An Exact Algorithm for Multilevel Uncapacitated Facility Location

Abstract

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Multi-level facility location problems

“…However, ever since these solution methods were proposed, only a few papers have dealt with the development of specialized exact solution algorithms for variants of the MUFLP. The papers of Marín [88], Landete and Marín [76], Gendron et al [49] and Ortiz-Astorquiza et al [101] are perhaps the exceptions. However, [49,101] study the more general case where fixed costs on the edges are considered, so these contributions will be discussed in the following sections.…”

“…The papers of Marín [88], Landete and Marín [76], Gendron et al [49] and Ortiz-Astorquiza et al [101] are perhaps the exceptions. However, [49,101] study the more general case where fixed costs on the edges are considered, so these contributions will be discussed in the following sections.…”

“…Also, in the uncapacitated case, we see that models and exact algorithms have been proposed for almost all categories listed in the table. However, only recently was an exact solution method designed for largescale instances of the general MUFLP-E with k > 2 [101]. On the other hand, in the capacitated versions, the effort appears to have focused on the two-level variants.…”

Solving the optimum communication spanning tree problem

“…One of the major drawbacks of this standard algorithm is that an integer MP needs to be solved at each iteration and there is no simple way to reoptimize when adding new constraints from one iteration to the next. To overcome this difficulty, recent implementations of Benders decomposition consider the solution of the Benders reformulation with a branch-and-cut algorithm, in which Benders cuts are separated not only at integer points but also at fractional points at the nodes of a single enumeration tree (see, for instance Fischetti et al, 2017;Zetina et al, 2017;Ortiz-Astorquiza et al, 2018). We use this approach to develop an exact algorithm for the OCT.…”

“…In the context of Benders decomposition, it is well-known that cutset inequalities are sufficient to guarantee the feasibility of Benders primal subproblems for the uncapacitated multicommodity network design problems (Magnanti et al, 1986;Costa et al, 2009;Ortiz-Astorquiza et al, 2018;Zetina et al, 2017). Given that the OCT is a special case of the uncapacitated multicommodity network design, cutset inequalities can also be used in lieu of Benders feasibility cuts for our problem.…”