  We study the Patient Assignment Scheduling (PAS) problem in a random
environment that arises in the management of patient flow in the hospital
systems, due to the stochastic nature of the arrivals as well as the Length of
Stay distribution. We develop a Markov Decision Process (MDP) which aims to
assign the newly arrived patients in an optimal way so as to minimise the total
expected long-run cost per unit time over an infinite horizon. We assume
Poisson arrival rates that depend on patient types, and Length of Stay
distributions that depend on whether patients stay in their primary wards or
not. Since the instances of realistic size of this problem are not easy to
solve, we develop numerical methods based on Approximate Dynamic Programming.
We illustrate the theory with numerical examples with parameters obtained by
fitting to data from a tertiary referral hospital in Australia, and demonstrate
the application potential of our methodology under practical considerations.
