Risk-averse flexible policy on ambulance allocation in humanitarian operations under uncertainty

Proactive ambulance management is constructive to improve the response efficiency for emergency medical service (EMS) systems under uncertainty. In this paper, we present a dynamic optimisation model concerning the ambulance dispatching and relocation. We develop a flexible operation policy driven by the interval rolling to match vehicles with calls in batch. We formulate the problem in Markov Decision Process and incorporate $M/G/c $M/G/c queues to minimise the average response and delay time. Considering the curse-of-dimensionality, we provide a simulation-based empirical dynamic programming with the state aggregation and post-decision state to solve the model. To further accelerate the computational efficiency, a greedy heuristic method is introduced to improve the quality of sampling operations. Then, a risk-averse model is developed based on the stochastic dominance strategy to improve operational reliability. We develop an equivalent linear programming to evaluate concave dominating functions. We test the performance by a numerical case and extract managerial insights for practitioners. Our results show that the proposed flexible and risk-averse solution outperforms the classic model on reducing the delay under uncertain calls. And the improvement is more active during peak hours, when real-time needs exceed available ambulances.