  In this paper, we propose an approximate dynamic programming (ADP) algorithm
to solve a Markov decision process (MDP) formulation for the admission control
of elective patients. To manage the elective patients from multiple specialties
equitably and efficiently, we establish a waiting list and assign each patient
a time-dependent dynamic priority score. Then, taking the random arrivals of
patients into account, sequential decisions are made on a weekly basis. At the
end of each week, we select the patients to be treated in the following week
from the waiting list. By minimizing the cost function of the MDP over an
infinite horizon, we seek to achieve the best trade-off between the patients'
waiting times and the over-utilization of surgical resources. Considering the
curses of dimensionality resulting from the large scale of realistically sized
problems, we first analyze the structural properties of the MDP and propose an
algorithm that facilitates the search for best actions. We then develop a novel
reinforcement-learning-based ADP algorithm as the solution technique.
Experimental results reveal that the proposed algorithms consume much less
computation time in comparison with that required by conventional dynamic
programming methods. Additionally, the algorithms are shown to be capable of
computing high-quality near-optimal policies for realistically sized problems.
