Dynamic Facility Location with Generalized Modular Capacities

Abstract

Centre interuniversitaire de recherche sur les réseaux d'entreprise, la logistique et le transport (CIRRELT); and Département d'informatique Centre interuniversitaire de recherche sur les réseaux d'entreprise, la logistique et le transport (CIRRELT); and Département d'informatique L ocation decisions are frequently subject to dynamic aspects such as changes in customer demand. Often, flexibility regarding the geographic location of facilities, as well as their capacities, is the only solution to such issues. Even when demand can be forecast, finding the optimal schedule for the deployment and dynamic adjustment of capacities remains a challenge, especially when the cost structure for these adjustments is complex. In this paper, we introduce a unifying model that generalizes existing formulations for several dynamic facility location problems and provides stronger linear programming relaxations than the specialized formulations. In addition, the model can address facility location problems where the costs for capacity changes are defined for all pairs of capacity levels. To the best of our knowledge, this problem has not been addressed in the literature. We apply our model to special cases of the problem with capacity expansion and reduction or temporary facility closing and reopening. We prove dominance relationships between our formulation and existing models for the special cases. Computational experiments on a large set of randomly generated instances with up to 100 facility locations and 1,000 customers show that our model can obtain optimal solutions in shorter computing times than the existing specialized formulations.

A cutting-plane approach for large-scale capacitated multi-period facility location using a specialized interior-point method

“…ii) Since the facilities involved in this problem are capacitated, the possibility of adjusting the set of operating facilities over time is a way for adjusting the overall capacity of the system as a response to changes in demands and costs. Some authors have explicitly considered capacity adjustments as part of the decision making process (e.g., [12,13]) within a multi-period modeling framework for facility location problems. iii) By specifying the values of p t , t ∈ T we are setting a maximum "speed" for making adjustments in the system in terms of the operating facilities.…”

Lagrangian Heuristics for Large-Scale Dynamic Facility Location with Generalized Modular Capacities

“…We consider the mixed-integer programming formulation introduced by Jena et al (2013) and extend it to include multiple commodities. We denote by J the set of candidate facility locations and by L = {0, 1, 2, .…”

“…As will be explained in Section 4, our solution approach can be tailored to take advantage of the special structure of each problem variant. Jena et al (2013) explicitly show how to model two problem variants, using the GMC formulation: facility location with closing and reopening of facilities and facility location with capacity expansion and reduction. In the first problem, the size of the facility is chosen from a discrete set of capacity levels.…”

“…The resulting model is denoted as the ER-GMC formulation. Jena et al (2013) also refer to a third problem variant, which combines both features of the two special cases. It is denoted as the Dynamic Modular Capacitated Facility Location Problem with Closing/Reopening and Capacity Expansion/Reduction (DMCFLP CR ER).…”

“…As the relation between the number of different units cannot be captured by a simple function, the costs for capacity changes need to be described in a transition matrix. Jena et al (2013) recently introduced the Dynamic Facility Location Problem with Generalized Modular Capacities (DFLPG), in which the costs for capacity changes are based on a cost matrix. The mixed-integer programming (MIP) model presented by the authors therefore allows taking into account not only the total capacity involved in the capacity change, but also the current capacity level.…”