Abstract
In this paper, we evaluate the impact on welfare implications of a 0-1 linear programming model to solve the Operating Room (OR) planning problem, taking a patient perspective. In particular, given a General Surgery Department made up of different surgical sub-specialties sharing a given number of OR block times, the model determines, during a given planning period, the allocation of those blocks to surgical sub-specialties, i.e. the so called Master Surgical Schedule Problem (MSSP), together with the subsets of elective patients to be operated on in each block time, i.e. the so called Surgical Case Assignment Problem (SCAP). The innovation of the model is two-fold. The first is that OR allocation is “optimal” if the available OR blocks are scheduled simultaneously to the proper sub-specialty, at the proper time to the proper patient. The second is defining what “proper” means and include that in the objective function. In our approach what is important is not number of patients who can be treated in a given period but how much welfare loss, due to clinical deterioration or other negative consequences related to excessive waiting, can be prevented. In other words we assume a societal perspective in that we focus on “outcome” (health improving or preventing from worsening) rather than on “output” (delivered procedures). The model can be used both to develop weekly OR planning with given resources (operational decision), and to perform “what if” scenario analysis regarding how to increase the amount of OR time available for the entire department (tactical decision). The model performance is verified by applying it to a real scenario, the elective admissions of the General Surgery Department of the San Martino University Hospital in Genova (Italy). Despite the complexity of this NP-hard combinatorial optimization problem, computational results indicate that the model can solve all test problems within 600 s and an average optimality tolerance of less than 0,01%.
References
Dexter F, Macario A (2002) Changing allocations of operating room time from a system based on historical utilization to one where the aim is to schedule as many surgical cases as possible. Anesth Analg 94:1272–1279. doi:10.1097/00000539-200205000-00042
Blake JT, Carter MW (2002) A goal programming approach to strategic resource allocation in acute care hospitals. Eur J Oper Res 140:541–561. doi:10.1016/S0377-2217(01)00219-3
Dexter F, Ledolter J, Wachtel RE (2005) Tactical decision making for selective expansion of operating room resources incorporating financial criteria and uncertainty in sub-specialties’ future workloads. Anesth Analg 100:1425–1432. doi:10.1213/01.ANE.0000149898.45044.3D
Blake JT, Dexter F, Donald J (2002) Operating room manager’s use of integer programming for assigning block time to surgical groups: A case study. Anesth Analg 94:143–148. doi:10.1097/00000539-200201000-00027
Jebali A, Alouane AB, Ladet P (2006) Operating rooms scheduling. Int J Prod Econ 99:52–62. doi:10.1016/j.ijpe.2004.12.006
Guinet A, Chaabane S (2003) Operating theatre planning. Int J Prod Econ 85:69–81. doi:10.1016/S0925-5273(03)00087-2
Ozkarahan I (2000) Allocation of surgeries to operating rooms using goal programming. J Med Syst 24(6):339–378. doi:10.1023/A:1005548727003
Testi A, Tanfani E, Torre GC (2007) A three phase approach for operating theatre schedules. Health Care Manage Sci 10:163–172. doi:10.1007/s10729-007-9011-1
Fei H, Chu C, Meskens N, Artiba A (2008) Solving surgical cases assignment problem by a branch-and-price approach. Int J Prod Econ 112:96–108. doi:10.1016/j.ijpe.2006.08.030
Pham DN, Klinkert A (2008) Surgical case scheduling as a generalized job shop scheduling problem. Eur J Oper Res 185:1011–1025. doi:10.1016/j.ejor.2006.03.059
Tànfani E, Testi A (2008) Planning surgical activities: a societal point of view. In press on Proceedings of the 33rd International Conference on Operational Research Applied to Health Services (ORAHS 07)
