Dynamic policies for inter-hospital patient transfers

Abstract

Geographical mismatch between demand for care and availability of healthcare resources was a major challenge during the COVID-19 pandemic. As such, inter-hospital patient transfers emerged as a key aspect of the pandemic response in many countries. We propose and study a class of transient queueing control problems to gain insights on the structure of optimal transfer policies and develop effective transfer policies. Specifically, we consider multiple parallel queues, starting with a large and possibly unbalanced initial condition, and seek discrete-time dynamic transfer policies that minimize the expected total cost over a finite-horizon. Costs are incurred as customers wait in queues, and are transferred between queues - including both variable and fixed transfer costs. We characterize the structure of the optimal policy for an associated discrete-time fluid control problem and investigate the robustness of the structure for the original stochastic system. Finally, we discuss how the structural results can be used to develop scalable approximate dynamic programming algorithms for the original stochastic control problem.