Sequential clinical scheduling with stochastic patient re-entrance: Case of Mohs

We study the problem of appointment scheduling for outpatient clinics with stochastic patient re-entrance. It is motivated by the scheduling problem for Mohs Micrographic Surgery, which is a popular technique for the excision of skin cancers. Re-entrance occurs when a patient repeats upstream processes during the single-day outpatient appointment, usually after a medical test. In some surgical procedures, the number of re-entrances for each patient is unknown until medical test results become available, causing long patient waiting time and clinic overtime. To address these challenges, we develop a stochastic slot model, SMART, that captures the key characteristics of the appointment processes and stochastic re-entrance, utilizing a delay before possible re-entrance. We then design a sequential scheduling algorithm that balances patient waiting, clinic overtime and patient throughput while considering stochastic complications such as no-shows, processing time variability, and the number of re-entrances per patient. We establish several theoretical properties of the algorithm, including the optimality of the resulting schedules for the sequential scheduling setting. We apply SMART to appointment scheduling for Mohs clinics, where patients may have same-day re-entrance due to repetitive skin excisions. We compare SMART schedules to others that ignore re-entrance and to current scheduling practices via simulation studies under a more realistic setting. Numerical experiments show that SMART schedules dominate other schedules, and ignoring re-entrance can cost huge loss in efficiency. Furthermore, SMART schedules exhibit a special 'stair-stepping' pattern for the number of appointments, with most patients assigned to the early slots and many empty slots at the end.