Skip to main content
Log in

Shift rostering using decomposition: assign weekend shifts first

  • Published:
Journal of Scheduling Aims and scope Submit manuscript

Abstract

This paper introduces a shift rostering problem that surprisingly has not been studied in the literature: the weekend shift rostering problem. It is motivated by our experience that employees’ shift preferences predominantly focus on the weekends, since many social activities happen during weekends. The weekend rostering problem (WRP) addresses the rostering of weekend shifts, for which we design a problem-specific heuristic. We consider the WRP as the first phase of the shift rostering problem. To complete the shift roster, the second phase assigns the weekday shifts. This decomposition reflects how shift rosters are often created manually in practice, which makes the decomposition method proposed in this paper a more intuitive approach for business users compared to approaches without this decomposition. We believe that such approaches enable business users to effectively analyze and steer the outcomes of algorithms for shift rostering especially on criteria that are relevant to them such as those concerning weekends. We analyze and discuss effects of this two-phase approach both on the weekend shift roster and on the roster as a whole. We demonstrate that our first-phase weekend rostering heuristic is effective both on generated instances and real-life instances. For situations where the weekend shift roster is one of the key determinants of the quality of the complete roster, our two-phase approach is shown to be effective.

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.

Fig. 1
Fig. 2
Fig. 3
Fig. 4

Similar content being viewed by others

References

  • Ahuja, R., Orlin, J., & Sharma, D. (2000). Very large-scale neighborhood search. International Transactions in Operational Research, 7(4–5), 301–317.

    Article  Google Scholar 

  • Aickelin, U., & Dowsland, K. A. (2000). Exploiting problem structure in a genetic algorithm approach to a nurse rostering problem. Journal of Scheduling, 3(3), 139–153.

    Article  Google Scholar 

  • Al-Yakoob, S. M., & Sherali, H. D. (2007a). Mixed-integer programming models for an employee scheduling problem with multiple shifts and work locations. Annals of Operations Research, 155(1), 119–142.

    Article  Google Scholar 

  • Al-Yakoob, S. M., & Sherali, H. D. (2007b). Multiple shift scheduling of hierarchical workforce with multiple work centers. Informatica, 18(3), 325–342.

    Google Scholar 

  • Ásgeirsson, E. (2012). Bridging the gap between self schedules and feasible schedules in staff scheduling. Annals of Operations Research. doi:10.1007/s10479-012-1060-2

  • Awadallah, M., Khader, A., Al-Betar, M., & Bolaji, A. (2011). Nurse rostering using modified harmony search algorithm. Swarm, evolutionary, and memetic computing. Lecture notes in computer science (Vol. 7077, pp. 27–37). Berlin: Springer.

    Chapter  Google Scholar 

  • Azaiez, M. N., & Al Sharif, S. S. (2005). A 0–1 goal programming model for nurse scheduling. Computers & Operations Research, 32(3), 491–507.

    Article  Google Scholar 

  • Bard, J. F., & Purnomo, H. W. (2005). Preference scheduling for nurses using column generation. European Journal of Operational Research, 164(2), 510–534. doi:10.1016/j.ejor.2003.06.046.

    Article  Google Scholar 

  • Bard, J. F., & Purnomo, H. W. (2007). Cyclic preference scheduling of nurses using a Lagrangian-based heuristic. Journal of Scheduling, 10(1), 5–23.

    Article  Google Scholar 

  • Baxter, J., & Mosby, M. (1988) Generating acceptable shift-working schedules. The Journal of the Operational Research Society, 39(6), 537–542. Retrieved from http://www.jstor.org/stable/2582858.

  • Beddoe, G., Petrovic, S., & Li, J. (2009). A hybrid metaheuristic case-based reasoning system for nurse rostering. Journal of Scheduling, 12(2), 99–119.

    Article  Google Scholar 

  • Berrada, I., Ferland, J. A., & Michelon, P. (1996). A multi-objective approach to nurse scheduling with both hard and soft constraints. Socio-Economic Planning Sciences, 30(3), 183–193.

