Surgical scheduling by Fuzzy model considering inpatient beds shortage under uncertain surgery durations

Operating Room (OR) management has been among the mainstream of hospital management research, as ORs are commonly considered as one of the most critical and expensive resources. The complicated connection and interplay between ORs and their upstream and downstream units has recently attracted research attention to focus more on allocating medical resources efficiently for the sake of a balanced coordination. As a critical step, surgical scheduling in the presence of uncertain surgery durations is pivotal but rather challenging since a patient cannot be hospitalized if a recovery bed will not be available to accommodate the admission. To tackle the challenge, we propose an overflow strategy that allows patients to be assigned to an undesignated department if the designated one is full. It has been proved that overflow strategy can successfully alleviate the imbalance of capacity utilization. However, some studies indicate that implementation of the overflow strategy exacerbates the readmission rate as well as the length of stay (LOS). To rigorously examine the overflow strategy and explore its optimal solution, we propose a Fuzzy model for surgical scheduling by explicitly considering downstream shortage, as well as the uncertainty of surgery duration and patient LOS. To solve the Fuzzy model, a hybrid algorithm (so-called GA-P) is developed, stemming from Genetic Algorithm (GA). Extensive numerical results demonstrate the plausible efficiency of the GA-P algorithm, especially for large-scale scheduling problems (e.g., comprehensive hospitals). Additionally, it is shown that the overflow cost plays a critical role in determining the efficiency of the overflow strategy; viz., benefits from the overflow strategy can be reduced as the overflow cost increases, and eventually almost vanishes when the cost becomes sufficiently large. Finally, the Fuzzy model is tested to be effective in terms of simplicity and reliability, yet without cannibalizing the patient admission rate.