Generating outpatient chemotherapy appointment templates with balanced flowtime and makespan

We study the problem of scheduling outpatient chemotherapy infusion appointments at oncology clinics. Patients are prepared during a fixed initial period of their infusion appointments. In the remainder of their appointments, the patients are monitored by nurses and if needed, taken care of. During preparation and the setting-up of the infusion device, one nurse must be fully assigned to the patient. Nurses who are neither on a break nor busy with preparing patients, simultaneously monitor up to a certain number of patients who are already receiving infusion. The prescribed infusion duration can significantly differ from patient to patient. The objective of this study is to generate an arrangement of vacant appointment slots, i.e., a template, subject to the nursing constraints. This is done while reaching a balance between starting the appointments as early as possible and completing the last appointments of the day, as early as possible. We solve this problem using integer programming. By adjusting two parameters in the objective function, the solution can be tuned between minimizing the weighted flowtime and minimizing the makespan. Thus, some appointments can be prioritized for starting as early as possible. Our numerical results show that the model can be solved to optimality with short computation times for large realistic size instances using commercial solver software. The generated template is intended to serve as a link between planning on a tactical level and online scheduling on an operational level.