A Wasserstein distributionally robust chance constrained programming approach for emergency medical system planning problem

Abstract

This paper proposes a distributionally robust chance constrained programming model for an emergency medical system location problem with uncertain demands. By minimising the total expected cost, the location of emergency medical stations, the allocation of the ambulances and demand assignments of system are optimised. The Wasserstein-metric is employed to construct the ambiguity set centred at an empirical distribution with a proper radius, which contains all the probability distributions of the uncertainties. We introduce a big-M technique to reformulate distributionally robust chance constrained programming into a corresponding mixed integer programm, which can be inner and outer approximated by Value-at-Risk (VaR) and Conditional-Value-at-Risk (CVaR). Numerical experiments are illustrated to demonstrate the effectiveness of the formulations.