Discrete ordered median problem with induced order
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Discrete ordered median problem with induced order Enrique Domínguez1 · Alfredo Marín2 Received: 5 November 2019 / Accepted: 14 May 2020 © Sociedad de Estadística e Investigación Operativa 2020
Abstract Ordered median functions have been developed to model flexible discrete location problems. To do this, a weight is associated to the distance from a customer to its closest facility, depending on the position of that distance relative to the distances of all the customers. In this paper this idea is extended in the following way. The position of each customer in the ordering with respect to the closest facility is used to choose a second weight that will be multiplied times a second measure of the customer. In our case, this second measure is the distance from the customer to the closest facility of a different type. For the solution of this model several integer programming formulations are built and computationally compared. Keywords Discrete location · Ordered median · Integer programming Mathematics Subject Classification 90B80 · 90C10 · 90C11
1 Introduction One of the most fruitful areas within Operations Research is, undoubtedly, Facility Location (Laporte et al. 2019). In particular, Discrete Location has a wide range of applications but is also an area that provides researchers with a rich variety of theoretical challenges. Discrete location problems involve a finite set of candidate sites where facilities can be installed, and a finite set of customers to be served from these facilities.
* Enrique Domínguez [email protected] Alfredo Marín [email protected] 1
Department of Computer Science, Universidad de Málaga, Bulevar Louis Pasteur 25, 29071 Málaga, Spain
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Department of Statistics and Operation Research, Universidad de Murcia, Campus de Espinardo, 30071 Murcia, Spain
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E. Domínguez, A. Marín
Some of the simplest and most studied problems in Discrete Location are the Simple Plant Location Problem (SPLP) (Cho et al. 1983; Cornuéjols et al. 1977; Cornuéjols and Thizy 1982; Fernández and Landete 2015; Guignard 1980), where the aim is to minimize the sum of the distances from installed facilities to customers; the p-median problem (pM), where the number of facilities to be installed is known beforehand (García et al. 2011; Marín and Pelegrín 2019; ReVelle and Swain 1970); and the p-center problem (pCP), where the objective is to minimize the maximum of these distances (Calik et al. 2015; Elloumi et al. 2004; Hakimi 1964). The simplicity of these models has given rise to many variants. Some examples are capacity restrictions, multi-echelon structures (Marín 2007), dynamic models, models with choice of facilities (Cánovas et al. 2007) or strategic supply chain decisions (Melo et al. 2006). The interested reader can find an exhaustive travel along a huge number of location models in the aforementioned book (Laporte et al. 2019). The main difference between the SPLP/pM on the one hand, and the pCP on the other hand, is the objective function. In the SPLP and pM, the median f
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