Formulations and Approximation Algorithms for Multilevel Uncapacitated Facility Location

Abstract

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Multi-level facility location problems

“…Therefore, for an MLFLP we have noted that the single-flow pattern is more common and in principle a non-nested structure is considered. In terms of the coherency criterion some papers have included certain assumptions while others simply impose single assignment constraints which in both cases imply a coherent structure [for example, 25,49,102].…”

“…Ortiz-Astorquiza et al [102] presented a new type of MILP for a slightly more general MUFLP in which for given values of p r , r = 1, • • • , k, cardinality constraints ( jr∈Vr y jr ≤ p r ) are imposed at each level. They called this problem the multilevel uncapacitated p-location problem (MUpLP) since it generalizes the well-known UpLP presented by Cornuéjols et al [29], which in turn subsumes the UFLP and the p-median problem (p-MP) [61].…”

“…The multi-level version of the p-median problem is denoted by MpMP. In [102], the authors developed the new formulation of the maximization version of the problem based on an alternative combinatorial representation given in [100], in which the objective function satisfies the submodularity property. Thus, considering the variables η i representing the profit (or cost) of serving customer i ∈ I, and Q the set of all possible paths q = j 1 , • • • j k having exactly one facility at each level, one can project out the variables x iq to x q from the PBF and obtain the submodular formulation…”

“…Note that the disaggregated version of constraints ( 16) may also be used. In [102] a computational comparison of formulations for the MUpLP was carried out. Because of the large number of constraints ( 14) the authors embedded the SF-MUpLP in a branch-and-cut framework exploiting an efficient way of solving the separation problem.…”

A simple multi-wave algorithm for the uncapacitated facility location problem

“…There also exist several recent studies of variants and extensions of UFLP, including Akbaripour et al (2017), Chalupa and Nielsen (2018), Han et al (2018), Jiang et al (2018), Pearce and Forbes (2018), Todosijević et al (2017), An and Svensson (2017). Also quite recently, Ortiz-Astorquiza et al (2017a, 2017b respectively provide formulations and approximation algorithms for Multilevel Uncapacitated Facility Location and a comprehensive review on multi-level facility location problems that extend several classical facility location problems.…”