Testi A, Tanfani E, Valente R, Ansaldo GL, Torre GC (2008) Prioritizing surgical waiting lists. J Eval Clin Pract 14(1):59–64. doi:10.1111/j1365-2753.2007.00794.x
Wachtel RE, Dexter F (2008) Tactical increases in Operating Room Block Time for Capacity Planning Should Not Be Based on Utilization. Anesth Analg 106(1):215–226
Belien J, Demeulemeester E (2008) A branch-and-price approach for integrating nurse and surgery scheduling. Eur J Oper Res 189(3):652–668. doi:10.1016/j.ejor.2006.10.060
Belien J (2007) Exact and heuristic methodologies for scheduling in hospitals: problems, formulations and algorithms. 4OR. 5(2):157–160. doi:10.1007/s10288-006-0006-4
Wullink G, van Houdenhoven M, Hans EW, van OOstrum JM, van der Lans M, Kazemier G (2007) Closing emergency operating rooms improves efficiency. J Med Syst 31(6):543–546. doi:10.1007/s10916-007-9096-6
Hans E, Wullink G, van Houdenhoven M, Kazemier G (2008) Robust surgery loading. Eur J Oper Res Volume 185(3):1038–1050. doi:10.1016/j.ejor.2006.08.022
Denton B, Viapiano J, Vogl A (2007) Optimization of surgery sequencing and scheduling decisions under uncertainty. Health Care Manage Sci 10:13–24. doi:10.1007/s10729-006-9005-4
van Oostrum JM, van Houdenhoven M, Hurink JL, Hans EW, Wullink G, Kazemier G (2008) A master surgical scheduling approach for cyclic scheduling in operating room departments. OR-Spectrum 30:355–374. doi:10.1007/s00291-006-0068-x
Chaabane S, Meskens N, Guinet A, Laurent M (2006) Comparison of two methods of operating theatre planning: application in Belgian hospital (2007). Proceedings of the International Conference on Service Systems and Service Management (ICSSSM’06) 1:386–392
Mullen PM (2003) Prioritising waiting lists: how and why? Eur J Oper Res 150(1):32–45. doi:10.1016/S0377-2217(02)00779-8
Vissers J, Adan I, Dellaert N (2007) Developing a platform for comparison of hospital admission systems: an illustration. Eur J Oper Res 180:1290–1301. doi:10.1016/j.ejor.2006.04.034
Wolsey LA (1999) Integer Programming. Wiley
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Appendix
Appendix
1.1 Basic Notation
- I :
-
set of patients, i ∈{1,2,...,n};
- W :
-
set of surgical sub-specialies, w ∈{1,2,...,m};
- K :
-
set of operating rooms, k ∈{1,2,...,c};
- T :
-
set of days belonging to the planning horizon, t ∈{1,2, ...,b};
- O :
-
set of block times, o ∈{1,2,...,v};
- I w :
-
subset of patients who belong to surgical sub-specialty w, so that I w ⊆I, I w ∩I z = Ø w,z∈W , \(\bigcup\limits_{w = 1}^m {I_w } = I\) and \(\left| {\left. {I_w } \right| \geqslant } \right.\left. {\left| {I_{w + 1} } \right.} \right|\);
- d i :
-
date of referral of patient i;
- p i :
-
Expected operating time (EOT) of patient i;
- α i :
-
Expected length of stay (ELOS) of patient i;
- ρ i :
-
urgency coefficient of patient i related to its URG;
- I h :
-
subset of patients who have an expected length of stay h, so that patients belong to I h if and only if α i =h;
- T h :
-
subset of days when patient i, \(\forall \) i∈I h , cannot be operated on;
- s kt :
-
block time length, i.e. number of hours available for surgery in OR k and day t;
- f kt :
-
maximum overtime (in hours) available in OR k and day t;
- l w :
-
lower bound on the minimum # of block times to be assigned to sub-specialty w;
- u w :
-
upper bound on the maximum # of block times to be assigned to sub-specialty w;
- e w :
-
# of operating teams/surgeons belonging to sub-specialty w;
- g t :
-
# of beds available on day t;
- q t :
-
# of ICU beds available on day t;
- β i :
-
1 if patient i needs an ICU bed after operation, 0 otherwise;
- N :
-
maximum # of patients to be scheduled in the planning horizon;
1.2 Model formulation
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Testi, A., Tànfani, E. Tactical and operational decisions for operating room planning: Efficiency and welfare implications. Health Care Manag Sci 12, 363–373 (2009). https://doi.org/10.1007/s10729-008-9093-4
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DOI: https://doi.org/10.1007/s10729-008-9093-4