A mixed integer programming approach for allocating operating room capacity

  • B Zhang
  • P Murali
  • M M Dessouky
  • D Belson
Case-Oriented Paper


We have developed a methodology for allocating operating room capacity to specialties. Our methodology consists of a finite-horizon mixed integer programming (MIP) model which determines a weekly operating room allocation template that minimizes inpatients' cost measured as their length of stay. A number of patient type priority (eg emergency over non-emergency patient) and clinical constraints (eg maximum number of hours allocated to each specialty, surgeon, and staff availability) are included in the formulation. The optimal solution from the analytical model is inputted into a simulation model that captures some of the randomness of the processes (eg surgery time, demand, arrival time, and no-show rate of the outpatients) and non-linearities (eg the MIP assumes proportional allocation of demand satisfaction (output) with room allocation (input)). The simulation model outputs the average length of stay for each specialty and the room utilization. On a case example of a Los Angeles County Hospital, we show how the hospital length of stay pertaining to surgery can be reduced.


mixed integer programming surgery operating room capacity block time scheduling simulation 


  1. Belien J and Demeulemeester E (2007). Building cyclic master surgery schedules with leveled resulting bed occupancy. Eur J Opl Res 176: 1185–1204.CrossRefGoogle Scholar
  2. Blake JT and Carter MW (2002). A goal programming approach to strategic resource allocation in acute care hospitals. Eur J Opl Res 140: 541–561.CrossRefGoogle Scholar
  3. Blake JT and Donald J (2002). Mount Sinai Hospital uses integer programming to allocate operating room time. Interfaces 32(2): 63–73.CrossRefGoogle Scholar
  4. Blake JT, Dexter F and Donald J (2002). Operating room managers' use of integer programming for assigning block time to surgical groups: a case study. Anesth Analg 94: 143–148.Google Scholar
  5. Clinical Scholars Program (2006). Interim Report July 2005–February 2006, UCLA—The Robert Wood Johnson Foundation. http://www.hsrcenter.ucla.edu/csp/sitevisit2006/Handouts/REVISED_UCLARJW_05-06_Internimrpt.doc, accessed 29 April 2007.
  6. Dexter F and Traub RD (2002). How to schedule elective surgical cases into specific operating rooms to maximize the efficiency of use of operating room time. Anesth Analg 94: 933–942.CrossRefGoogle Scholar
  7. Dexter F, Macario A and Traub RD (1999a). Which algorithm for scheduling add-on elective cases maximizes operating room utilization? Anesthesiology 91: 1491–1500.CrossRefGoogle Scholar
  8. Dexter F, Macario A, Traub RD, Hopwood M and Lubarsky DA (1999b). An operating room scheduling strategy to maximize the use of operating room block time: computer simulation of patient scheduling and survey of patients' preferences for surgical waiting time. Anesth Analg 89: 7–20.Google Scholar
  9. Dexter F, Blake JT, Penning DH, Sloan B, Chung P and Lubarsky DA (2002). Use of linear programming to estimate impact of changes in a hospital's operating room time allocation on perioperative variable costs. Anesthesiology 96: 718–724.CrossRefGoogle Scholar
  10. Gerchak Y, Gupta D and Henig M (1996). Reservation planning for elective surgery under uncertain demand for emergency surgery. Mngt Sci 42: 321–334.CrossRefGoogle Scholar
  11. Kourie DG (1975). A length of stay index to monitor efficiency of service to general surgery in-patients. Opl Res Quart 26 (Part 1): 63–69.Google Scholar
  12. Kuzdrall PJ, Kwak NK and Schmitz HH (1974). The Monte Carlo simulation of operating-room and recovery-room usage. Oper Res 22: 434–440.CrossRefGoogle Scholar
  13. Lapierre SD, Batson C and McCaskey S (1999). Improving on-time performance in healthcare organizations: a case study. Health Care Mngt Sci 2: 27–34.CrossRefGoogle Scholar
  14. Litvak E and Long MC (2000). Cost and quality under managed care: Irreconcilable differences. Am J Managed Care 6: 305–312.Google Scholar
  15. Marshall A, Vasilakis C and El-Darzi E (2005). Length of stay-based patient flow models: recent developments and future directions. Health Care Mngt Sci 8: 213–220.CrossRefGoogle Scholar
  16. May JH, Strum DP and Vargas LG (2000). Fitting the lognormal distribution to surgical procedure times. Decision Sci 31: 129–148.CrossRefGoogle Scholar
  17. Ogulata SN and Erol R (2003). A hierarchical multiple criteria mathematical programming approach for scheduling general surgery operations in large hospitals. J Med Syst 27: 259–270.CrossRefGoogle Scholar
  18. Ozkarahan I (2000). Allocation of surgeries to operating rooms by goal programming. J Med Sys 24: 339–378.CrossRefGoogle Scholar
  19. Pritsker AAB and O'Reilly JJ (1999). Simulation with Visual SLAM and AweSim, (2nd edn). John Wiley & Sons, New York, and Systems Publishing Corporation: West Lafayette, Indiana.Google Scholar
  20. Schmitz HH and Kwak NK (1972). Monte carlo simulation of operating-room and recovery-room usage. Oper Res 20: 1171–1180.CrossRefGoogle Scholar
  21. Sier D, Tobin P and McGurk C (1997). Scheduling surgical procedures. J Opl Res Soc 48: 884–891.CrossRefGoogle Scholar
  22. Spangler WE, Strum DP, Vargas LG and May JH (2004). Estimating procedure times for surgeries by determining location parameters for the lognormal model. Health Care Mngt Sci 7: 97–104.CrossRefGoogle Scholar
  23. Strum DP, May JH and Vargas LG (2000). Modelling the uncertainty of surgical procedure times: comparison of log-normal and normal models. Anesthesiology 92: 1160–1167.CrossRefGoogle Scholar
  24. Vasilakis C, Sobolev BG, Kuramoto L and Levy AR (2007). A Simulation study of scheduling clinical appointments in surgical care. J Opl Res Soc 58: 202–211.CrossRefGoogle Scholar

Copyright information

© Palgrave Macmillan 2008

Authors and Affiliations

  • B Zhang
    • 1
  • P Murali
    • 1
  • M M Dessouky
    • 1
  • D Belson
    • 1
  1. 1.University of Southern CaliforniaLos AngelesUSA

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