We consider a patient admission problem to a hospital with multiple resource constraints (e.g. OR and beds) and a stochastic evolution of patient care requirements across multiple resources. There is a small but significant proportion of emergency patients who arrive randomly and have to be accepted at the hospital. However, the hospital needs to decide whether to accept, postpone or even reject the admission from a random stream of non-emergency elective patients. We formulate the control process as a Markov Decision Process to maximize expected contribution net of overbooking costs. We develop bounds using approximate dynamic programming and use this to construct heuristics. We test our methods on data from the Ronal
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