Robust Bi-Objective Operating Rooms Scheduling Problem Regarding the Shared Resources

Document Type : Article


1 Department of industrial engineering; Babol Noshirvani University of Technology, Babol, Iran

2 Department of industrial engineering; Babol Noshirvani University of Technology; Babol; Iran

3 Department of surgery; Babol University of Medical Sciences; Babol; Iran


In recent years, many efforts have been made to provide different strategies for enhancing the scheduling and planning of the operating rooms. The efficient planning and scheduling of ORs is a complex task since it has to account for the availability of human resources, medical equipment, and medication required for each surgery but that are often shared between different ORs. This paper proposes a mathematical approach to enhance the management of OR resources. It presents a bi-objective robust optimization approach for scheduling the surgeries in the ORs and recovery room, regarding the uncertainty of the surgery time, uncertainty of hospitalization time in the recovery room, and shared resources. The first objective function aims to minimize the maximum completion time of the surgeries and the second one minimizes the sum of the earliness-tardiness of the surgical operations. The suggested approach utilizes the multi-choice goal programming approach with utility function to solve the proposed model. The proposed approach is applied to a real case in the Shahid Beheshti hospital, Babol, Iran. The obtained results show that the suggested bi-objective robust optimization approach can enhance OR scheduling and should be designed into a decision support system for OR management.


