Online capacity planning for rehabilitation treatments: an approximate dynamic programming approach

We study an online capacity planning problem in which arriving patients require a series of appointments at several departments, within a certain access time target.
This research is motivated by a study of rehabilitation planning practices at the Sint Maartenskliniek hospital (the Netherlands). In practice, the prescribed treatments and activities are typically booked starting in the rst available week, leaving no space for urgent patients who require a series of appointments at a short notice. This leads to rescheduling of appointments or long access times for urgent patients, which has a negative effect on the quality of care and on patient satisfaction.
We propose an approach for allocating capacity to patients at the moment of their arrival, in such a way that the total number of requests booked within their corresponding access time targets is maximized. The model considers online decision making regarding multi-priority, multi-appointment, and multi-resource capacity allocation. We formulate this problem as a Markov decision process (MDP) that takes into account the current patient schedule, and future arrivals. We develop an approximate dynamic programming (ADP) algorithm to obtain approximate optimal capacity allocation policies. We provide insights into the characteristics of the optimal policies and evaluate the performance of the resulting policies using simulation.