Mixed integer optimization for the combined capacitated facility location-routing problem

Abstract

Given a set of potential facilities (with individual opening cost and finite capacity) and a set of client demands, the capacitated Facility Location Problem (cFLP) consists in selecting a set of facilities to open and performing an assignment of demands to open facilities that minimize the sum of the facility opening cost, supplying cost and transportation/connection cost. This problem shares many similarities with the one consisting in minimizing the cost for opening a set of servers or replicas for storing a set of data objects (files) and connecting clients to facility locations so as to satisfy their demands. The multi-source dimension of the problem translates the situation where the same data object may be available simultaneously at different facility locations. When various data objects with different properties are available at (possibly multiple) opened facility locations, the problem shares the characteristics of the multi-product or multi-commodity model. On the other hand, the combination of the cFLP with the network design problem, referred to as the Capacitated Facility Location-Network Design Problem (cFLNDP), has been subject to several studies since the early 2000s. This (class of) problem(s) was initially motivated by the observation that when the (physical) network topology is determined endogenously, it may be more effective to change the configuration of the underlying network physical topology instead of locating additional facilities in order to account for the spatio-temporal variability in clients demands. However, in the context of communication networks, one does not require to physically rewire the network to obtain a new logical topology. Hence, in this paper we combine the capacitated multi-source multi-product facility location with the traffic routing problem and propose a mixed-integer program formulation. As dynamic routing offers the flexibility to re-configure routing tables entries and adapt routing decisions, our combined model also enables to dynamically re-allocate demands upon facility failure.