Dynamic multistage scheduling for patient-centered care plans.

We investigate the scheduling practices of multistage outpatient health programs that offer care plans customized to the needs of their patients. We formulate the scheduling problem as a Markov decision process (MDP) where patients can reschedule their appointment, may fail to show up, and may become ineligible. The MDP has an exponentially large state space and thus, we introduce a linear approximation to the value function. We then formulate an approximate dynamic program (ADP) and implement a dual variable aggregation procedure. This reduces the size of the ADP while still producing dual cost estimates that can be used to identify favorable scheduling actions. We use our scheduling model to study the effectiveness of customized-care plans for a heterogeneous patient population and find that system performance is better than clinics that do not offer such plans. We also demonstrate that our scheduling approach improves clinic profitability, increases throughput, and decreases practitioner idleness as compared to a policy that mimics human schedulers and a policy derived from a deep neural network. Finally, we show that our approach is fairly robust to errors introduced when practitioners inadvertently assign patients to the wrong care plan.