Skip to main content
Log in

Master physician scheduling problem

  • General Paper
  • Published:
Journal of the Operational Research Society

Abstract

We study a real-world problem arising from the operations of a hospital service provider, which we term the master physician scheduling problem. It is a planning problem of assigning physicians’ full range of day-to-day duties (including surgery, clinics, scopes, calls, administration) to the defined time slots/shifts over a time horizon, incorporating a large number of constraints and complex physician preferences. The goals are to satisfy as many physicians’ preferences and duty requirements as possible while ensuring optimum usage of available resources. We propose mathematical programming models that represent different variants of this problem. The models were tested on a real case from the Surgery Department of a local government hospital, as well as on randomly generated problem instances. The computational results are reported together with analysis on the optimal solutions obtained. For large-scale instances that could not be solved by the exact method, we propose a heuristic algorithm to generate good solutions.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Figure 1
Figure 2
Figure 3
Figure 4
Figure 5
Figure 6
Figure 7
Figure 8
Figure 9
Figure 10
Figure 11
Figure 12
Figure 13
Figure 14

Similar content being viewed by others

Notes

  1. In Gunawan and Lau (2009), we defined an additional notation Lc to represent a set of duties with limited number of resources available. In this journal version, L is used to simplify notations.

References

  • Aggarwal S (1982). A focussed review of scheduling in services. European Journal of Operational Research 9 (2): 114–121.

    Article  Google Scholar 

  • Bard JF and Purnomo HW (2005). Preference scheduling for nurses using column generation. European Journal of Operational Research 164 (2): 510–534.

    Article  Google Scholar 

  • Beaulieu H, Ferland JA, Gendron B and Philippe M (2000). A mathematical programming approach for scheduling physicians in the emergency room. Health Care Management Science 3 (3): 193–200.

    Article  Google Scholar 

  • Beliën J (2007). Exact and heuristic methodologies for scheduling in hospitals: Problems, formulations and algorithms. 4OR: A Quarterly Journal of Operations Research 5 (2): 157–160.

    Article  Google Scholar 

  • Beliën J and Demeulemeester E (2006). Scheduling trainees at a hospital department using a branch-and-price approach. European Journal of Operational Research 175 (1): 258–278.

    Article  Google Scholar 

  • Beliën J and Demeulemeester E (2007). Building cyclic master surgery schedules with leveled resulting bed occupancy. European Journal of Operational Research 176 (2): 1185–1204.

    Article  Google Scholar 

  • Bourdais S, Galinier P and Pesant G (2003). HIBISCUS: A constraint programming application to staff scheduling in health care. Lecture Notes in Computer Science 2833: 153–167.

    Article  Google Scholar 

  • Burke EK, De Causmaecker P, Vanden Berghe G and Van Landeghem H (2004). The state of the art of nurse rostering. Journal of Scheduling 7 (6): 441–499.

    Article  Google Scholar 

  • Burke EK, Li J and Qu R (2009). A Pareto-based search methodology for multi-objective nurse scheduling. Annals of Operations Research, http://www.springerlink.com/content/gr4j121131272772/.

  • Buzon I and Lapierre SD (1999). A tabu search algorithm to schedule emergency room physicians. Technical report, Centre de Recherche sur les Transports, Montréal, Canada.

  • Carter MW and Lapierre SD (2001). Scheduling emergency room physicians. Health Care Management Science 4 (4): 347–360.

    Article  Google Scholar 

  • Deb K (2003). Multi-objective Optimization Using Evolutionary Algorithms. Wiley & Sons: Chichester, New York.

    Google Scholar 

  • Ernst AT, Jiang H, Krishnamoorthy M, Owens B and Sier D (2004a). An annotated bibliography of personnel scheduling and rostering. Annals of Operations Research 127 (1–4): 21–144.

    Article  Google Scholar 

  • Ernst AT, Jiang H, Krishnamoorthy M, Owens B and Sier D (2004b). Staff scheduling and rostering: A review of applications, methods and models. European Journal of Operational Research 153 (1): 3–27.

