An mathematical model for surgery scheduling with considering Intensive Care Unit capacity constraint and multiple treatment routes

Document Type : Research Paper


1 گروه مهندسی صنایع، دانشگاه پیام نور، تهران، ایران

2 مهندسی صنایع، دانشگاه پیام نور، واحد تهران شمال، تهران، ایران


Scheduling and sequencing operations, as a decision making process, plays an integral role in most manufacturing and producing systems as well as most services environments. Scheduling is especially important in the field of healthcare. The proper scheduling of health wards in a hospital can lead to the optimum use of resources and reduce the cost of staff, overtimes of surgeons, nurses, anesthesiologists and so forth. Along with these achievements, the proper scheduling with the reduction of the waiting time of patients for the reception of services and accelerating the provision of services to emergency patients can upgrade the level of service provision. In this research, the problem of planning and scheduling of the operating room in the heart surgery department is examined. This scheduling is done due to the capacity constraint of the intensive care unit. A very important point in this study is that there are multiple treatment routes for treating patients. In this study first, the pathway for treating patients is estimated by a multinomial logistic regression model. Then the planning and scheduling of patients is done using a mixed integer mathematical model. The goal of this scheduling is to minimize the total treatment time, length of stay and waiting time of patients. In order to measure the effectiveness of the proposed models, the data and processes of the heart center of Tehran have been used.


Main Subjects

  1. عتیقه چیان، آرزو، (1390) . » زمان بندی عمل های جراحی با مدت زمان احتمالی« . رسالۀ دکتری رشدتۀ مهندسد ی صدنا یع، دانشدگاه تربیدت مددرس
  2. Guerriero, F., and Guido, R., (2011). “Operational Research in the Management of the Operating Theatre: A Survey”, Health Care Management Science, Vol. 14, No.1, PP.89-114.
  3. Fei, H., Chu, C., and Meskens, N., (2009). “Solving a Tactical Operating Room Planning Problem by a Column-Generation-Based Heuristic Procedure with Four Criteria”, Annals of Operations Research, Vol. 166, No. 1, PP. 91-108.
  4. Testi, A., Tanfani, E., and Torre, G., (2007). “A Three-Phase Approach for Operating Theatre Schedules”, Health Care Management Science, Vol. 10, No. 2, PP.163-172.
  5. Magerlein, J. M., and Martin, J. B., (1978). “Surgical Demand Scheduling: A Review”, Health Services Research, Vol. 13, No. 4, PP. 418- 433
  6. Ogulata, S. N., and Erol, R., (2003). “A Hierarchical Multiple Criteria Mathematical Programming Approach for Scheduling General Surgery Operations in Large Hospitals”, Journal of Medical Systems, Vol. 27, No. 3, PP. 259-270.
  7. Denton, B. T., Rahman, A. S., Nelson, H., and Bailey, A. C., (2006). “Simulation of a Multiple Operating Room Surgical Suite”, In Simulation Conference, PP. 414-424.
  8. Mancilla, C., and Storer, R. H., (2012). “Stochastic Integer Programming Based Algorithms for Adaptable Open Block Surgery Scheduling”, Industrial and System Engineering.
  9. Lee, S., and Yih, Y., (2014). “Reducing Patient-Flow Delays in Surgical Suites Through Determining Start-

       Times of Surgical Cases”, European Journal of Operational Research, Vol. 238, No. 2, PP. 620-629.

