Providing radiology health care services to stochastic demand of different customer classes

We consider two CT-scanners in a radiology department of a hospital providing medical service to three patient groups with different arrival patterns and cost-structures: scheduled outpatients, non-scheduled inpatients, and emergency patients. Scheduled outpatients arrive based on an appointment schedule with some randomness due to no-shows. Inpatients and emergency patients arrive at random. The problem is to allocate the available resources dynamically to the patients of the groups such that the expected total reward consisting of revenues, waiting costs, and penalty costs is maximized. We model the problem as as Markov Decision Process and compare it with three decision rules which can be applied in hospitals.