Abstract
Planning and scheduling of operating rooms (ORs) is important for hospitals to improve efficiency and achieve high quality of service. Due to significant uncertainty in surgery durations, scheduling of ORs can be very challenging. In this paper, surgical case scheduling problem with uncertain duration of surgeries in multi resource environment is investigated. We present a two-stage stochastic mixed-integer programming model, named SOS, with the objective of total ORs idle time and overtime. Also, in this paper a two-step approach is proposed for solving the model based on the L-shaped algorithm. Proposing the model in a multi resources environment with considering real-life limitations in academic hospitals and developing an approach for solving this stochastic model efficiently form the main contributions of this paper. The model is evaluated through several numerical experiments based on real data from Hasheminejad Kidney Center (HKC) in Iran. The solutions of SOS are compared with the deterministic solutions in several real instances. Numerical results show that SOS enjoys a better performance in 97% of the cases. Furthermore, the results of comparing with actual schedules applied in HKC reveal a notable reduction of OR idle time and over time which illustrate the efficiency of the proposed model in practice.
Similar content being viewed by others
References
Atighehchian, A., Sepehri, M. M., & Shadpour, P. (2015). Operating room scheduling in teaching hospitals: A novel stochastic optimization model. International Journal of Hospital Research,4(4), 171–176.
Batun, S., Denton, B. T., Huschka, T. R., & Schaefer, A. J. (2011). Operating room pooling and parallel surgery processing under uncertainty. Informs Journal on Computing,23(2), 220–237.
Beaulieu, I., Gendreau, M., & Soriano, P. (2012). Operating rooms scheduling under uncertainty. In E. Tanfani & A. Testi (Eds.), Advanced decision making methods applied to health care (Vol. 173, pp. 13–32). Berlin: Springer.
Belake, J., & Carter, M. (1997). surgical process scheduling: A structured review. Journal of Medical Systems,30, 343–350.
Birge, J. R., & Louveaux, F. (1997). Introduction to stochastic programming (Springer Series in Operations Research). New York: Springer.
Cardoen, B., Demeulemeester, E., & Beliën, J. (2010). Operating room planning and scheduling: A literature review. European Journal of Operational Research,201, 921–932.
Chaabane, S., Meskens, N., Guinet, A., & Laurent, M. (2006). Comparison of two methods of operating theatre planning: Application in Belgian hospitals. In Paper presented at the International Conference on Service Systems and Service Management, Troyes, October 2006.
Dantzig, G. B. (1955). Linear programming under uncertainty. Management Science,1, 197–206.
Denton, B., & Gupta, D. (2003). A sequential bounding approach for optimal appointment scheduling. IIE Transactions,35, 1003–1016.
Denton, B., Viapiano, J., & Vogl, A. (2007). Optimization of surgery sequencing and scheduling decisions under uncertainty. Health Care Management Science,10(1), 13–24.
Denton, B. T., Miller, A. J., Balasubramanian, H. J., & Huschka, T. R. (2010). Optimal allocation of surgery blocks to operating rooms under uncertainty. Operations Research, 58(4), 802–816.
Erdogan, S. A., & Denton, B. (2013). Dynamic appointment scheduling of a stochastic server with uncertain demand. INFORMS Journal on Computing,25(1), 116–132.
Gauthier, J. B., & Legrain, A. (2015). Operating room management under uncertainty. Constraints. https://doi.org/10.1007/s10601-015-9236-4.
Guerriero, F., & Guido, R. (2011). Operational research in the management of the operating theatre: A survey. Health Care Management Science,14, 89–114. https://doi.org/10.1007/s10729-010-9143-6.
Gul, S., Denton, B. T., Fowler, J. W., & Huschka, T. (2011). Bi-criteria scheduling of surgical services for an outpatient procedure center. Production and Operations Management,20(3), 406–417.
Jensen, J. L. (1906). Sur les fonctions convexes et les ine’galite’s entre les valeurs moyennes. Acta Mathematica,30, 175–193.
Keller, B., & Bayraksan, G. (2010). Scheduling jobs sharing multiple resources under uncertainty: A stochastic programming approach. IIE Transactions,42(1), 16–30.
Keller, B. D. (2009). Models and methods for multiple resource constrained job scheduling under uncertainty. Tucson: The University of Arizona.
Laporte, G., & Louveaux, F. (1993). The integer L-shaped method for stochastic integer programs with complete recourse. Operations Research Letters,13, 133–142.
Magerlein, J., & Martin, J. (1978). Surgical demand scheduling: A review. Health Services Research,13, 418–433.
Mancilla, C., & Storer, R. H. (2009). Stochastic sequencing and scheduling of an operating room. In Paper presented at the MOPTA, Bethlehem, PA, Augest 2009.
Mancilla, C., & Storer, R. H. (2013). Stochastic sequencing of surgeries for a single surgeon operating in parallel operating rooms. IIE Transactions on Healthcare Systems Engineering,3(2), 127–138.
Min, D., & Yih, Y. (2010). Scheduling elective surgery under uncertainty and downstream capacity constraints. European Journal of Operational Research,206, 642–652.
Pulido, R., Aguirre, A. M., Ibáñez-Herrero, N., Ortega-Mier, M., García-Sánchez, Á., & Méndez, C. A. (2014). Optimization methods for the operating room management under uncertainty: Stochastic programming vs. decomposition approach. Journal of Applied Operational Research,6(3), 145–157.
Rachuba, S., & Werners, B. (2015). A fuzzy multi-criteria approach for robust operating room schedules. Annals of Operations Research,1, 1–26. https://doi.org/10.1007/s10479-015-1926-1.
Saadouli, H., Jerbi, B., Dammak, A., Masmoudi, L., & Bouaziz, A. (2015). A stochastic optimization and simulation approach for scheduling operating rooms and recovery beds in an orthopedic surgery department. Computers and Industrial Engineering,80, 72–79.
Wang, Y., Tang, J., & Fung, R. Y. K. (2014). A column-generation-based heuristic algorithm for solving operating theater planning problem under stochastic demand and surgery cancellation risk. International Journal of Production Economics,158, 28–36.
Xiao, G., Jaarsveld, W. V., Dong, M., & Klundert, J. V. D. (2016). Stochastic programming analysis and solutions to schedule overcrowded operating rooms in China. Computers and Operations Research,74, 78–91.
Zhiming, Z. (2011). A two-stage scheduling approach of operation rooms considering uncertain operation time In International conference on information science and technology (ICIST), Nanjing 26–28 March 2011 (pp. 1225–1228). IEEE.
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Atighehchian, A., Sepehri, M.M., Shadpour, P. et al. A two-step stochastic approach for operating rooms scheduling in multi-resource environment. Ann Oper Res 292, 191–214 (2020). https://doi.org/10.1007/s10479-019-03353-5
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10479-019-03353-5