OR Spectrum

, Volume 30, Issue 2, pp 355–374 | Cite as

A master surgical scheduling approach for cyclic scheduling in operating room departments

  • Jeroen M. van Oostrum
  • M. Van Houdenhoven
  • J. L. Hurink
  • E. W. Hans
  • G. Wullink
  • G. Kazemier
Regular Article

Abstract

This paper addresses the problem of operating room (OR) scheduling at the tactical level of hospital planning and control. Hospitals repetitively construct operating room schedules, which is a time-consuming, tedious, and complex task. The stochasticity of the durations of surgical procedures complicates the construction of operating room schedules. In addition, unbalanced scheduling of the operating room department often causes demand fluctuation in other departments such as surgical wards and intensive care units. We propose cyclic operating room schedules, so-called master surgical schedules (MSSs) to deal with this problem. In an MSS, frequently performed elective surgical procedure types are planned in a cyclic manner. To deal with the uncertain duration of procedures we use planned slack. The problem of constructing MSSs is modeled as a mathematical program containing probabilistic constraints. Since the resulting mathematical program is computationally intractable we propose a column generation approach that maximizes the operation room utilization and levels the requirements for subsequent hospital beds such as wards and intensive care units in two subsequent phases. We tested the solution approach with data from the Erasmus Medical Center. Computational experiments show that the proposed solution approach works well for both the OR utilization and the leveling of requirements of subsequent hospital beds.

Keywords

Scheduling Master surgical schedules Healthcare planning Mathematical modeling 

Mathematics Subject Classification (2000)

