Optimal distribution of operating hours over operating rooms using probabilities

Usually, all operating rooms in a hospital have the same daily capacity although differing operating hours might be advantageous to match the demand. We propose and evaluate an optimization model that tactically distributes the total available operating time over the different operating rooms in order to improve performance. The probability of a perfect day without overtime or cancellations serves as objective criterion. Hence, the solution obtained has a maximum probability of no overtime or cancellations in all operating rooms. Uncertainties handled are mainly the surgery duration of patients and the daily number of patients to treat. To assess the number of patients, a method for sampling from multidimensional distribution functions for health care purposes is introduced. It is demonstrated that optimal operating hours for operating rooms can significantly influence key performance indicators such as overtime, rescheduling of patients and utilization. Implications for research and practical purposes can be deduced from an extensive simulation study with realistic data.