Locating Dimensional Facilities in a Continuous Space

Schöbel, Anita

doi:10.1007/978-3-030-32177-2_7

Cited by 1 publication

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“…(Bar) has already been introduced in the 17th century by Fermat for three points a 1 ,a 2 , and a 3 and for n weighted facilities by Weber in 1909, see, e.g., the survey [DKSW02]. Actual research concerns versions with p facilities [MBHMP07, DBMS15, MP20], barriers [Kla02], obnoxious facility location [DDS18], different types of facilities to be placed [MS98,Sch20], ordered median location problems [NP05,PRC20], location under uncertainty [CdG19], and others, see [LNdG20] and references therein for a recent overview. Here, we consider the following two extensions of (Bar).…”

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

confidence: 99%

Location problems with cutoff

Müller¹,

Schöbel²,

Schuhmacher³

2022

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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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