A policy approximation of a Markov decision process for scheduling clients in an outpatient mental healthcare clinic.

The main issues within the department of mood and anxiety issues of Mediant are long waiting times for clients and a high experienced workload for practitioners. A method to schedule clients is developed. The goal is to reduce both waiting times and experienced workload. Since it is known how many appointments a client needs before a new client needs to be notified for an initial appointment, it is possible to delay the scheduling of a new client until a current client leaves. To make scheduling easier and reduce irregularity, a blueprint schedule is made. To decide which type of client to plan with which type of practitioner, a Markov Decision Process (MDP) is formulated. Due to the curses of dimensionality, this is too large to solve for real-life cases. Therefore an approximation is made, which uses simple scheduling rules: a combination of a trunk reservation policy and a threshold policy. This approximation gives an expected penalty of 27% higher and an expected queue length of 29% higher than the MDP for small cases, while the runtime is much shorter. The approximation outperforms the current policy of assigning clients to practitioners assuming back-to-back scheduling in a realistic sized simulation.