MDP model for the preference-based appointment scheduling problem with multi-priority patients

This thesis consists of three parts that analyze various aspects of appointment scheduling procedures in healthcare facilities. In the first part, we study an outpatient clinic with multiple types of patients that contact with the clinic to schedule an appointment. The clinic dynamically decides on the set of appointment days offered to each patient. Patients have different utility weights for each day in the booking horizon. Based on these utility weights, they either select one of the appointment days offered in the set or they leave the system without making an appointment. We model this system using a periodically time-inhomogeneous Markov decision process and derive analytical results on the structure of the optimal policy. To develop a solution for the model, we implement a simulation-based booking limit improvement algorithm by approximating the value function. In the second part, we consider a primary care clinic with strategic patients who choose between making an appointment, with an indirect wait cost, and walking in, with an inconvenience cost and a risk of being rejected. We consider two types of patients, regular, and urgent, based on their indirect waiting cost. Considering the equilibrium behavior of patients, the clinic should determine the optimal number of slots reserved for walk-ins, to maximize expected revenues. We analyze the system under observable and unobservable indirect waiting time information and characterize the equilibrium patient behavior for both of the settings. Finally, in the third part, we consider a model that combines patients' walk-in, no-show and cancellation behavior and appointment day preferences. In this study, the clinic decides on the number of slots allocated for walk-in patients and the set of appointment days offered to a patient. Given the offered set, patients may select making an appointment for one of the offered days or walking in on a day that is not included in the set. Walk-in patients have a risk of not receiving service, which we call "blockage" and blockage probability of a patient depends on the other patients' walk-in behavior. Thus, patients consider the other patients' choices while making a walk-in decision, which results in endogenously determined walk-in rate. We formulate the problem with a deterministic fluid model to maximize the expected net profit. Furthermore, we characterize the structure of the optimal fluid solution and establish its asymptotic optimality.