Separation linearization approach for the capacitated facility location problem under disruption

Facility location problems (FLP) are often solved as uncapacitated facility location (UFL) instances. Also, typical solution approaches in the literature assume that the established facilities are totally reliable. However, in practice, facilities have limited capacity and can be under risk of partial disruptions whereby their failure leads to a notably higher cost. In this context, this paper presents a novel integer programming formulation for the capacitated FLP under disruption, namely the reliable capacitated facility location (RCFL) problem. The latter considers heterogeneous facility failure probabilities, one layer of backup for supply locations, limited supply capacity and facility fortification within a limited budget to mitigate failure risk. The proposed solution approach involves a linearization of the proposed model and an iterative approach for the fortification budget allocation in conjunction with the CPLEX solver. Moreover, a relevant case study is used to illustrate the approach and benchmark result are also provided.