Data-Driven and Congestion-Aware Patient-to-Window Assignment in Outpatient Pharmacy Services

Long waiting time and uneven queueing congestion remain key challenges in outpatient pharmacy services. This study investigates the data-driven patient-to-window assignment problem in a hospital pharmacy, where multiple dispensing windows operate as heterogeneous parallel service counters. Using timestamps from patient check-in, machine processing, dispensing completion and pharmacist handover, we estimate arrival rates and window-specific service rates, as well as their time variations and correlations due to varied congestion levels. Based on queueing theory, we propose a proportional assignment policy considering the correlated uncertainty in both expected rates of total arrivals and service at each dispensing window. A robust model is developed to minimize the worst-case maximum expected number of customers across windows, which helps control the waiting time and queue-length imbalance by Little’s Law. We show that the original nonconvex problem admits a tractable second-order cone program reformulation. The effectiveness of the proposed assignment policy is verified by comparing to two benchmark approaches based on real-world data set from a local hospital in Ningbo, China. This study contributes to healthcare operations by integrating empirical queueing analysis, data-driven service rate estimation and congestion-aware robust routing logic within an outpatient pharmacy setting. The findings are expected to enhance hospital pharmacy service levels without changing the internal mechanisms of the dispensing machine.