Korean Management Science Review (경영과학)

The Korean Operations Research and Management Science Society (한국경영과학회)
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Stochastic Programming Approach to Scheduling Elective Surgeries and the Effects of Newsvendor Ratio on Operating Room Utilization

추계적 계획법을 이용한 수술실 예약 모델과 Newsvendor 비율의 자원 효율성에 대한 영향 분석

  • Received : 2011.03.04
  • Accepted : 2011.07.13
  • Published : 2011.07.31
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Abstract

The purpose of this paper is to schedule elective surgery patients using a stochastic programming approach and to illustrate how operating room utilization behaves when a decision-maker varies costs associated with utilization. Because of the uncertainty in surgery durations, the underage and overage costs that a decision-maker considers plays an important role in allocating surgery cases into available operating room capacity. We formulate the problem as a stochastic mixed integer programming and propose a sampling-based approximation method for a computational purpose. Newsvendor model is employed to explain the results from numerical experiments that are conducted with the actual data from a hospital. The results show that the operating room utilization is more sensitive when the unit overtime cost is relatively larger than the unit cost for underutilized time.

Keywords

References

  1. Adan, I.J.B.F. and J.M.H. Vissers, "Patient Mix Optimization in Hospital Admission Planning:A Case Study," International Journal of Operations and Production Management, Vol.22, No.4(2002), pp.445-461. https://doi.org/10.1108/01443570210420430
  2. Ahmed, S. and A. Shapiro, "The Sample Average Approximation Method for Stochastic Programs with Integer Recourse," Technical Report, School of Industrial and Systems Engineering, Georgia Institute of Technology, 2002.
  3. Ayhan, H., J. Dai, R.D. Foley, and J. Wu, Newsvendor Notes, ISyE 3232 Stochastic Manufacturing and Service Systems, 2004.
  4. Birge, J.R. and F. Louveaux, Introduction to Stochastic Programming, Springer, New York, 1997.
  5. Blake, J.T. and J. Donald, "Mountain Sinai Hospital Uses Integer Programming to Allocate Operating Room Time," Interfaces, Vol. 32, No.2(2002), pp.63-73. https://doi.org/10.1287/inte.32.2.63.57
  6. Channel, D.A., V.B. Navarro, and P.W. Kidwell, "Operating Room Time is A Terrible Thing to Waste:An Operating Room Workimprovement Project," Insight, Vol.23(1998), pp.43-47.
  7. Dexter, F., A. Macario, and R.D. Traub, "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, Vol.91(1999), pp.1491-1500. https://doi.org/10.1097/00000542-199911000-00043
  8. Dexter, F., A. Macario, and J. Ledolter, "Identification of Systematic Underestimation(Bias) of Case Durations during Case Scheduling Would Not Markedly Reduce Overutilized Operating Room Time," Journal of Clinical Anesthesia, Vol.19, No.3(2007), pp.198-203. https://doi.org/10.1016/j.jclinane.2006.10.009
  9. Gerchak, Y., D. Gupta and M. Henig, "Reservation Planning for Elective Surgery under Uncertain Demand for Emergency Surgery," Management Science, Vol.42, No.3(1996), pp. 321-334. https://doi.org/10.1287/mnsc.42.3.321
  10. Gordon, T., S. Paul, A. Lyles, and J. Fountain, "Surgical Unit Time Utilization Review :Resource Utilization and Management Implications," Journal of Medical Systems, Vol. 12(1988), pp.169-179. https://doi.org/10.1007/BF00996639
  11. Gupta D., "Surgical Suites Operations Management," Production and Operations Management, Vol.16, No.6(2007), pp.689-700.
  12. Hurst, J. and L. Siciliani, "Tackling Excessive Waiting Times for Elective Surgery: A Comparison of Policies in Twelve OECD Countries," OECD Health Working Papers, 2003.
  13. Jebali, A., A. Alouane and P. Ladet, "Operating Rooms Scheduling," International Journal of Production Economics, Vol.99(2006), pp.52-62. https://doi.org/10.1016/j.ijpe.2004.12.006
  14. Kleywegt, A.J., A. Shapiro and Homem-de- Mello, "The Sample Average Approximation Method for Stochastic Discrete Optimization," SIAM Journal on Optimization, Vol. 12, No.2(2001), pp.479-502.
  15. Lamiri, M., X. Xie, and S. Zhang, "Column Generation Approach to Operating Theatre Planning with Elective and Emergency Patients," IIE Transactions, Vol.40, No.9(2008), pp.838-852. https://doi.org/10.1080/07408170802165831
  16. May, J.H., D.P. Strum, and L.G. Vargas, "Fitting the Lognormal Distribution to Surgical Procedure Times," Decision Sciences, Vol.31, No.1(2000), pp.129-148. https://doi.org/10.1111/j.1540-5915.2000.tb00927.x
  17. Min, D. and Y. Yih, "Scheduling Elective Surgery under Uncertainty and Downstream Capacity Constraints," European Journal of Operational Research, Vol.206(2010), pp.642-652. https://doi.org/10.1016/j.ejor.2010.03.014
  18. Olivares, M., C. Terwiesch and L. Cassorla, "Structural Estimation of The Newsvendor Model：An Application to Reserving Operating Room Time," Management Science, Vol.54, No.1(2008), pp.41-55. https://doi.org/10.1287/mnsc.1070.0756
  19. Pandit J. and A. Carey, "Estimating The Duration of Common Elective Operations:Implications for Operating List Management," Anaesthesia, Vol.61, No.8(2006), pp.768-776. https://doi.org/10.1111/j.1365-2044.2006.04719.x
  20. Shapiro, A. and T. Homem-de-Mello, "On The Rate of Convergence of Optimal Solutions of Monte Carlo Approximations of Stochastic Programs," SIAM Journal on Optimization, Vol.11, No.1(2001), p.7086.
  21. Steele, J.T., B.D. Hoyt and R.K. Simons, "Is Operating Room Resuscitation A Way to Save Time?" American Journal of Surgery, Vol.174(1997), pp.683-687. https://doi.org/10.1016/S0002-9610(97)00194-3
  22. Stodd, K., A. Ortiz and I. Tenzer, "Operating Room Benchmarking：The Kaiser Performance Experience," The Performance Journal, Vol.2, No.4(1998), pp.5-16.
  23. Strum, D.P., L.G. Varga, J.H. May and G. Bashein, "Surgical Suite Utilization and Capacity Planning:A Minimal Cost Analysis Model," Journal of Medical Systems, Vol.21, No.5(1997), pp.309-322. https://doi.org/10.1023/A:1022824725691