Planning facility location under generally correlated facility disruptions: Use of supporting stations and quasi-probabilities

Many real-world service facilities are subject to probabilistic disruptions. Such disruptions often exhibit correlations that arise from shared external hazards or direct interactions among these facilities. This paper builds an overarching methodological framework for reliable facility location design under correlated facility disruptions. We first incorporate and extend the concepts of supporting station structure and quasi-probability from Li et al. (2013) and Xie et al. (2015), such that any correlated facility disruptions (positive and/or negative) can be equivalently represented by independent failures of a layer of properly constructed supporting stations, which are virtually added to the original facility system for capturing the effect of correlations among facilities. We then develop a compact mixed-integer mathematical model to optimize the facility location and customer assignment decisions in order to strike a balance between system reliability and cost efficiency. Lagrangian relaxation based algorithms, including modules for obtaining upper bound and lower bounds of relaxed subproblems, are proposed to effectively solve the optimization model. Numerical case studies are carried out to demonstrate the methodology, to test the performance of the framework, and to draw managerial insights.