Disaggregated Benders decomposition and branch-and-cut for solving the budget-constrained dynamic uncapacitated facility location and network design problem

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

“…Additional recent investigations of UFLP have been carried out by Albareda-Sambola et al (2017), Atta et al (2018), Galli et al (2018), Sahman et al (2017), Tsuya et al (2017). 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.…”

Towards a general formulation of lazy constraints

“…The same method for proving Pareto-optimality appears in the paper by Pearce and Forbes [2], shown in Section 3.7. It is also useful for finding algorithms that generate Pareto-optimal Benders cuts analytically.…”

“…The notion of Pareto-optimality of Benders cuts was introduced by Magnanti and Wong [46]. The following definitions are derived from their original description, and are taken directly from [2]. The Benders cuts are all defined for a minimisation problem, but the theory holds for a maximisation problem by reversing inequalities appropriately.…”

“…• Uncapacitated Facility Location problem (UFL) [46,60] • Network Design problem [47] • Dynamic UFL and Network Design problem (DUFLNDP) [2,83] • Two-Level UFL problem with Single-Assignment [85] • Urban Rapid Transit Network Design problem [86] • Hub and Shuttle Public Transit System Design problem [67] • Tree of Hubs Location problem [52] • Hub Line Location problem [53] • Gateway hub location problem [87] • Integrated Urban Heirarchy and Transportation Network Planning [88] • TSP with Generalised Latency [54] Each of these problems is essentially a network design problem with a multi-commodity flow component. A number of these studies show that Benders decomposition is useful for solving these problems [2, 46, 47, 52-54, 60, 67, 86, 87], particularly when the sub-problems are disaggregated [2, 52-54, 60, 67, 86] and when Benders decomposition is implemented in a branch-and-cut framework [2,52,53,60]. Here, we present the formulation of the GUFLNDP, show how to apply Benders decomposition to it and discuss some of the common improvements.…”

“…3.2. THEORY 43 more effective than traditional Benders feasibility cuts[2,52,55] and are easy to obtain using the functionality available in Gurobi and CPLEX. All examples of Benders decomposition in this thesis that require feasibility cuts use combinatorial Benders cuts.…”