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Azar, M., Carrasco, R. A., & Mondschein, S. (2021). Dealing with Uncertain Surgery Times in Operating Room Scheduling. Eur. J. Oper. Res., Early Access.
Abstract: The operating theater is one of the most expensive units in the hospital, representing up to 40% of the total expenses. Because of its importance, the operating room scheduling problem has been addressed from many different perspectives since the early 1960s. One of the main difficulties that
has reduced the applicability of the current results is the high variability in surgery duration, making schedule recommendations hard to implement.
In this work, we propose a time-indexed scheduling formulation to solve the operational problem. Our main contribution is that we propose the use of chance constraints related to the surgery duration's probability distribution for each surgeon to improve the scheduling performance. We show how to implement these chance constraints as linear ones in our time-indexed formulation, enhancing the performance of the resulting schedules significantly.
Through data analysis of real historical instances, we develop specific constraints that improve the schedule, reducing the need for overtime without affecting the utilization significantly. Furthermore, these constraints give the operating room manager the possibility of balancing overtime and utilization through a tunning parameter in our formulation. Finally, through simulations and the use of real instances, we report the performance for four different metrics, showing the importance of using historical data to get the right balance between the utilization and overtime.
Barrera, J., Carrasco, R. A., Mondschein, S., Canessa, G., & Rojas-Zalazar, D. (2020). Operating room scheduling under waiting time constraints: the Chilean GES plan. Ann. Oper. Res., 286(1-2), 501–527.
Abstract: In 2000, Chile introduced profound health reforms to achieve a more equitable and fairer system (GES plan). The reforms established a maximum waiting time between diagnosis and treatment for a set of diseases, described as an opportunity guarantee within the reform. If the maximum waiting time is exceeded, the patient is referred to another (private) facility and receives a voucher to cover the additional expenses. This voucher is paid by the health provider that had to do the procedure, which generally is a public hospital. In general, this reform has improved the service for patients with GES pathologies at the expense of patients with non-GES pathologies. These new conditions create a complicated planning scenario for hospitals, in which the hospital's OR Manager must balance the fulfillment of these opportunity guarantees and the timely service of patients not covered by the guarantee. With the collaboration of the Instituto de Neurocirugia, in Santiago, Chile, we developed a mathematical model based on stochastic dynamic programming to schedule surgeries in order to minimize the cost of referrals to the private sector. Given the large size of the state space, we developed an heuristic to compute good solutions in reasonable time and analyzed its performance. Our experimental results, with both simulated and real data, show that our algorithm performs close to optimum and improves upon the current practice. When we compared the results of our heuristic against those obtained by the hospital's OR manager in a simulation setting with real data, we reduced the overtime from occurring 21% of the time to zero, and the non-GES average waiting list's length from 71 to 58 patients, without worsening the average throughput.