Skip to main content
Log in

A fuzzy robust stochastic mathematical programming approach for multi-objective scheduling of the surgical cases

  • Application Article
  • Published:
OPSEARCH Aims and scope Submit manuscript

Abstract

In this paper, the problem of elective surgery scheduling is studied, and resources like surgeons, nurses and operating rooms (ORs) are considered. The problem is to assign surgeries to operating rooms in order to meet three goals: (1) maximizing the number of surgeries that can be done using given fixed resources, (2) minimizing the total fixed costs and overtime costs of the ORs, and (3) minimizing the maximum of completion time of operating rooms. We take into account the uncertainty with the stochastic parameter for the regular operating time of OR in model and fuzzy constraint for resources and overtime. A multi-objective model is proposed to choose the operations to be scheduled on the selected day, and to assign the elective surgeries to OR sessions. In the first phase, we formulated a fuzzy robust optimization model and in the second phase, the sensitivity of the model to different values for penalties in the objective function, is analyzed. The efficiency of the proposed solution is validated by numerical results of applying the model to the case of a public hospital in Iran.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6

Similar content being viewed by others

References

  1. Adan, I., Bekkers, J., Dellert, N., Vissers, J., Yu, X.: Patient mix optimization and stochastic resource requirements: a case study in cardiothoracic surgery planning. Health Care Manag. Sci. 12, 129–141 (2009)

    Article  Google Scholar 

  2. Akbari, K., Nasiri, M.M., Jolai, F., Ghaderi, S.F.: Optimal investment and unit sizing of distributed energy systems under uncertainty: a robust optimization approach. Energy Build. 85, 275–286 (2014)

    Article  Google Scholar 

  3. Bardossy, A., Duckstein, L.: Fuzzy Rule-Based Modeling with Applications to Geophysical, Biological and Engineering Systems, p. 1995. CRC Press, Boca Raton (1995)

    Google Scholar 

  4. Baril, C., Yacout, S., Clement, B.: Design for six sigma through collaborative multiobjective optimization. Comput. Ind. Eng. 60(1), 43–55 (2011)

    Article  Google Scholar 

  5. Beliën, J., Demeulemeester, E.: Building cyclic master surgery schedules with leveled resulting bed occupancy. Eur. J. Oper. Res. 176, 1185–1204 (2007)

    Article  Google Scholar 

  6. Brandaa, M., Novotný, J., Olstad, A.: Fixed interval scheduling under uncertainty—a tabu search algorithm for an extended robust coloring formulation. Comput. Ind. Eng. 93(2016), 45–54 (2016)

    Article  Google Scholar 

  7. Cadenas, J.M., Verdegay, J.L.: Using fuzzy numbers in linear programming. IEEE Trans. Syst. Man Cybern. Part B Cybern. 27, 1016–1022 (1997)

    Article  Google Scholar 

  8. Dauer, J.P., Krueger, R.J.: An iterative approach to goal programming. Oper. Res. Q. 28(3), 671–681 (1977)

    Article  Google Scholar 

  9. Denton, B., Viapiano, J., Vogl, A.: Optimization of surgery sequencing and scheduling decisions under uncertainty. Health Care Manag. Sci. 10(2007), 13–24 (2007)

    Article  Google Scholar 

  10. Dexter, F., Macario, A., Traub, R.D.: Which algorithm for scheduling add-on elective cases maximizes operating room utilization? Use of bin packing algorithms and fuzzy constraints in operating room management. Anesthesiology 91(5), 1491–1500 (1999)

    Article  Google Scholar 

  11. Gerami, F., Saidi-Mehrabad, M.: Stochastic reactive scheduling model for operating rooms considering the moral and human virtues. Appl. Ecol. Environ. Res. 15(3), 563–592 (2017)

    Article  Google Scholar 

  12. Hamid, M., Nasiri, M.M., Werner, F., Sheikhahmadi, F., Zhalechian, M.: Operating room scheduling by considering the decision-making styles of surgical team members: a comprehensive approach. Comput. Oper. Res. 108, 166–181 (2019)

    Article  Google Scholar 

  13. Hans, E.W., Oostrum, J.M., Houdenhoven, M.V., Hurink, J.L., Wullink, G., Kazemier, G.: A master surgical scheduling approach for cyclic scheduling in operating room departments. OR Spectr. 30, 355–374 (2008)

    Article  Google Scholar 

  14. Heydari, M., Soudi, A.: Predictive/reactive planning and scheduling of a surgical suite with emergency patient arrival. J. Med. Syst. 40, 30, 1–9 (2016)

  15. Jebali, A., Alouane, A.B.H., Ladet, P.: Operating rooms scheduling. Int. J. Prod. Econ. 99, 52–62 (2006)

    Article  Google Scholar 

  16. Lahijanian, B., Zarandi, M.F., Farahani, F.V. (2016). Proposing a model for operating room scheduling based on fuzzy surgical duration. In: 2016 Annual Conference of the North American Fuzzy Information Processing Society (NAFIPS) (pp. 1–5). IEEE. https://doi.org/10.1109/NAFIPS.2016.7851627

  17. Mancilla, C.: Stochastic scheduling in operating rooms. Ph.D. Thesis, Lehigh University (2011)

  18. May, J.H., Spangler, W.E., Strum, D.P., Vargas, L.G.: The surgical scheduling problem: current research and future opportunities. Prod. Oper. Manag. 20, 392–405 (2011)

    Article  Google Scholar 

  19. Molina-Pariente, J.M., Fernandez-Viagas, V., Framinan, J.M.: Integrated operating room planning and scheduling problem with assistant surgeon dependent surgery durations. Comput. Ind. Eng. 82(2015), 8–20 (2015)

