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Robust surgery loading. (English) Zbl 1178.90229
Summary: We consider the robust surgery loading problem for a hospital’s operating theatre department, which concerns assigning surgeries and sufficient planned slack to operating room days. The objective is to maximize capacity utilization and minimize the risk of overtime, and thus canceled patients. This research was performed in collaboration with the Erasmus MC, a large academic hospital in the Netherlands, which has also provided historical data for the experiments. We propose various constructive heuristics and local search methods that use statistical information on surgery durations to exploit the portfolio effect, and thereby to minimize the required slack. We demonstrate that our approach frees a lot of operating room capacity, which may be used to perform additional surgeries. Furthermore, we show that by combining advanced optimization techniques with extensive historical statistical records on surgery durations can significantly improve the operating room department utilization.

90B90 Case-oriented studies in operations research
90B35 Deterministic scheduling theory in operations research
Full Text: DOI
[1] Aarts, E.H.L.; Korst, J.H.M., Simulated annealing and Boltzmann machines, (1989), John Wiley & Sons New York
[2] Beliën, J.; Demeulemeester, E., Building cyclic master surgery schedules with leveled resulting bed occupancy, European journal of operational research, 176, 2, 1185-1204, (2007) · Zbl 1103.90336
[3] Blake, J.; Donald, J., Mount Sinai hospital uses integer programming to allocate operating room time, Interfaces, 32, 2, 63-73, (2002)
[4] Brehob, M.; Torng, E.; Uthaisombut, P., Applying extra-resource analysis to load balancing, Journal of scheduling, 3, 273-288, (2000) · Zbl 1153.90416
[5] Chen, B.; Potts, C.N.; Woeginger, G.J., A review of machine scheduling: complexity, algorithms and approximability, (), 21-169 · Zbl 0944.90022
[6] Cooper, D.F., Heuristics for scheduling resource-constrained projects: an experimental investigation, Management science, 22, 11, 1186-1194, (1976) · Zbl 0326.90029
[7] De Kreuk, A.C.C.; Winands, E.M.M.; Vissers, J.M.H., Master scheduling of medical specialists, ()
[8] Dell’Olmo, P.; Speranza, M.G., Approximation algorithms for partitioning small items in unequal bins to minimize the total size, Discrete applied mathematics, 94, 181-191, (1999) · Zbl 0932.68008
[9] Dexter, F., Cost implications of various operating room scheduling strategies, American society of anesthesiologist’s clinical update program, 52, 262, 1-6, (2001)
[10] Dexter, F.; Macario, A.; Traub, RD., Which algorithm for scheduling add-on elective cases maximizes operating room utilization?, Anesthesiology, 91, 1491-1500, (1999)
[11] Drexl, A., Scheduling of project networks by job assignment, Management science, 37, 1590-1602, (1991) · Zbl 0729.91011
[12] Goldman, J.; Knappenberger, H.A.; Moore, EW., An application of OR scheduling policies, Hospital management, 107, 40-51, (1969)
[13] Graham, RL., Bounds for certain multiprocessing anomalies, Bell system technical journal, 45, 1563-1581, (1966) · Zbl 0168.40703
[14] Graham, R.L., Bounds on multiprocessing timing anomalies, SIAM journal on applied mathematics, 17, 416-429, (1969) · Zbl 0188.23101
[15] Guinet, A.; Chaabane, S., Operating theatre planning, International journal of production economics, 85, 1, 69-81, (2003)
[16] Hartmann, S.; Kolisch, R., Experimental evaluation of state-of-the-art heuristics for the resource-constrained scheduling problem, European journal of operational research, 127, 394-407, (2000) · Zbl 0985.90036
[17] Hopp, W.J.; Spearman, M.L., Factory physics – foundations of manufacturing management, (2000), McGraw-Hill/Irwin New York
[18] Kallenberg, O., Foundations of modern probability, (1997), Springer-Verlag New York · Zbl 0892.60001
[19] Kirkpatrick, S.; Gerlatt, C.D.; Vecchi, M.P., Optimization by simulated annealing, Science, 220, 671-680, (1983) · Zbl 1225.90162
[20] Kolisch, R.; Drexl, A., Adaptive search for solving hard project scheduling problems, Naval research logistics, 43, 23-40, (1996) · Zbl 0870.90069
[21] Kuo, P.C.; Schroeder, R.A.; Mahaffey, M.; Bollinger, R.R., Optimization of operating room allocation using linear programming techniques, Journal of American college of surgeons, 197, 6, 889-895, (2003)
[22] Markowitz, H.M., Portfolio selection: efficient diversification of investments, (1991), Blackwell Cambridge, MA
[23] Metropolis, N.; Rosenbluth, A.W.; Rosenbluth, M.N.; Teller, A.H.; Teller, E., Equation of state calculations by fast computing machines, Journal of chemical physics, 21, 6, 1087-1092, (1953)
[24] Ozkarahan, I., Allocation of surgeries to operating rooms by goal programming, Journal of medical systems, 24, 6, 339-378, (2000)
[25] Roth, A.V.; Van Dierdonck, R., Hospital resource planning, Production and operations management, 4, 2-29, (2005)
[26] Strum, D.P.; May, J.H.; Vargas, L.G., Modeling the uncertainty of surgical procedure times: comparison of log-normal and normal models, Anesthesiology, 92, 4, 1160-1167, (2000)
[27] TPG, 2004. Het kan echt: betere zorg voor minder geld. Eindrapportage TPG voor Sneller Beter - De logistiek in de zorg (in Dutch). Can be obtained from: http://www.snellerbeter.nl.
[28] Van Laarhoven, P.J.M.; Aarts, E.H.L., Simulated annealing: theory and applications, (1987), Reidel Dordrecht · Zbl 0643.65028
[29] Van Oostrum, J.M., Van Houdenhoven, M., Hurink, J.L., Hans, E.W., Wullink, G., Kazemier, G., 2006. A master surgical scheduling approach for cyclic scheduling in operating room departments. Working paper, Erasmus MC, Rotterdam. · Zbl 1170.90402
[30] Ye, D., Zhang, G., 2003. On-line extensible bin packing with unequal bin sizes. Proceedings of the First Workshop on Approximation and Online Algorithms (WAOA 2003). Springer LNCS 2909, pp. 235-247. · Zbl 1213.68713
[31] Zhou, J.; Dexter, F., Method to assist in the scheduling of add-on surgical cases – upper prediction bounds for surgical case durations based on the log normal distribution, Anesthesiology, 89, 1228-1232, (1998)
[32] Zijm, W.H.M., Towards intelligent manufacturing planning and control systems, OR spectrum, 22, 313-345, (2000) · Zbl 0973.90030
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