Markov decision process and approximate dynamic programming for a patient assignment scheduling problem

We study the patient assignment scheduling (PAS) problem in a random environment that arises in the management of patient flow in hospital systems, due to the stochastic nature of the arrivals as well as the length of stay (LoS) distribution. At the start of each time period, emergency patients in the waiting area of a hospital system need to be admitted to relevant wards. Decisions may involve allocation to less suitable wards, or transfers of the existing inpatients to accommodate higher priority cases when wards are at full capacity. However, the LoS for patients in non-primary wards may increase, potentially leading to long-term congestion. To assist with decision-making in this PAS problem, we construct a discrete-time Markov decision process over an infinite horizon, with multiple patient types and multiple wards. Since the instances of realistic size of this problem are not easy to solve, we develop numerical methods based on approximate dynamic programming. We demonstrate the application potential of our methodology under practical considerations with numerical examples, using parameters obtained from data at a tertiary referral hospital in Australia. We gain valuable insights, such as the number of patients in non-primary wards, the number of transferred patients, and the number of patients redirected to other facilities, under different policies that enhance the system’s performance. This approach allows for more realistic assumptions and can also help determine the appropriate size of wards for different patient types within the hospital system.