A Chance-constrained operating room planning with elective and emergency cases under downstream capacity constraints

Operating room planning is an important and challenging decision making problem that should be tackled by hospitals. The present work is aimed at investigating this planning problem by accounting for the availability of two scarce and costly resources; the operating rooms and the Intensive Care Unit (ICU) which are shared between elective and emergency patients. The consideration of ICU beds is particularly important for operating room planning including cases where the patient requires an ICU bed after surgery. Indeed, in this case, without the availability of both an operating room time and an ICU bed, the surgery cannot be performed. A novel two-stage chance-constrained stochastic programming model is proposed for operating room planning by considering random surgery duration, random patient Length Of Stay (LOS) in the ICU and random resource capacity reserved for emergency cases. The objective is to minimize patient-related costs and expected operating room utilization costs and penalty costs for exceeding ICU capacity while ensuring a low risk level on surgery cancellation. A featured Sample Average Approximation (SAA) algorithm is developed to solve the model. Numerical experiments are carried out to verify the convergence property of the proposed algorithm and evaluate its performance. The results demonstrate the superiority of the operating room plans obtained by the proposed approach in terms of robustness. However, it is shown that this robustness is achieved at the expense of higher costs and lower operating room utilization.