distance

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