    Article  Google Scholar 

  • Gendreau M, Ferland J, Gendron B, Hail N, Jaumard B, Lapierre S, Pesant G and Soriano P (2007). Physician scheduling in emergency rooms. In: PATAT'06 Lecture Notes in Computer Science. Vol. 3867, pp 53–66.

  • Glass C and Knight R (2010). The nurse rostering problem: A critical appraisal of the problem structure. European Journal of Operational Research 202 (2): 379–389.

    Article  Google Scholar 

  • Gunawan A and Lau HC (2009). Master physician scheduling problem. In: Blazewicz J, Drozdowski M, Kendall G and McCollum B (eds). Proceedings of the 4th Multidisciplinary International Scheduling Conference: Theory and Applications (MISTA 2009), 10–12 August 2009, Dublin, Ireland, pp 145–156.

  • Gunawan A and Lau HC (2010). The bi-objective master physician scheduling problem. In: McCollum B, Burke EK and White G (eds). Proceedings of the 8th International Conference on the Practice and Theory of Automated Timetabling – PATAT 2010, Belfast, Northern Ireland, 10–13 August, pp 241–258.

  • Ogulata SN and Erol R (2003). A hierarchical multiple criteria mathematical programming approach for scheduling general surgery operations in large hospitals. Journal of Medical Systems 27 (3): 259–270.

    Article  Google Scholar 

  • Ogulata SN, Koyuncu M and Karakas E (2008). Personnel and patient scheduling in the high demanded hospital services: A case study in the physiotherapy service. Journal of Medical Systems 32 (3): 221–228.

    Article  Google Scholar 

  • Petrovic S and Vanden Berghe G (2008). Comparison of algorithms for nurse rostering problems. In: Burke EK and Gendreau M (eds). Proceedings of the 7th International Conference on the Practice and Theory of Automated Timetabling – PATAT 2008, Montreal, Canada, 18–22 August, pp 1–18.

  • Puente J, Gómez A, Fernández I and Priore P (2009). Medical doctor rostering problem in a hospital emergency department by means of genetic algorithms. Computers & Industrial Engineering 56 (4): 1232–1242.

    Article  Google Scholar 

  • Roland B, Di Martinelly C, Riane F and Pochet Y (2010). Scheduling an operating theatre under human resource constraints. Computers & Industrial Engineering 58 (2): 212–220.

    Article  Google Scholar 

  • Rousseau LM, Gendreau M and Pesant G (2002). A general approach to the physician rostering problem. Annals of Operations Research 115 (1–4): 193–205.

    Article  Google Scholar 

  • Testi A, Tanfani E and Torre G (2007). A three-phase approach for operating theatre schedules. Health Care Management Science 10 (2): 163–172.

    Article  Google Scholar 

  • Topaloglu S (2006). A multi-objective programming model for scheduling emergency medicine residents. Computers & Industrial Engineering 51 (3): 375–388.

    Article  Google Scholar 

  • Vanberkel PT, Boucherie RJ, Hans EW, Hurink JL, van Lent WAM and van Harten WH (2011). An exact approach for relating recovering surgical patient workload to the master surgical schedule. Journal of the Operational Research Society 62 (10): 1851–1860.

    Article  Google Scholar 

  • White CA, Nano E, Nguyen-Ngoc DH and White GM (2006). An evaluation of certain heuristic optimization algorithms in scheduling medical doctors and medical students. In: Burke EK and Rudová H (eds). Proceedings of the 6th International Conference on the Practice and Theory of Automated Timetabling – PATAT 2006, Brno, the Czech Republic, 30 August–1 September, pp 320–328.

Download references

Acknowledgements

We thank the Department of Surgery, Tan Tock Seng Hospital (Singapore) for providing valuable comments and test situations.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to H C Lau.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Gunawan, A., Lau, H. Master physician scheduling problem. J Oper Res Soc 64, 410–425 (2013). https://doi.org/10.1057/jors.2012.48

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1057/jors.2012.48

Keywords

Navigation