1. Cardoen, B., Demeulemeester, E., Beliën, J. “Operating room planning and scheduling: A literature review”, Eur. J. Oper Res.,201, pp. 921-932 (2010).
2. Abedini, A., Lia, W., Ye, H. “An optimization model for operating room scheduling to reduce blocking across the perioperative process”, Procedia Manuf.,10, pp. 60-70 (2017).
3. Rath, S., Rajaram, K., Mahajan, A. “Integrated Anesthesiologist and Room Scheduling for Surgeries: Methodology and Application”, Oper Res.,65, pp. 1-19 (2017).
4. Cappanera, P., Visintin, F., Banditori, C. “A Goal-Programming Approach to the Master Surgical Scheduling Problem”, Health Care Systems Engineering for Scientists and Practitioners., Springer Proceedings in Mathematics & Statistics.,169, pp. 155-166 (2016).
5. Oostrum, J.M.V., Houdenhoven, M.V., Hurink, J.L., et al. “A master surgical scheduling approach for cyclic scheduling in operating room departments”, OR Spectrum.,30, pp. 355–374 (2008).
6. Hooshmand, F., MirHassani, S.A., Akhvein, A. “Adapting GA to solve a novel model for operating room scheduling problem with endogenous uncertainty”, Oper Res. Health Care.,19, pp. 26-43 (2018).
7. Azadeh, A., , Farahani, M.H., Torabzadeh, M., et al. “Scheduling prioritized patients in pmergency department laboratories”, Comput Meth Prog Bio., 117, pp. 61–70 (2014).
8. Li, X., Rafaliya, N., Baki, M.F., et al. “Scheduling elective surgeries: the tradeoff among bed capacity,waiting patients and operating room utilization using goal programming”, Health Care Manag Sci., 20, pp. 33–54 (2015).
9. Denton, B.T., Millner, A.J., Balasubramanian, J., et al. “Optimal allocation of surgery blocks to operating rooms under uncertainty”, Oper. Res., 58, pp. 802-816 (2010).
10. Rachuba, S., Werners, B. “A fuzzy multi-criteria approach for robust operating room schedules”, Ann Oper Res.,251, pp. 325-350 (2017).
11. Jebali, A., Diabat, A. “A Chance-constrained operating room planning with elective and emergency cases under downstream capacity constraints”, Comput. Ind. Eng.,144, pp. 329-344 (2017).
12. Liu, H., Zhang, T., Luo, S., et al. “Operating room scheduling and surgeon assignment problem under surgery durations uncertainty”, Technol. Health Care., 26, pp. 297-304 (2017).
13. Molina-Pariente, J. M., Hans, E.W., Framinan, J.M. “A stochastic approach for solving the operating room scheduling problem”, Flex Serv Manuf J., 30,pp. 224-251 (2018).
14. Neyshabouria, S., Berg, B. “Two-stage robust optimization approach to elective surgery and downstream capacity planning”, Eur. J. Oper. Res.,260, pp. 21-40 (2016).
15. Liu, L., Wang, C., Wang, J. “A combinatorial auction mechanism for surgical scheduling considering surgeon’s private availability information”, J. Comb. Optim., 37, pp. 405-417 (2018).
16. Ravnskjær Kroer, L., Foverskov, K., Vilhelmsen, C., et al. “Planning and scheduling operating rooms for elective and emergency surgeries with uncertain duration”, Oper. Res. Health Care.,19, pp.107-119 (2018).
17. Koppka, L., Wiesche, L., Schacht, M., et al. “Optimal distribution of operating hours over operating rooms using probabilities”, Eur. J. Oper. Res., 267, pp. 1156–1171 (2018).
18. Moosavi, A., Ebrahimnejad, S. “Scheduling of elective patients considering upstream and downstream units and emergency demand using robust optimization”, Comput. Ind. Eng., 120, pp.216-233 (2018).
19. Sagnol, G., Barner, C., Borndörfer, R., et al. “Robust allocation of operating rooms: A cutting plane approach to handle lognormal case durations”, Eur. J. Oper Res., 271, pp. 420-435 (2018).
20. Kamran, M. A., Karimi, B., Dellaert, N. “Uncertainty in Advance Scheduling Problem in Operating Room Planning”, Comput. Ind. Eng.,126, pp. 252-268 (2018).
21. Hamid, M., Nasiri, M.M., Werner, F., et al. “Operating room scheduling by considering the decision-making styles of surgical team members: a comprehensive approach”, Comput. Oper Res., 108, pp. 166-181 (2019).
22. Lin, Y.K., Chou, Y.Y. “A hybrid genetic algorithm for operating room scheduling”, Health Care Manag. Sci., 23, pp.1–15 (2019).
23. Vali-Siar, M. M., Gholami, S., Ramezanian, R. “Multi-period and multi-resource operating room scheduling under uncertainty: A case study”, Comput. Ind. Eng., 126, pp. 549-568 (2018).
24. Silva, T.A.O., de Souza, M. C. “Surgical scheduling under uncertainty by approximate dynamic programming”, Omega., 95, pp. 12-28 (2020).
25. Zhang, J., Dridi, M., Moudni, A.E. “Column-generation-based heuristic approaches to stochastic surgery scheduling with downstream capacity constraints”, Int. J. Prod. Econ., 229, pp.33-47 (2020).
26. Akbarzadeh, B., Moslehi, G., Reisi-Nafchi, M., et al. “The re-planning and scheduling of surgical cases in the operating room department after block release time with resource rescheduling”, Eur. J. Oper Res.,278, pp. 596-614 (2019).
27. Nasiri, M.M., Shakouhi, F., Jolai, F. “A fuzzy robust stochastic mathematical programming approach for multi‑objective scheduling of the surgical cases”, OPSEARCH., 56, pp. 1–21 (2019).
28. Najjarbashi, A., Lim, G. J. “A variability reduction method for the operating room scheduling problem under uncertainty using CVaR”, Oper. Res. Health Care., 20, pp. 25-32 (2019).
29. 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, pp. 191-214 (2019).
30. Marchesi, J. F., Hamacher, S., Fleck, J. L. “A Stochastic Programming Approach to the Physician Staffing and Scheduling Problem”, Comput. Ind. Eng., 142, pp. 23-37 (2020).
31. Barrera, J., Carrasco, R. A., Mondschein, S., et al. “Operating room scheduling under waiting time constraints: the Chilean GES plan”,  Ann. Oper. Res., 286, pp. 501–527 (2020).
32. Bovim, T. R., Christiansen, M., Gullhav, A.N., et al. “Stochastic Master Surgery Scheduling”,  Eur. J. Oper. Res., 258,pp. 695-711 (2020).
33. Khaniyev, T., Kayis, E., Gullu, R. “Next-Day Operating Room Scheduling with Uncertain Surgery Durations: Exact Analysis and Heuristics”, Eur. J. Oper. Res., 286, pp. 49-62(2020).
34. Bertsimas, D., Sim, M. “The price of robustness”, Oper Res.,50, pp. 35-53 (2004).
35. Pouriani, S., Asadi-Gangraj, E., Paydar, M.M. “A robust bi-level optimization modelling approach for municipal solid waste management; a real case study of Iran”,  J. Clean. Prod., 240, pp. 41-58 (2019).
36. Li, Z., Ierapetritou, M. “Robust Optimization for Process Scheduling Under Uncertainty”, Ind. Eng. Chem. Res., 47, pp. 4148-4157 (2008).
37. Lin, X., Janak, S., Floudas,C. “A new robust optimization approach for scheduling under uncertainty: I. Bounded uncertainty”, Comput. Chem. Eng., 28, pp. 1069-1085 (2004).
38. Charns, A., Cooper,W.W. “Goal programming and multiple objective optimization”, Eur. J. Oper Res., 1, pp. 39-54 (1977).  39. Chang, C. “Multi-choice goal programming with utility functions” Eur. J. Oper Res.,215, pp. 439-445 (2011).
40. Nayeri, S., Asadi-Gangraj, E., Emami, S. “Goal programming-based post-disaster decision making for allocation and scheduling the rescue units in natural disaster with time-window”, Int. J. Ind. Eng. Prod. Res., 29, pp. 65–7 (2018).