    Article  Google Scholar 

  20. Mula, J., Poler, R., Garcia, J.P.: MRP with flexible constraints: a fuzzy mathematical programming approach. Fuzzy Sets Syst. 157(2006), 74–97 (2006)

    Article  Google Scholar 

  21. Nasiri, M.M., Rahvar, M.: A two-step multi-objective mathematical model for nurse scheduling problem considering nurse preferences and consecutive shifts. Int. J. Serv. Oper. Manag. 27, 83–101 (2017)

    Google Scholar 

  22. Nasiri, M.M., Yazdanparast, R., Jolai, F.: A simulation optimisation approach for real-time scheduling in an open shop environment using a composite dispatching rule. Int. J. Comput. Integr. Manuf. 30, 1239–1252 (2017)

    Article  Google Scholar 

  23. Nazemi, A.-R., Akbarzadeh, M.-R., Hosseini, S.-M.: Fuzzy-stochastic linear programming in water resources engineering. In: 2002 Annual Meeting of the North American Fuzzy Information Processing Society, 2002. Proceedings. NAFIPS (2002)

  24. Ogulata, S.N., Erol, R.: A hierarchical multiple criteria mathematical programming approach for scheduling general surgery operations in large hospitals. J. Med. Syst. 27(3), 12 (2003)

    Article  Google Scholar 

  25. Ozkarahan, I., Edis, E.B., Ozfirat, P.M.: Operating room management in health care: operations research and artificial intelligence approaches. In: Handbook of Research on ICTs and Management Systems For Improving Efficiency in Healthcare and Social Care (2 Volumes) 2013 Chapter 27, pp. 518–538 (2013)

  26. Peidro, D., Mula, J., Poler, R., Verdegay, J.L.: Fuzzy optimization for supply chain planning under supply, demand and process uncertainties. Fuzzy Sets Syst. 160(2009), 2640–2657 (2009)

    Article  Google Scholar 

  27. Pishvaee, M.S., Khalaf, M.F.: Novel robust fuzzy mathematical programming methods. Appl. Math. Model. 40(1), 407–418 (2016)

    Article  Google Scholar 

  28. Pishvaee, M.S., Razmi, J., Torabi, S.A.: Robust possibilistic programming for socially responsible supply chain network design: a new approach. Fuzzy Sets Syst. 206, 1–20 (2012)

    Article  Google Scholar 

  29. Rachuba, S., Werners, B.: A fuzzy multi-criteria approach for robust operating room schedules. Ann. Oper. Res. 251(1–2), 325–350 (2017)

    Article  Google Scholar 

  30. Rahbari, A., Nasiri, M.M., Werner, F., Musavi, M., Jolai, F.: The vehicle routing and scheduling problem with cross-docking for perishable products under uncertainty: two robust bi-objective models. Appl. Math. Model. 70, 605–625 (2019)

    Article  Google Scholar 

  31. Razmi, J., Yousefi, M., Barati, M.: A stochastic model for operating room unique equipment planning under uncertainty. IFAC-PapersOnLine 48(3), 1796–1801 (2015)

    Article  Google Scholar 

  32. Saadouli, H., Jerbi, B., Dammaka, A., Masmoudi, L., Bouaziz, A.: A stochastic optimization and simulation approach for scheduling operating rooms and recovery beds in an orthopedic surgery department. Comput. Ind. Eng. 80(2015), 72–79 (2015)

    Article  Google Scholar 

  33. Santibanez, P., Begen, M., Atkins, D.: Surgical block scheduling in a system of hospitals: an application to resource and wait list management in a British Columbia health authority. Health Care Manag. Sci. 103(2007), 269–282 (2007)

    Article  Google Scholar 

  34. Saremi, A., Jula, P., ElMekkawy, T., Wang, G.G.: Appointment scheduling of outpatient surgical services in a multistage operating room department. Int. J. Prod. Econ. 141(2), 646–658 (2013)

    Article  Google Scholar 

  35. Saremia, A., Julab, P., ElMekkawyc, T., Wang, G.G.: Bi-criteria appointment scheduling of patients with heterogeneous service sequences. Expert Syst. Appl. 42(8), 4029–4041 (2015)

    Article  Google Scholar 

  36. Vijayakumar, B., Parikh, P.J., Scott, R., Barnes, A., Gallimore, J.: A dual bin-packing approach to scheduling surgical cases at a publicly-funded hospital. Eur. J. Oper. Res. 224, 583–591 (2013)

    Article  Google Scholar 

  37. Wang, S., Su, H., Wan, G.: Resource-constrained machine scheduling with machine eligibility restriction and its applications to surgical operations scheduling. J. Comb. Optim. 30(4), 982–995 (2015)

    Article  Google Scholar 

  38. Wang, T., Meskens, N., Duvivier, D.: Scheduling operating theatres: mixed integer programming vs. constraint programming. Eur. J. Oper. Res. 247(2,1), 401–413 (2015)

    Article  Google Scholar 

  39. Zhao, Z., Li, X.: Scheduling elective surgeries with sequence-dependent setup times to multiple operating rooms using constraint programming. Oper. Res. Health Care (2014)

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Mohammad Mahdi Nasiri.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Nasiri, M.M., Shakouhi, F. & Jolai, F. A fuzzy robust stochastic mathematical programming approach for multi-objective scheduling of the surgical cases. OPSEARCH 56, 890–910 (2019). https://doi.org/10.1007/s12597-019-00379-y

Download citation

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12597-019-00379-y

Keywords

Navigation