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A mixed integer programming approach for allocating operating room capacity

Author

Listed:
  • B Zhang

    (University of Southern California)

  • P Murali

    (University of Southern California)

  • M M Dessouky

    (University of Southern California)

  • D Belson

    (University of Southern California)

Abstract

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.

Suggested Citation

  • B Zhang & P Murali & M M Dessouky & D Belson, 2009. "A mixed integer programming approach for allocating operating room capacity," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 60(5), pages 663-673, May.
    • Handle: RePEc:pal:jorsoc:v:60:y:2009:i:5:d:10.1057_palgrave.jors.2602596
    DOI: 10.1057/palgrave.jors.2602596
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    References listed on IDEAS

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    1. Homer H. Schmitz & N. K. Kwak, 1972. "Monte Carlo Simulation of Operating-Room and Recovery-Room Usage," Operations Research, INFORMS, vol. 20(6), pages 1171-1180, December.
    2. Belien, Jeroen & Demeulemeester, Erik, 2007. "Building cyclic master surgery schedules with leveled resulting bed occupancy," European Journal of Operational Research, Elsevier, vol. 176(2), pages 1185-1204, January.
    3. Blake, John T. & Carter, Michael W., 2002. "A goal programming approach to strategic resource allocation in acute care hospitals," European Journal of Operational Research, Elsevier, vol. 140(3), pages 541-561, August.
    4. Yigal Gerchak & Diwakar Gupta & Mordechai Henig, 1996. "Reservation Planning for Elective Surgery Under Uncertain Demand for Emergency Surgery," Management Science, INFORMS, vol. 42(3), pages 321-334, March.
    5. Paul J. Kuzdrall & N. K. Kwak & Homer H. Schmitz, 1974. "Technical Note—The Monte Carlo Simulation of Operating-Room and Recovery-Room Usage," Operations Research, INFORMS, vol. 22(2), pages 434-440, April.
    6. John T. Blake & Joan Donald, 2002. "Mount Sinai Hospital Uses Integer Programming to Allocate Operating Room Time," Interfaces, INFORMS, vol. 32(2), pages 63-73, April.
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    Cited by:

    1. Mahdi Noorizadegan & Abbas Seifi, 2018. "An efficient computational method for large scale surgery scheduling problems with chance constraints," Computational Optimization and Applications, Springer, vol. 69(2), pages 535-561, March.
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    3. Morteza Lalmazloumian & M. Fazle Baki & Majid Ahmadi, 2023. "A two-stage stochastic optimization framework to allocate operating room capacity in publicly-funded hospitals under uncertainty," Health Care Management Science, Springer, vol. 26(2), pages 238-260, June.
    4. Brecht Cardoen & Jeroen Beliën & Mario Vanhoucke, 2015. "On the design of custom packs: grouping of medical disposable items for surgeries," International Journal of Production Research, Taylor & Francis Journals, vol. 53(24), pages 7343-7359, December.
    5. Şeyda Gür & Tamer Eren & Hacı Mehmet Alakaş, 2019. "Surgical Operation Scheduling with Goal Programming and Constraint Programming: A Case Study," Mathematics, MDPI, vol. 7(3), pages 1-24, March.
    6. Loïc Deklerck & Babak Akbarzadeh & Broos Maenhout, 2022. "Constructing and evaluating a master surgery schedule using a service-level approach," Operational Research, Springer, vol. 22(4), pages 3663-3711, September.
    7. Mariana Oliveira & Filippo Visintin & Daniel Santos & Inês Marques, 2022. "Flexible master surgery scheduling: combining optimization and simulation in a rolling horizon approach," Flexible Services and Manufacturing Journal, Springer, vol. 34(4), pages 824-858, December.
    8. Shuwan Zhu & Wenjuan Fan & Shanlin Yang & Jun Pei & Panos M. Pardalos, 2019. "Operating room planning and surgical case scheduling: a review of literature," Journal of Combinatorial Optimization, Springer, vol. 37(3), pages 757-805, April.
    9. Zexian Zeng & Xiaolei Xie & Heidi Menaker & Susan G. Sanford-Ring & Jingshan Li, 2018. "Performance evaluation of operating room schedules in orthopedic surgery," Flexible Services and Manufacturing Journal, Springer, vol. 30(1), pages 198-223, June.
    10. Sebastian Rachuba & Brigitte Werners, 2017. "A fuzzy multi-criteria approach for robust operating room schedules," Annals of Operations Research, Springer, vol. 251(1), pages 325-350, April.
    11. Michael R. Miller & Robert J. Alexander & Vincent A. Arbige & Robert F. Dell & Steven R. Kremer & Brian P. McClune & Jane E. Oppenlander & Joshua P. Tomlin, 2017. "Optimal Allocation of Students to Naval Nuclear-Power Training Units," Interfaces, INFORMS, vol. 47(4), pages 320-335, August.
    12. Michael Samudra & Carla Van Riet & Erik Demeulemeester & Brecht Cardoen & Nancy Vansteenkiste & Frank E. Rademakers, 2016. "Scheduling operating rooms: achievements, challenges and pitfalls," Journal of Scheduling, Springer, vol. 19(5), pages 493-525, October.
    13. Choi, Sangdo & Wilhelm, Wilbert E., 2014. "An approach to optimize block surgical schedules," European Journal of Operational Research, Elsevier, vol. 235(1), pages 138-148.
    14. van den Broek d’Obrenan, Anne & Ridder, Ad & Roubos, Dennis & Stougie, Leen, 2020. "Minimizing bed occupancy variance by scheduling patients under uncertainty," European Journal of Operational Research, Elsevier, vol. 286(1), pages 336-349.
    15. Michael R. Wagner & Zinovy Radovilsky, 2012. "Optimizing Boat Resources at the U.S. Coast Guard: Deterministic and Stochastic Models," Operations Research, INFORMS, vol. 60(5), pages 1035-1049, October.
    16. Francesca Guerriero & Rosita Guido, 2011. "Operational research in the management of the operating theatre: a survey," Health Care Management Science, Springer, vol. 14(1), pages 89-114, March.

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