Improving appointment scheduling for medical screening

We investigate the optimization of appointment scheduling for breast cancer screening, using the fact that a woman's attendance probability can be predicted. The methodology used applies to medical screening in general. The results of the mathematical investigation presented in this paper include a new formula for the cost of a screening session, a probabilistic model of rebooking appointments, a model of attendance probability as a function of previous performance, and a heuristic cost optimization procedure. Breast Test Wales have improved efficiency by introducing heavily overbooked sessions for patients who are unlikely to attend. We use simulation modelling and insights from probability theory to confirm the gain achieved by the Wales procedure and to assess the further gain achievable by optimization of appointment scheduling. It is found that a gain in throughput of at least 10% can be obtained by optimizing appointment scheduling for screening sessions, in particular by inviting patients in decreasing order of attendance probability, and by overbooking near the end of the session. This avoids the need to set up dedicated sessions for poor attenders. Another possibility is to book patients who change their appointment time, and who are therefore very likely to attend, into dedicated sessions. The provision of appointment scheduling software with a built-in simulation and optimization module along the lines described in this paper could enable radiographers to tailor appointment scheduling for each area and so to schedule appointments very efficiently.