This paper considers a multiperiod Emergency Medical Services (EMS) location problem and introduces two two-stage stochastic programming formulations that account for uncertainty about emergency demand. While the first model considers both a constraint on the probability of covering the realized emergency demand and minimizing the expected cost of doing so, the second one employs probabilistic envelope con- straints which allow us to control the degradation of coverage under the more severe scenarios. These models give rise to large mixed-integer programs, which can be tackled directly or using a conservative approximation scheme. For the former, we implement the Branch-and-Benders-Cut method, which improves significantly the solution time when compared to a state-of-the art Branch-and-Bound algorithm proposed in the recent literature and to using the CPLEX solver. Finally, a practical study is conducted using historical data from Northern Ireland Ambulance Service and sheds some light on optimal EMS location configuration for this region and necessary trade-offs that must be made between emergency demand coverage and expected cost. These insights are confirmed through an out-of-sample performance analysis.
C. Peng, E. Delage, J. Li, Probabilistic Envelope Constrained Multiperiod Stochastic Emergency Medical Services Location Model and Decomposition Scheme, working paper, 2019