  1. Bruni, M. E., Beraldi, P., and Conforti, D. (2015). “A Stochastic Programming Approach for Operating Theatre Scheduling Under Uncertainty”, IMA Journal of Management Mathematics, Vol. 26, No. 1, PP. 99-119.
  2. Bai, M., Storer, R. H., and Tonkay, G. L., (2016). “A Sample Gradient-Based Algorithm for a Multiple-Or and Pacu Surgery Scheduling Problem”, IISE Transactions, Vol. 49, No. 4, PP. 367-380.
  3. Bam, M., Denton, B. T., Van Oyen, M. P., and Cowen, M. E., (2017). “Surgery Scheduling with Recovery Resources”, IISE Transactions, Vol. 49, No. 10, PP. 942-955.
  4. Wang, J., Guo, H., Bakker, M., and Tsui, K., (2018). “An Integrated Approach for Surgery Scheduling under Uncertainty”, Computers and Industrial Engineering, Vol. 118, No. 1, PP.1-8.
  5. Marques, I., Captivo, E., and Barros, N., (2019). “Optimizing the Master Surgery Schedule in s Private Hospital”, Operations Research for Health Care, Vol. 20, No. 1, Pp. 11-24.
  6. ناظریانی، محمدرضا، ابراهیم نژاد، سعداله و موسوی، سیدامیرحسین. (1394) . »حل مسللۀ برنامه زمان بندی اتاق های عمل با استفاده از رویکرد کلونی بهینه سازی مورچگان« . اولین کنفرانس بین المللی مهندسی صنایع، مدیریت و حسابداری، تهران.


  1. Eskandari, H., and Bahrami, M. (2017). “Multi-Objective Operating Room Scheduling Using Simulation-Based Optimization”, Journal of Industrial Engineering, Vol. 51, No. 1, PP. 1-13.
  2. Barkaoui, K., Dechambre, P., and Hachicha, R., (2002). “Verification and Optimization of an Operating Room Workflow. In System Sciences, HICSS”, Proceedings of the 35th Annual Hawaii International Conference on, PP. 2581-2590.
  3. Huschka, T. R., Denton, B. T., Gul, S., and Fowler, J. W. (207). “Bi-Criteria Evaluation of an Outpatient Procedure Center Via Simulation”, In Proceedings of the 39th Conference on Winter Simulation: 40 Years! The Best Is Yet To Come, PP. 1510-1518.
  4. Chu, F., and Meskens, N., (2009). “Solving a Tactical Operating Room Planning Problem by a Column-Generation-Based Heuristic Procedure with Four Criteria”, Annals of Operations Research, Vol. 166, No.1, PP. 83-91.
  5. Min, D., and Yih, Y., (2010). “Scheduling Elective Surgery Under Uncertainty and Downstream Capacity Constraints”, European Journal of Operational Research, Vol. 206, No. 3, PP. 642-652.
  6. Niu, Q., Peng, Q., El Mekkawy, T., Tan, Y. Y., Bruant, H., and Bernaerdt, L., (2011). “Performance Analysis of the Operating Room Using Simulation”, Proceedings of the Canadian Engineering Education Association.
  7. Saremi, A., Jula, P., Elmekkawy, T., and Wang, G. G., (2012). “Appointment Scheduling of Outpatient Surgical Services in a Multistage Operating Room Department”, International Journal of Production Economics, Vol. 141, No. 2, PP. 646-658.
  8. Saremi, A., Jula, P., Elmekkawy, T., and Wang, G. G., (2014). “Bi-Criteria Appointment Scheduling of Patients with Heterogeneous Service Sequences”, Expert Systems with Applications, Vol. 42, No. 8, PP. 4029-4041.
  9. Astaraky, D., and Patrick, J., (2015). “A Simulation Based Approximate Dynamic Programming Approach to Multi-Class, Multi-Resource Surgical Scheduling”, European Journal Of Operational Research, Vol. 245, No. 1, PP. 309-319.
  10. Siqueira, C. L., Arruda, E. F., Bahiense, L., Bahr, G. L., and Motta, G. R. (2016). “Long-Term Integrated Surgery Room Optimization and Recovery Ward Planning, with a Case Study in the Brazilian National Institute of Traumatology and Orthopedics (INTO)”, European Journal of Operational Research, Vol. 264, No. 3, PP. 870-883.
  11. Agresti, A., (2002). “Categorical Data Analysis”, New Jersey: John Wiley and Sons, Inc.