Facility Location with Joint Disruptions

Abstract

Classical facility location problems do not incorporate the possibility of disruptions among facilities and usually result in solutions that do not perform well under disruptions. Existent literature on disreputable facility locations focuses on independent or extreme dependence scenarios where the probability structure is simplistic but has the advantage of allowing for efficient optimization. We propose the use of partially subordinated Markov Chains to model the probability of the dependent risk of disruptions. This parsimonious approach o ers a realistic model for disruptions. We also propose algorithms to calibrate a partially subordinated Markov Chain model and to optimize for the facility locations under dependent disruptions. We calibrate our model on two different cases with four different disruption data sets each and solve for the optimal facility location choice. We show that the resulting solutions significantly outperform those yielded from stronger assumptions like independence or extreme dependence.