Block Scheduling in Two-stage Outpatient Clinics: Appointment Template Design

Abstract: Increasing the efficiency and effectiveness of the healthcare system is a challenge faced worldwide. Many outpatient clinics have implemented two-stage service systems, with both a physician and physician assistant, to enhance capacity and reduce costs. Some patients only visit a physician assistant while some patients visit both providers depending on their patient type. However, minimizing provider idle time and overtime while reducing patient waiting time is challenging in two-stage service systems. Thus, our objective is to find daily appointment templates, based on block scheduling, that minimize a weighted sum of these metrics. A block schedule divides the overall schedule into several time blocks and assigns patients of different types into each block in proportion to their daily demand to balance the workload throughout the day. Since the problem is shown to be strongly $\mathcal{NP}$-Hard, we develop a heuristic algorithm that provides a no-idle time appointment template that is easily implementable. We expand our study to include stochastic service times and show that our algorithm yields an efficient block schedule under practically relevant conditions. The algorithm is able to provide a solution similar in cost to the stochastic model when patient wait time costs are low by maintaining lower physician idle times with at most a 16 minute/patient increase in patient wait times. Comparing our heuristic to a First Come, First Appointment scheduling rule, we show that our heuristic is able to better minimize provider idle time, which mimics many real-life settings where clinics prioritize the efficiency of the healthcare providers.