90B35 

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References

  1. Bakker H, Zuurbier JJ (2002) Pareto’s law (In Dutch). Zorgvisie 7Google Scholar
  2. Barnhart C, Johnson EL, Neuhauser GL, Savelbergh MWP, Vance PH (1998) Branch-and-price: column generation for solving huge integer programs. Oper Res 46(3):316–329Google Scholar
  3. Beliën J, Demeulemeester E (2005) Building cyclic master surgery schedules with leveled resulting bed occupancy. Eur J Oper Res (in press)Google Scholar
  4. Bisschop J (1999) AIMMS – optimization modeling. Paragon Decision Technology B.V., HarlemGoogle Scholar
  5. Blake JT, Donald J (2002) Mount sinai hospital uses integer programming to allocate operating room time. Interfaces 32(2):63–73CrossRefGoogle Scholar
  6. Brucker P, Drexl A, Mohring R, Neumann K, Pesch E (1999) Resource-constrained project scheduling: notation, classification, models, and methods. Eur J Oper Res 112:3–41CrossRefGoogle Scholar
  7. Carter M (2002) Diagnosis: mismanagement of resources. Oper Res Manage Sci Today April 26–32Google Scholar
  8. Charnes A, Cooper W, Thompson G (1964) Critical path analyses via chance constrained and stochastic programming. Oper Res 12:460–470Google Scholar
  9. Dell’Olmo P, Speranza MG (1999) Approximation algorithms for partitioning small items in unequal bins to minimize the total size. Discret Appl Math 94:181–191CrossRefGoogle Scholar
  10. Gerhak Y, Gupta D, Henig M (1996) Reservation planning for elective surgery under uncertain demand for emergency surgery. Manage Sci 42(3):321–334Google Scholar
  11. Glouberman S, Mintzberg H (2001) Managing the care of health and the cure of disease Part i: Differentiation. Health Care Manage Rev 26(1):56–69Google Scholar
  12. Goldratt EM (1997) Critical chain. The North River Press, Great BarringtonGoogle Scholar
  13. Guinet A, Chaabane S (2003) Operating theatre planning. Int J Prod Econ, 85:69–81CrossRefGoogle Scholar
  14. Gupta JND, Ho JC (1999) A new heuristic algorithm for the one-dimensional bin-packing problem. Prod Plan Control 10(6):598–603CrossRefGoogle Scholar
  15. Hans EW, Wullink G, Van Houdenhoven M, Kazemier G (2006) Robust surgery loading. Eur J Oper Res (accepted for publication)Google Scholar
  16. Jebali A, Hadj Alouane AB, Ladet P (2006) Operating room scheduling. Int J Prod Econ 99:52–62CrossRefGoogle Scholar
  17. Kim S, Horowitz I (2002) Scheduling hospital services: the efficacy of elective-surgery quotas. Omega 30:335–346CrossRefGoogle Scholar
  18. Lamiri M, Xie X, Dolgui A, Grimaud F (2005) A stochastic model for operating room planning with elective and emergency surgery demands. In: Conference Proceedings ORAHS, Southampton, UKGoogle Scholar
  19. McManus ML, Long MC, Copper A, Mandell J, Berwick DM, Pagano M, Litvak E (2003) Variability in surgical caseload and access to intensive care services. Anesthesiology 98:1491–1496CrossRefGoogle Scholar
  20. Millar HH, Kiragu M (1998) Cyclic and non-cyclic scheduling of 12 h shift nurses by network programming. Eur J Oper Res 104:582–592CrossRefGoogle Scholar
  21. Neumann K, Zimmermann J (2000) Procedures for resource leveling and net present value problems in project scheduling with general temporal and resource constraints. Eur J Oper Res 127:425–443CrossRefGoogle Scholar
  22. OECD (2005) Oecd health data 2005 – statistics and indicators for 30 countriesGoogle Scholar
  23. Ogulata SN, Erol R (2003) A hierarchical multiple criteria mathematical programming approach for scheduling general surgery operatons in large hospitals. J Med Syst 27(3):259–270CrossRefGoogle Scholar
  24. Ozkaraham I (2000) Allocation of surgeries to operating rooms by goal programming. J Med Syst 24(6):339–378CrossRefGoogle Scholar
  25. Pinedo M (2005) Planning and scheduling in manufacturing and services. Springer Series in Operations Research and Financial Engineering. Springer, Berlin Heidelberg New YorkGoogle Scholar
  26. Schmidt E, Dada M, Adams D (2001) Using cyclic planning to manage capacity at alcoa. Interfaces 31(3):16–27CrossRefGoogle Scholar
  27. Sier D, Tobin P, McGurk C (1997) Scheduling surgical procedures. J Oper Res Soc 48:884–891CrossRefGoogle Scholar
  28. Strum DP, May JH, Vargas LG (2000) Modeling the uncertainty of surgical procedure times: comparison of log-normal and normal models. Anesthesiology 92:1160–1167CrossRefGoogle Scholar
  29. Tayur S (2000) Improving operations and quoting accurate lead times in a laminate plant. Interfaces 30(5):1–15CrossRefGoogle Scholar
  30. van den Akker JM, Hoogeveen JA, van de Velde SL (1999) Parallel machine scheduling by column generation. Oper Res 47(6):862–872CrossRefGoogle Scholar
  31. Vissers JMH, Adan IJBF, Bekkers JA (2005) Patient mix optimisation in cardiothoracic surgery planning: a case study. IMA J Manage Math 16(3):281–304CrossRefGoogle Scholar
  32. Weissman C (2005) The enhanced postoperative care system. J Clin Anesth 17:314–322CrossRefGoogle Scholar
  33. Williams HP (1999) Model building in mathematical programming, 4th edn. Wiley, New YorkGoogle Scholar

Copyright information

© Springer-Verlag 2006

Authors and Affiliations

  • Jeroen M. van Oostrum
    • 1
  • M. Van Houdenhoven
    • 1
  • J. L. Hurink
    • 3
  • E. W. Hans
    • 4
  • G. Wullink
    • 1
  • G. Kazemier
    • 1
    • 2
  1. 1.Department of operating rooms, Anesthesiology, and Intensive CareErasmus MCRotterdamThe Netherlands
  2. 2.Department of SurgeryErasmus MCRotterdamThe Netherlands
  3. 3.Department of Electrical Engineering, Mathematics and Computer ScienceUniversity of TwenteEnschedeThe Netherlands
  4. 4.School of Business, Public Administration and TechnologyUniversity of TwenteEnschedeThe Netherlands

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