Abstract
In some hospitals, an “open scheduling” strategy is applied to solve the operating room planning problem; i.e., surgeons can choose any workday for his surgical cases, and the staffing of anesthetists and nurses is adjusted to maximize the efficiency of operating room utilization. In this paper, we aim at obtaining an efficient operating program for an operating theatre with several multifunctional operating rooms by using this “open scheduling” strategy. First, a mathematical model is constructed to assign surgical cases to operating rooms within one week. This model complies with the availability of operating rooms and surgeons, and its objective is not only to maximize utilization of operating rooms, but to minimize their overtime cost. Then a column-generation-based heuristic (CGBH) procedure is proposed, where four different criteria are compared with each other so as to find a solution with the best performance. In addition, the best approximate solution, obtained by this CGBH procedure after running all the criteria proposed, is compared with the lower bound obtained by an explicit column generation (CG) procedure, LP, to evaluate the distance between the approximate solution obtained and the optimum one. Although no criterion, according to the experimental results, is found superior to all other three in both robustness and quality of the solution obtained, it is found that the best solution obtained among those four criteria is often very close to LP, which means that the proposed algorithm can obtain a near optimal solution. In one word, the CGBH procedure proposed in this paper can obtain an efficient assignment of the surgical cases if the other resources (anesthesia and nursing staff, equipment, beds in the recovery room and etc.) are well organized.
Similar content being viewed by others
References
Barnhart, C., Johnson, E. L., Nemhauser, G. L., Savelsbergh, M. W. P., & Vance, P. H. (1998). Branch-and-price: column generation for solving huge integer programs. Operations Research, 46, 316–329.
Blake, J. T., Dexter, F., & Donald, J. (2002). Operating room manager’s use of integer programming for assigning block time to surgical groups: A case study. Anesthesia and Analgesia, 94, 143–148.
Chen, Z., & Powell, W. B. (1999). Solving parallel machine scheduling problems by column generation. Journal of Computing, 11(1), 78–94.
Combes, C., Dussauchoy, A., Chaabane, S., Smolski, N., Viale, J. P., & Souquet, J. C. (2004). Démarche méthodologique d’analyse des données pour la planification des blocs opératoires: une application à un service d’endoscopie, Actes GISEH’04, Mons, Belgium.
Corens, D., (2007). Belgium: Health system review. S. Merkur, N. Jemiai & W. Palm (Eds.), Health systems in transition, 9(2). World Health Organization.
Dantzig, G. B., & Wolfe, P. (1960). Decomposition principle for linear programs. Operations Research, 8, 101–111.
Dexter, F. (2000). A strategy to decide whether to move the last case of the day in an operating room to other empty operating room to decrease overtime labor costs. International Anesthesia Research Society, 91, 925–928.
Dexter, F., Macario, A., & Traub, R. D. (1999). Which algorithm for scheduling add-on Elective cases maximizes operating room utilization? Anesthesiology, 91, 1491–1500.
Dexter, F., Traub, R. D., & Macario, A. (2003). How to release allocated operating room time to increase efficiency: predicting which surgical service will have the most underutilized operating room time. Anesthesia and Analgesia, 96, 507–512.
Fei, H., Combes, C., Meskens, N., & Chu, C. (2006). Endoscopy scheduling problem: a case study, INCOM2006 (pp. 635–640), st-Etienne, France.
Gordon, T., Lyles, A. P. S., & Fountain, J. (1988). Surgical unit time utilization review: Resource utilization and management implications. Journal of Medical Systems, 12, 169–179.
Guinet, A., & Chaabane, S. (2003). Operating theatre planning. International Journal of Production Economics, 85(1), 69–81.
Jebali, A., Hadj Alouane, A. B., & Ladet, P. (2006). Operating room scheduling. International Journal of Productions Economics, 99, 52–62.
Macario, A., Vitez, T. S., Dunn, B., & Mcdonaled, T. (1995). Where are the costs in perioperative care? Anesthesiology, 83(6), 2–4.
Martello, S., & Toth, P. (1990). Knapsack problems: algorithms and computer implementation. New York: Wiley.
Ozkarahan, I. (1995). Allocation of surgical procedures to operating rooms. Journal of Medical Systems, 19, 333–352.
Ozkarahan, I. (2000). Allocation of surgeries to operating rooms using goal programming. Journal of Medical Systems, 24(6), 339–378.
Patterson, P. (1996). What makes a well-oiled scheduling system. OR Manager, 12(9), 19–23.
Valvério de Carvalho, J. M. V. (1998). Exact solution of cutting stock problems using column generation and branch-and-bound. International Transactions in Operational Research, 5(1), 35–44.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Fei, H., Chu, C. & Meskens, N. Solving a tactical operating room planning problem by a column-generation-based heuristic procedure with four criteria. Ann Oper Res 166, 91–108 (2009). https://doi.org/10.1007/s10479-008-0413-3
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10479-008-0413-3