Discretized reformulations for a capacitated network loading problem arising in a facility location context

In this paper we present a discretization reformulation technique in the context of a facility location problem with modular link costs. We present a ‘traditional’ model and a straightforward discretized model with a general objective function. The linear relaxation bounds provided by both formulations are compared. Furthermore, we state that a restricted version of the discretized model gives an extended description of the convex hull of a “small” polytope that arises in the original model. Several valid inequalities induced by the discretized variables are also presented. We summarize the computational experience performed, highlighting that in the context of facility location problems with modular costs, a lot can be gained by making use of the proposed discretized models instead of the ‘traditional’ models.