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.

设施位置问题（FLP）通常作为无能力设施位置（UFL）实例解决。而且，文献中的典型解决方案方法假定已建立的设施是完全可靠的。但是，实际上，设施的能力有限，并且可能会遭受部分破坏的风险，由此导致的失败会导致成本显着提高。在这种情况下，本文提出了一种用于中断条件下的带功能FLP的新型整数规划公式，即可靠的带功能设施位置（RCFL）问题。后者考虑了异构设施故障的可能性，供应位置的一层备份，有限的供应能力和有限预算内的设施设防，以减轻故障风险。拟议的解决方案方法包括对拟议的模型进行线性化，以及与CPLEX求解器一起用于设防预算分配的迭代方法。此外，通过相关案例研究来说明该方法，并提供了基准结果。