A polynomial-time algorithm for the discrete facility location problem with limited distances and capacity constraints

Fernandes, Isaac F.; Aloise, Daniel; Aloise, Dario José; Jeronimo, Thiago P.

doi:10.14488/bjopm.2017.v14.n2.a1

Cited by 2 publications

(1 citation statement)

References 10 publications

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“…At the end of Section 3 we present the algorithm of [DMW91] for solving the Weber problem with limited distances. [FAAJ17] where the authors consider a discrete version of a barycenter problem in which they restrict how many existing points have to be within the cutoff distance. The problem is solved by a global optimization algorithm based on a decomposition of the plane into regions for which we know which given points are within the cutoff value C. A reversed approach in which one tries to cover as many points as possible within a given threshold value C and measures only the distance to the non-covered points is investigated in [BJKS15].…”

Section: Extensions Of the Barycenter Location Problem: Cutoff And Em...mentioning

confidence: 99%

Location problems with cutoff

Müller¹,

Schöbel²,

Schuhmacher³

2022

Preprint

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In this paper we study a generalized version of the Weber problem of finding a point that minimizes the sum of its distances to a finite number of given points. In our setting these distances may be cut off at a given value C > 0, and we allow for the option of an empty solution at a fixed cost C . We analyze under which circumstances these problems can be reduced to the simpler Weber problem, and also when we definitely have to solve the more complex problem with cutoff.We furthermore present adaptions of the algorithm of [Drezner et al., 1991, Transportation Science 25(3), 183-187] to our setting, which in certain situations are able to substantially reduce computation times as demonstrated in a simulation study. The sensitivity with respect to the cutoff value is also studied, which allows us to provide an algorithm that efficiently solves the problem simultaneously for all C > 0.

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Section: Extensions Of the Barycenter Location Problem: Cutoff And Em...mentioning

confidence: 99%

Location problems with cutoff

Müller¹,

Schöbel²,

Schuhmacher³

2022

Preprint

View full text Add to dashboard Cite

show abstract

Location Problems with Cutoff

Muller

Schöbel

Schuhmacher

2023

Asia Pac. J. Oper. Res.

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In this paper, we study a generalized version of the Weber problem of finding a point that minimizes the sum of its distances to a finite number of given points. In our setting, these distances may be cut off at a given value [Formula: see text], and we allow for the option of an empty solution at a fixed cost [Formula: see text]. We analyze under which circumstances these problems can be reduced to the simpler Weber problem, and also when we definitely have to solve the more complex problem with cutoff. We furthermore present adaptions of the algorithm of Drezner, Mehrez and Wesolowsky (1991 [The facility location problem with limited distances. Transportation Science, 25(3), 183–187, INFORMS]) to our setting, which in certain situations are able to substantially reduce computation times as demonstrated in a simulation study. The sensitivity with respect to the cutoff value is also studied, which allows us to provide an algorithm that efficiently solves the problem simultaneously for all [Formula: see text].

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A polynomial-time algorithm for the discrete facility location problem with limited distances and capacity constraints

Abstract: ABSTRACTproblem with capacity constraints regarding the number of served clients. These constraints are relevant for introducing

Cited by 2 publications

References 10 publications

Location problems with cutoff

Location problems with cutoff

Location Problems with Cutoff

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