Multi-period distributionally robust emergency medical service location model with customized ambiguity sets

Considering the dynamic and stochasticity of demand for emergency medical service, this paper proposes two multi-period distributionally robust optimization models with first-order moment and Wasserstein ambiguity sets. To handle non-independent and non-identically distributed demand, we construct two different multi-period models and reformulate the two models into mixed-integer second-order cone programming (MISOCP) based on first-order moment and Wasserstein ambiguity sets. Taking into account the problem size increase caused by multiple periods, we develop a lifted polyhedral approximation algorithm to handle large-scale MISOCP. The numerical experiments demonstrate that our algorithm can significantly improve the solution efficiency compared to benchmarks including the outer approximation algorithm and Gurobi solver. Finally, based on real-world data from Montgomery County, Pennsylvania, we perform sensitivity analysis and compare different models. The results indicate that by comprehensively accounting for the dynamic and stochasticity of demand, managers can significantly mitigate cost while maintaining a heightened reliability level.