# A pattern based, robust approach to cyclic master surgery scheduling

- 823 Downloads
- 23 Citations

## Abstract

The Master Surgery Scheduling problem consists of finding a suitable allocation of operating resources to surgical groups. A myriad of variants of the problem has been addressed in literature. Here we focus on two major variants, arising during a cooperation with Sykehuset Asker og Bærum HF, a large hospital in the city of Oslo. The first variant asks for balancing patient queue lengths among different specialties, whereas the second for minimizing resort to overtime. To cope with these problems we introduce a new mixed integer linear formulation and show its beneficial properties. Both problems require the estimation of demand levels. As such estimation is affected by uncertainty, we also develop a light robustness approach to the second variant. Finally we present computational results on a number of real-world instances provided by our reference hospital.

## Keywords

Health-care optimization Master surgery scheduling Robust optimization Mixed-integer programming## Notes

### Acknowledgements

The authors wish to thank Tone Jensen and Anne Dorthe Røsvik from the hospital ’Sykehuset Asker og Bærum HF’ for providing us with data and their precious comments and suggestions throughout our research. We also thank the anonymous referees for their comments.

## References

- Adan, I., & Vissers, J. (2002). Patient mix optimisation in hospital admission planning: a case study.
*International Journal of Operations & Production Management*,*22*(4), 445–461. CrossRefGoogle Scholar - Beliën, J., Demeleulemeester, E., & Cardoen, B. (2009). A decision support system for cyclic master surgery scheduling with multiple objectives.
*Journal of Scheduling*,*12*, 147–161. doi: 10.1007/s10951-008-0086-4. CrossRefGoogle Scholar - Beliën, J., & Demeulemeester, E. (2007). Building cyclic master surgery schedules with leveled resulting bed occupancy.
*European Journal of Operational Research*,*176*(2), 1185–1204. CrossRefGoogle Scholar - Beliën, J., Demeulemeester, E., & Cardoen, B. (2006). Visualizing the demand for various resources as a function of the master surgery schedule: a case study.
*Journal of Medical Systems*,*30*, 343–350. CrossRefGoogle Scholar - Ben-Tal, A., & Nemirovski, A. (2002). Robust optimization methodology and applications.
*Mathematical Programming*,*92*(3), 453–480. CrossRefGoogle Scholar - Blake, J. T., Dexter, F., & Donald, J. (2002). Operating room managers’ use of integer programming for assigning block time to surgical groups: a case study.
*Anesthesia and Analgesia*,*94*(1), 143–148. Google Scholar - Blake, J. T., & Donald, J. (2002). Mount Sinai hospital uses integer programming to allocate operating room time.
*Interfaces*,*32*(2), 63–73. CrossRefGoogle Scholar - Cardoen, B., Demeulemeester, E., & Beliën, J. (2010). Operating room planning and scheduling: a literature review.
*European Journal of Operational Research*,*201*, 921–932. CrossRefGoogle Scholar - de Werra, D., Asratian, A. S., & Durand, S. (2002). Complexity of some special types of timetabling problems.
*Journal of Scheduling*,*5*, 171–183. CrossRefGoogle Scholar - Bertsimas, D., & Sim, M. (2004). The price of robustness.
*Operations Research*,*52*, 35–53. CrossRefGoogle Scholar - Burke, E., Curtois, T., Nordlander, T. E., & Riise, A. (2010). In
*Handbook of Healthcare Delivery Systems*(p. 840). Boca Raton: CRC Press. Google Scholar - Fischetti, M., & Monaci, M. (2009). Light Robustness. In R. K. Ahuja, R. Moehring, & C. Zaroliagis (Eds.),
*Lecture Notes in Computer Science: Vol.**5868*.*Robust and Online Large-Scale Optimization*(pp. 61–84). Berlin: Springer. CrossRefGoogle Scholar - Fischetti, M., Salvagnin, D., & Zanette, A. (2009). Fast approaches to improve the robustness of a railway timetable.
*Transportation Science*,*43*(3), 321–335. CrossRefGoogle Scholar - Hans, E., Wullink, G., van Houdenhovenand, M., & Kazemier, G. (2008). Robust surgery loading.
*Central European Journal of Operations Research*,*185*, 1038–1050. Google Scholar - Macario, A., Vitez, T. S., Dunn, B., & McDonald, T. (1995). Where are the costs in perioperative care? Analysis of hospital costs and charges for inpatient surgical care.
*Anesthesiology*,*83*(6), 1138–1144. CrossRefGoogle Scholar - Mannino, C., Nilssen, E. J., & Nordlander, T. E. (2010). Sintef ict: Mss-adjusts surgery data. [WWW] Available from: http://www.comihc.org/index.php/Test-Bed/3-yearsof-surgery-data-at-sab.html.
- Marler, T. R., & Arora, J. S. (2004). Survey of multi-objective optimization methods for engineering.
*Structural and Multidisciplinary Optimization*,*26*(6), 369–395. CrossRefGoogle Scholar - Oostrum, J. M., van Houdenhoven, M., Hurink, J. L., Hans, E. W., Wullink, G., & Kazemier, G. (2008). A master surgical scheduling approach for cyclic scheduling in operating room departments.
*OR-Spektrum*,*30*(2), 355–374. CrossRefGoogle Scholar - Santibanez, P., Begen, M., & Atkins, D. (2007). Surgical block scheduling in a system of hospitals: an application to resource and wait list management in a British Columbia health authority.
*Health Care Management Science*,*10*(3), 269–282. CrossRefGoogle Scholar - Soyster, J. (1973). Convex programming with set-inclusive constraints and applications to inexact linear programming.
*Operations Research*,*21*, 1154–1157. CrossRefGoogle Scholar