Operating room scheduling is an important operational problem in most hospitals. In this paper, a novel mixed integer programming (MIP) model is presented for minimizing Cmax and operating room idle times in hospitals. Using this model, we can determine the allocation of resources including operating rooms, surgeons, and assistant surgeons to surgeries, moreover the sequence of surgeries within operating rooms and the start time of them. The main features of the model will include the chronologic curriculum plan for training residents and the real-life constraints to be observed in teaching hospitals. The proposed model is evaluated against some real-life problems, by comparing the schedule obtained from the model and the one currently developed by the hospital staff. Numerical results indicate the efficiency of the proposed model compared to the real-life hospital scheduling, and the gap evaluations for the instances show that the results are generally satisfactory. 1. Introduction Health care expenditures comprise a meaningful portion of the Gross Domestic Product in both developed and developing countries. Expenditure on healthcare in the UK as a percentage of the UK Gross Domestic Product (GDP) was estimated to be 8.4% in 2007, from which the public share was 69% [1]. Also, according to the statics released by the WHO (World Health Organization), health care expenditures in 2007 in Iran as a developing country were estimated to be about 6.4% of its GDP, and the portion covered by the government was about 46.8%. This fact makes health systems an important research field for industrial engineering and operations research to improve their operational efficiency. Operating rooms are simultaneously the largest cost centers and the greatest source of revenues for most hospitals. OR planning and scheduling is a key tool which can be useful to improve the productivity level of ORs and the related departments. Basically, there are three OR scheduling strategies commonly employed:(1)blocked scheduling strategy,(2)open scheduling strategy, and(3)modified scheduling strategy. Under a blocked scheduling strategy, individual surgeons or surgical groups are assigned times in a particular OR in a periodic (typically weekly or monthly) schedule. The planning within the framework of a blocked strategy consists of three stages. In the first stage, the OR capacity is divided among the surgeons, surgical groups, or departments on a strategic level. Then, a cyclic timetable called “Master Surgical Schedule” is constructed that defines the number and type of operating
References
[1]
J. Haynes, UK Centre for the Measurement of Government Activity Expenditure on Healthcare in the UK, The Office of Public Sector Information, Norwich, UK, 2010.
[2]
S. Chaabane, N. Meskens, A. Guinet, and M. Laurent, “Comparison of two methods of operating theatre planning: application in Belgian hospital,” in Proceedings of the International Conference on Service Systems and Service Management (ICSSSM '06), Troyes, France, October 2006.
[3]
J. M. Magerlein and J. B. Martin, “Surgical demand scheduling: a review,” Health Services Research, vol. 13, no. 4, pp. 418–433, 1978.
[4]
D. N. Pham and A. Klinkert, “Surgical case scheduling as a generalized job shop scheduling problem,” European Journal of Operational Research, vol. 185, no. 3, pp. 1011–1025, 2008.
[5]
B. Roland, C. D. Martinelly, F. Riane, and Y. Pochet, “Scheduling an operating theatre under human resource constraints,” Computers and Industrial Engineering, vol. 58, no. 2, pp. 212–220, 2010.
[6]
J. T. Blake and M. W. Carter, “Surgical process scheduling: a structured review,” Journal of the Society for Health Systems, vol. 5, no. 3, pp. 17–30, 1997.
[7]
B. Cardoen, E. Demeulemeester, and J. Belien, “Operating room planning and scheduling: a literature review,” European Journal of Operational Research, vol. 201, no. 3, pp. 921–932, 2010.
[8]
M. Kennedy, Bin-packing, knapsack and chance constrained approaches to scheduling operating rooms, Ph.D. thesis, Rensselaer Polytechnic Institute, Troy, NY, USA, 1992.
[9]
S. N. Ogulata and R. Erol, “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, 2003.
[10]
J. Vissers, I. Adan, and J. A. Bekkers, “Patient mix optimization in tactical cardiothoracic surgery planning: a case study,” IMA Journal of Management Mathematics, vol. 16, no. 3, pp. 281–304, 2005.
[11]
A. Jebali, A. B. Hadj Alouane, and P. Ladet, “Operating rooms scheduling,” International Journal of Production Economics, vol. 99, no. 1-2, pp. 52–62, 2006.
[12]
A. Testi, E. Tanfani, and G. Torre, “A three-phase approach for operating theatre schedules,” Health Care Management Science, vol. 10, no. 2, pp. 163–172, 2007.
[13]
H. Fei, C. Chu, N. Meskens, and A. Artiba, “Solving surgical cases assignment problem by a branch-and-price approach,” International Journal of Production Economics, vol. 112, no. 1, pp. 96–108, 2008.
[14]
A. Riis and E. Burke, “Surgery allocation and scheduling,” in Proceedings of the 7th International Conference on the Practice and Theory of Automated Timetabling, Montreal, Canada, 2008.
[15]
B. Cardoen, E. Demeulemeester, and J. Beli？n, “Sequencing surgical cases in a day-care environment: an exact branch-and-price approach,” Computers and Operations Research, vol. 36, no. 9, pp. 2660–2669, 2009.
[16]
H. Fei, C. Chu, N. Meskens, and A. Artiba, “A planning and scheduling problem for an operating theatre using an open scheduling strategy,” Computers and Industrial Engineering, vol. 58, no. 2, pp. 221–230, 2010.
[17]
A. Hanset, N. Meskens, and D. Duvivier, “Using constraint programming to schedule an operating theatre,” in Proceedings of the IEEE Workshop on Health Care Management (WHCM '10), pp. 1–6, February 2010.
[18]
A. Hanset, N. Mesken, and D. Duvivier, “Comparison of two models to schedule the operating theatre,” in Proceedings of the 8th International Conference of Modeling and Simulation (MOSIM '10), Hammamet, Tunisia, May 2010.
[19]
S. Topaloglu and I. Ozkarahan, “A constraint programming-based solution approach for medical resident scheduling problems,” Computers & Operations Research, vol. 38, no. 1, pp. 246–255, 2011.
[20]
H. D. Sherali, M. H. Ramahi, and J. Saifeeq, “Hospital resident scheduling problem,” Production Planning and Control, vol. 13, no. 2, pp. 220–233, 2002.
[21]
F. Dexter, R. E. Wachtel, R. H. Epstein, J. Ledolter, and M. M. Todd, “Analysis of operating room allocations to optimize scheduling of specialty rotations for anesthesia trainees,” Anesthesia and Analgesia, vol. 111, no. 2, pp. 520–524, 2010.