    Article  Google Scholar 

  • Bilgin, B., Demeester, P., Misir, M., Vancroonenburg, W., Vanden Berghe, G., & Wauters, T. (2010). A hyper-heuristic combined with a greedy shuffle approach to the nurse rostering competition. In Proceedings of the 8th International Conference on Practice and Theory of Automated Timetabling.

  • Bilgin, B., De Causmaecker, P., Rossie, B., & Vanden Berghe, G. (2012). Local search neighbourhoods for dealing with a novel nurse rostering model. Annals of Operations Research, 194(1), 33–57.

    Article  Google Scholar 

  • Brucker, P., Burke, E., Curtois, T., Qu, R., & Vanden Berghe, G. (2010). A shift sequence based approach for nurse scheduling and a new benchmark dataset. Journal of Heuristics, 16(4), 559– 573.

  • Burke, E. K., & Curtois, T. (2010). An ejection chain method and a branch and price algorithm applied to the instances of the first international nurse rostering competition, 2010. In Proceedings of the 8th International Conference on Practice and Theory of Automated Timetabling.

  • Burke, E., Cowling, P., De Causmaecker, P., & Vanden Berghe, G. (2001). A memetic approach to the nurse rostering problem. Applied Intelligence, 15(3), 199–214.

    Article  Google Scholar 

  • Burke, E., De Causmaecker, P., Petrovic, S., & Berghe, G. V. (2004a). Variable neighborhood search for nurse rostering problems. Norwell, MA: Kluwer Academic Publishers.

  • Burke, E. K., De Causmaecker, P., vanden Berghe, G., van Landeghem, H. (2004b). The state of the art of nurse rostering. Journal of Scheduling, 7(6), 441–499.

  • Burke, E. K., De Causmaecker, P., Petrovic, S., & Vanden Berghe, G. (2006). Metaheuristics for handling time interval coverage constraints in nurse scheduling. Applied Artificial Intelligence, 20(9), 743–766.

    Article  Google Scholar 

  • Burke, E. K., Curtois, T., Post, G., Qu, R., & Veltman, B. (2008). A hybrid heuristic ordering and variable neighbourhood search for the nurse rostering problem. European Journal of Operational Research, 188(2), 330–341.

    Article  Google Scholar 

  • Burke, E. K., Curtois, T., & Qu, R. (2010a). A scatter search methodology for the nurse rostering problem. Journal of the Operational Research Society, 61(11), 1667–1679.

    Article  Google Scholar 

  • Burke, E. K., Li, J. P., & Qu, R. (2010b). A hybrid model of integer programming and variable neighbourhood search for highly-constrained nurse rostering problems. European Journal of Operational Research, 203(2), 484–493.

    Article  Google Scholar 

  • Burke, E. K., Curtois, T., van Draat, L. F., van Ommeren, J. K., & Post, G. (2011). Progress control in iterated local search for nurse rostering. Journal of the Operational Research Society, 62(2), 360–367.

    Article  Google Scholar 

  • Burns, R. N., & Carter, M. W. (1985). Work force size and single shift schedules with variable demands. Management Science, 31(5), 599–607.

    Article  Google Scholar 

  • Burns, R. N., & Koop, G. J. (1987). A modular approach to optimal multiple-shift manpower scheduling. Operations Research, 35(1), 100–110.

    Article  Google Scholar 

  • Burns, R. N., Narasimhan, R., & Smith, L. D. (1988). A set-processing algorithm for scheduling staff on 4-day or 3-day work weeks. Naval Research Logistics, 45(8), 839–853. doi:10.1002/(SICI)1520-6750(199812)45:8<839:AID-NAV5>3.0.CO;2-R.

  • De Causmaecker, P., & Vanden Berghe, G. (2003). Relaxation of coverage constraints in hospital personnel rostering. Practice and theory of automated timetabling IV. Lecture notes in computer science (Vol. 2740, pp. 129–147). Berlin: Springer.

