Locating a single facility and a high-speed line

Díaz-Báñez, José Miguel; Korman, Matias; Pérez-Lantero, Pablo; Ventura, Inmaculada

doi:10.1016/j.ejor.2013.11.019

Cited by 3 publications

(2 citation statements)

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“…Since v > 1 we have that 0 < ϕ v < π 4 . The angle ϕ v , which depends on the speed v, is a critical angle that has been used to characterize the shortest paths from the demand points to the facility in presence of a freeway of variable length (Díaz-Báñez et al 2013b …”

Section: Lemma 6 For Any R ≥ 0 the Set B H ( F R) Is Convexmentioning

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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Section: Lemma 6 For Any R ≥ 0 the Set B H ( F R) Is Convexmentioning

confidence: 99%

The 1-Center and 1-Highway problem revisited

et al. 2015

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“…The next lemma characterizes the way in which demand points move optimally to the facility. A detailed proof is given in [8] for the case in which the length is a variable. The proof can be easily adapted for the fixed length case.…”

Section: Freeway Locationmentioning

confidence: 99%

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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Walk the Line: Optimizing the Layout Design of Moving Walkways

Boysen

Briskorn

Schwerdfeger

2021

Transportation Science

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A moving walkway (also denoted as moving sidewalk, travelator, autowalk, pedestrian conveyor, or skywalk) is a slow moving conveyor that transports standing or walking people horizontally over a short to medium distance. Constantly moving walkways have a long-lasting tradition especially inside large buildings, such as airport terminals and railway stations. Novel technological developments allow to accelerate walkways in their middle sections up to 12 km/h, while still providing a safe and much slower entrance and exit. Furthermore, first applications of moving walkways as environmentally friendly and space-efficient alternatives for urban public transport exist. In this context, our paper aims to support the layout design of moving walkways with optimization. Given a straight corridor (e.g., an airport terminal) and the passenger flows within the corridor (e.g., among gates), we aim to optimally place bidirectional walkway segments. We show that the resulting optimization problem is efficiently solvable by dynamic programming even if multiple relevant extensions, such as multiple objectives, budget constraints, and minimum safety distances, among subsequent segments are relevant. We apply our algorithm to explore the impact of constantly moving and accelerating walkways on total travel times and benchmark solutions without walkway support in a real-world case study. Our results reveal that wrongly placed walkways may considerably slow down passenger transport, but a very simple design rule leads to near-optimal results.

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Locating a single facility and a high-speed line

Cited by 3 publications

References 20 publications

The 1-Center and 1-Highway problem revisited

The 1-Center and 1-Highway problem revisited

The 1-Center and 1-Highway Problem

Walk the Line: Optimizing the Layout Design of Moving Walkways

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