Robust Facility Location under Demand Location Uncertainty

Facility location models typically assume demand locations are known at the time of facility siting. However, in many practical problems, the locations of demand points may be subject to uncertainty. One setting in which demand location uncertainty is a major feature is in the deployment of automated external defibrillators (AEDs) in public locations, which are used to treat sudden cardiac arrest. Since the exact locations of future cardiac arrests cannot be known a priori, AEDs must be placed strategically in public locations to ensure their accessibility in the event of a cardiac arrest emergency. Motivated by the AED location problem, we propose a distributionally robust model for siting facilities in an environment where demand points are realized in continuous space according to a partially-known distribution. Our approach involves discretizing continuous space into a finite set of scenarios, with each scenario representing a possible location for the realization of the next demand point. We propose a solution technique based on row-and-column generation that scales extremely efficiently in the number of scenarios. We also provide bounds on the error induced by the discretization as a function of the granularity of discretization. Combined with the efficiency of the row-and-column generation algorithm, these bounds allow us to tractably and tightly approximate the underlying continuous problem. Lastly, we present numerical results from a case study that demonstrates that hedging against demand location uncertainty has the potential to improve survival outcomes by mitigating the risk of long response times.