    Chapter  Google Scholar 

  • Cheang, B., Li, H., Lim, A., & Rodrigues, B. (2003). Nurse rostering problems—A bibliographic survey. European Journal of Operational Research, 151(3), 447–460.

    Article  Google Scholar 

  • Chiaramonte, M. V., & Chiaramonte, L. M. (2008). An agent-based nurse rostering system under minimal staffing conditions. International Journal of Production Economics, 114(2), 697–713.

    Article  Google Scholar 

  • Dowsland, K., & Thompson, J. (2000). Solving a nurse scheduling problem with knapsacks, networks and tabu search. Journal of the Operational Research Society, 51(7), 825–833.

    Article  Google Scholar 

  • Eitzen, G., Panton, D., & Mills, G. (2004). Multi-skilled workforce optimisation. Annals of Operations Research, 127(1–4), 359–372.

    Article  Google Scholar 

  • Elshafei, M., & Alfares, H. K. (2008). A dynamic programming algorithm for days-off scheduling with sequence dependent labor costs. Journal of Scheduling, 11(2), 85–93.

    Article  Google Scholar 

  • Emmons, H., & Burns, R. N. (1991). Off-day scheduling with hierarchical worker categories. Operations Research, 39(3), 484–495.

    Article  Google Scholar 

  • Emmons, H., & Fuh, D. S. (1997). Sizing and scheduling a full-time and part-time workforce with off-day and off-weekend constraints. Annals of Operations Research, 70, 473–492.

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Gärtner, J., Musliu, N., & Slany, W. (2001). Rota: A research project on algorithms for workforce scheduling and shift design optimization. AI Communications, 14(2), 83–92.

    Google Scholar 

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

    Article  Google Scholar 

  • De Grano, M. L., Medeiros, D., & Eitel, D. (2009). Accommodating individual preferences in nurse scheduling via auctions and optimization. Health Care Management Science, 12(3), 228–242.

    Article  Google Scholar 

  • Gutjahr, W. J., & Rauner, M. S. (2007). An ACO algorithm for a dynamic regional nurse-scheduling problem in Austria. Computers & Operations Research, 34(3), 642–666.

    Article  Google Scholar 

  • Hao, G., Lai, K. K., & Tan, M. (2004). A neural network application in personnel scheduling. Annals of Operations Research, 128(1–4), 65–90.

    Article  Google Scholar 

  • Haspeslagh, S., De Causmaecker, P., Schaerf, A., & Stølevik, M. (2012). The first international nurse rostering competition 2010. Annals of Operations Research. doi:10.1007/s10479-012-1062-0.

  • Hung, R. (1994a). Multiple-shift workforce scheduling under the 3–4 workweek with different weekday and weekend labor requirements. Management Science, 40(2), 280–284.

    Article  Google Scholar 

  • Hung, R. (1994b). Single-shift off-day scheduling of a hierarchical workforce with variable demands. European Journal of Operational Research, 78(1), 49–57.

    Article  Google Scholar 

  • Ikegami, A., & Niwa, A. (2003). A subproblem-centric model and approach to the nurse scheduling problem. Mathematical Programming, 97(3), 517–541.

    Article  Google Scholar 

  • Jarray, F. (2009). A 4-day or 3-day workweeks scheduling problem with a given workforce size. Asia–Pacific Journal of Operational Research, 26(5), 685–696.

    Google Scholar 

  • Jaumard, B., Semet, F., & Vovor, T. (1998). A generalized linear programming model for nurse scheduling. European Journal of Operational Research, 107(1), 1–18.

    Article  Google Scholar 

  • Kellogg, D., & Walczak, S. (2007). Nurse scheduling: From academia to implementation or not? Interfaces, 37(4), 355–369.

    Article  Google Scholar 

  • Knust, S., & Schumacher, E. (2011). Shift scheduling for tank trucks. Omega-International Journal of Management Science, 39(5), 513–521.

    Article  Google Scholar 

  • Koop, G. J. (1986). Cyclic scheduling of offweekends. Operations Research Letters, 4(6), 259–263.

