Models and solution methods for the uncapacitated r‐allocation p‐hub equitable center problem

Abstract

Hub networks are commonly used in telecommunications and logistics to connect origins to destinations in situations where a direct connection between each origin-destination (o-d) pair is impractical or too costly. Hubs serve as switching points to consolidate and route traffic in order to realize economies of scale. The main decisions associated with hub-network problems include (1) determining the number of hubs (p), (2) selecting the p-nodes in the network that will serve as hubs, (3) allocating non-hub nodes (terminals) to up to r-hubs, and (4) routing the pairwise o-d traffic. Typically, hub location problems include all four decisions while hub allocation problems assume that the value of p is given. In the hub median problem, the objective is to minimize total cost, while in the hub center problem the objective is to minimize the maximum cost between origin-destination pairs. We study the uncapacitated (i.e., links with unlimited capacity) r-allocation p-hub equitable center problem (with 1 < r < p) and explore alternative models and solution procedures.

Layout optimization of a multi-centre distribution mode

“…Facility location problems can be defined as hub network problems. In this case hubs can serve as switching points to consolidate and route traffic [26]. A very special field of multi-depot facility location problems is represented by underground logistic systems.…”

On hub location problems in geographically flexible networks

“…All the above papers deal with exact methods but also some heuristics and metaheuristic approaches have been proposed for the problem (see, for instance, Abdinnour‐Helm, 1998; Topcuoglu et al., 2005). One can also find several extensions of the UHLPFC, as the incorporation of congestion and service time (Alumur et al., 2018), modular capacities (Hoff et al., 2017), incomplete but graph‐structured backbone networks (Contreras et al., 2009, 2010; Martins de Sá et al., 2015; Blanco and Marín, 2019) flow‐dependent transportation costs (Tanash et al., 2017), robust and uncertain versions (Habibzadeh Boukani et al., 2016; Peiró et al., 2019), extensions to $$r$$‐allocation rules (Peiró et al., 2018; Brimberg et al., 2022), or covering models (Ernst et al., 2017). Also, a flexible approach based on ordered median functions have been incorporated to different hub location problems (Puerto et al., 2011, 2013, 2016), which is particularly useful to obtain robust solutions in hub problems by applying $$k$$‐centrum, trimmed‐mean, or antitrimmed‐mean criteria.…”

The uncapacitated r‐allocation p‐hub center problem

“…For these reasons, we extend the p-hub center problem by restricting the number of hubs assigned to any node to a maximum of r (a parameter), and hence, propose the uncapacitated r-allocation p-hub center problem (UrApHCP). The r-allocation scheme has been already considered in hub location problems in Peir ó et al (2014, 2018), and Janković and Stanimirović (2017, for example. For the UrApHCP, the similar general assumptions are made as in the single and multiple allocation variants of the problem.…”