A continuum approximation approach to reliable facility location design under correlated probabilistic disruptions

This paper studies the reliable uncapacitated fixed charge location problem (RUFL) where facilities are subject to spatially correlated disruptions that occur with location-dependent probabilities (due to reasons such as natural or man-made disasters). If a facility fails, its customers are diverted to other facilities and incur excessive transportation cost. We develop a continuum approximation (CA) model to minimize the sum of initial facility construction costs and expected customer transportation costs under normal and failure scenarios. The paper presents ways to formulate the correlation among adjacent facility disruptions, and incorporates such correlations into the CA model. Numerical experiments are conducted to illustrate how the proposed model can be used to optimize facility location design, and how the correlations influence the total system cost.