Simultaneous location of a service facility and a rapid transit line

Espejo, Inmaculada; Rodríguez‐Chía, Antonio M.

doi:10.1016/j.cor.2010.07.013

Cited by 15 publications

(28 citation statements)

References 15 publications

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“…By using similar arguments to those given in [11] (Lemma 2.1) we can prove that there always exists an optimal location in which one of the turnpike endpoints coincides with the facility. Therefore, throughout this section we assume that f = t thus the distance from a demand point p ∈ S to f is now…”

Section: Locating a Turnpikementioning

confidence: 89%

“…In this paper we have considered several variants of the facility location problem introduced in [11]. Two models for the minmax criterion have been addressed, the turnpike case, in which we only allow entering and leaving the highway at its endpoints, and the freeway case, in which one is allowed to enter and leave at any point.…”

Section: Discussionmentioning

confidence: 99%

“…In a recent paper, Espejo and Chía [11] introduced a variant of the problem in which we are given a set of clients (represented by a set of points S) located in a city and one is interested in locating a service facility and a highway simultaneously in a way that the average supply time between the clients and the supply point is minimized. The state of the art and applications of this problem can be found in their paper and the references therein.…”

Section: Introductionmentioning

confidence: 99%

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The 1-Center and 1-Highway Problem

Díaz-Báñez

Korman

Pérez-Lantero

et al. 2012

Lecture Notes in Computer Science

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Abstract. We study a variation of the 1-center problem in which, in addition to a single supply facility, we are allowed to locate a highway. This highway increases the transportation speed between any demand point and the facility. That is, given a set S of points and v > 1, we are interested in locating the facility point f and the highway h that minimize the expression maxp∈S d h (p, f ), where d h is the time needed to travel between p and f . We consider two types of highways (freeways and turnpikes) and study the cases in which the highway's length is fixed by the user (or can be modified to further decrease the transportation time).

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Section: Locating a Turnpikementioning

confidence: 89%

Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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The 1-Center and 1-Highway Problem

Díaz-Báñez

Korman

Pérez-Lantero

et al. 2012

Lecture Notes in Computer Science

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“…Rather than the average travel time, we study minimizing the largest travel time between the clients and the facility. As in many other related problems (Díaz-Báñez et al 2013a;Espejo and Rodríguez-Chía 2011), in this paper we use the L 1 -metric as the underlying metric.…”

Section: Introductionmentioning

confidence: 99%

“…In many cases one is interested in locating a highway that optimizes some given function that depends on the distance between elements of a given point set (Ahn et al 2009;Aichholzer et al 2004;Aloupis et al 2010;Cardinal et al 2008;Korman and Tokuyama 2008;Körner and Schöbel 2010). Espejo and Rodríguez-Chía (2011) and Díaz-Báñez et al (2013a) study a variant of this problem in which a set of clients located in a city is given (represented by points), and the objective is to simultaneously locate a service facility (represented by a point) and a highway (represented by a straight segment of fixed length and any orientation) in a way that the average supply time between the clients and the facility point is minimized. In this model clients enter and exit the highway at the endpoints only, and move through it with a given constant speed.…”

Section: Introductionmentioning

confidence: 99%

The 1-Center and 1-Highway problem revisited

et al. 2015

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In this paper we extend the Rectilinear 1-center problem as follows: given a set S of n demand points in the plane, simultaneously locate a facility point f and a rapid transit line (i.e. highway) h that together minimize the expression max p∈S T h ( p, f ), where T h ( p, f ) denotes the travel time between p and f . A point of S uses h to reach f if h saves time: every point p ∈ S moves outside h at unit speed under the L 1 metric, and moves along h at a given speed v > 1. We consider two types of highways: (1) a turnpike in which the demand points can enter/exit the highway only at the endpoints; and (2) a freeway problem in which the demand points can enter/exit the highway at any point. We solve the location problem for the turnpike case in O(n 2 ) or O(n log n) time, depending on whether or not the highway's length is fixed. In the freeway case, independently of whether the highway's length is fixed or not, the location problem can be solved in O(n log n) time.A preliminary version of this research appeared in the XIV Spanish Meeting on Computational Geometry (Díaz-Báñez et al. 2011).

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Mixed planar and network single‐facility location problems

2016

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We consider the problem of optimally locating a single facility anywhere in a network to serve both on-network and off-network demands. Off-network demands occur in a Euclidean plane, while on-network demands are restricted to a network embedded in the plane. On-network demand points are serviced using shortest-path distances through links of the network (e.g., on-road travel), whereas demand points located in the plane are serviced using more expensive Euclidean distances. Our base objective minimizes the total weighted distance to all demand points. We develop several extensions to our base model, including: (i) a threshold distance model where if network distance exceeds a given threshold, then service is always provided using Euclidean distance, and (ii) a minimax model that minimizes worst-case distance. We solve our formulations using the "Big Segment Small Segment" global optimization method, in conjunction with bounds tailored for each problem class. Computational experiments demonstrate the effectiveness of our solution procedures. Solution times are very fast (often under one second), making our approach a good candidate for embedding within existing heuristics that solve multi-facility problems by solving a sequence of single-facility problems.

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Simultaneous location of a service facility and a rapid transit line

Abstract: In this paper we provide a finite set of candidates to be one of the endpoints of an optimal solution for the problem of locating simultaneously a service facility and a rapid transit line.

Cited by 15 publications

References 15 publications

The 1-Center and 1-Highway Problem

The 1-Center and 1-Highway Problem

The 1-Center and 1-Highway problem revisited

Mixed planar and network single‐facility location problems

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