Patient Assignment and Prioritization for Multi-Stage Care with Reentrance

In this paper, we study a queueing model that incorporates patient reentrance to reflect patients' recurring requests for nurse care and their rest periods between these requests. Within this framework, we address two levels of decision-making: the priority discipline decision for each nurse and the nurse-patient assignment problem. We introduce the shortest-first and longest-first rules in the priority discipline decision problem and show the condition under which each policy excels through theoretical analysis and comprehensive simulations. For the nurse-patient assignment problem, we propose two heuristic policies. We show that the policy maximizing the immediate decrease in holding costs outperforms the alternative policy, which considers the long-term aggregate holding cost. Additionally, both proposed policies significantly surpass the benchmark policy, which does not utilize queue length information.