    Article  Google Scholar 

  • Laporte, G., & Pesant, G. (2004). A general multi-shift scheduling system. Journal of the Operational Research Society, 55(11), 1208–1217.

    Article  Google Scholar 

  • Lezaun, M., Pérez, G., & Sáinz de la Maza, E. (2006). Crew rostering problem in a public transport company. Journal of the Operational Research Society, 57(10), 1173–1179.

    Article  Google Scholar 

  • Lezaun, M., Pérez, G., & Sáinz de la Maza, E. (2007). Rostering in a rail passenger carrier. Journal of Scheduling, 10(4–5), 245– 254.

  • Lezaun, M., Pérez, G., & Sáinz de la Maza, E. (2010). Staff rostering for the station personnel of a railway company. Journal of the Operational Research Society, 61(7), 1104–1111.

    Article  Google Scholar 

  • Li, J., Burke, E. K., Curtois, T., Petrovic, S., & Rong, Q. (2012). The falling tide algorithm: a new multi-objective approach for complex workforce scheduling. Omega, 40(3), 283–293.

    Article  Google Scholar 

  • Lu, Z., & Hao, J. K. (2012). Adaptive neighborhood search for nurse rostering. European Journal of Operational Research, 218(3), 865–876.

    Article  Google Scholar 

  • Maenhout, B., & Vanhoucke, M. (2013). An integrated nurse staffing and scheduling analysis for longer-term nursing staff allocation problems. Omega, 41(2), 485–499.

    Article  Google Scholar 

  • Maier-Rothe, C., & Wolfe, H. B. (1973). Cyclical scheduling and allocation of nursing staff. Socio-Economic Planning Sciences, 7(5), 471–487. doi:10.1016/0038-0121(73)90043-8.

    Article  Google Scholar 

  • Metivier, J. P., Boizumault, P., & Loudni, S. (2009). Solving nurse rostering problems using soft global constraints. In I. P. Gent (Ed.), 15th international conference on principles and practice of constraint programming. Lecture notes in computer science (Vol. 5732). Berlin: Springer.

    Google Scholar 

  • Miller, H. E., Pierskalla, W. P., & Rath, G. J. (1976). Nurse scheduling using mathematical programming. Operations Research, 24(5), 857–870.

    Article  Google Scholar 

  • Mirrazavi, S. K., & Beringer, H. (2007). A web-based workforce management system for Sainsburys Supermarkets Ltd. Annals of Operations Research, 155(1), 437–457.

    Article  Google Scholar 

  • Musliu, N., Gärtner, J., & Slany, W. (2002). Efficient generation of rotating workforce schedules. Discrete Applied Mathematics, 118(1–2), 85–98.

  • Nonobe, K. (2010). INRC2010: An approach using a general constraint optimization solver. In Proceedings of the 8th International Conference on Practice and Theory of Automated Timetabling.

  • ORTEC Workforce Scheduling. (2013). Retrieved October 2013, from http://www.ortec.com/products/ortec_workforce_scheduling.aspx.

  • Ovchinnikov, A., & Milner, J. (2008). Spreadsheet model helps to assign medical residents at the University of Vermont’s College of Medicine. Interfaces, 38(4), 311–323.

    Article  Google Scholar 

  • PATAT 2010 Nurse Rostering Competition. (2010). Retrieved October 2013, from http://www.kuleuven-kulak.be/nrpcompetition.

  • Post, G., & Veltman, B. (2004). Harmonious personnel scheduling. In Proceedings of the 5th International Conference on the Practice and Theory of Automated Timetabling (pp. 557–559).

  • Post, G., Ahmadi, S., & Geertsema, F. (2012). Cyclic transfers in school timetabling. OR Spectrum, 34(1), 133–154.

    Article  Google Scholar 

  • Purnomo, H. W., & Bard, J. F. (2007). Cyclic preference scheduling for nurses using branch and price. Naval Research Logistics, 54(2), 200–220. doi:10.1002/nav.20201.

    Article  Google Scholar 

  • Qi, X. T., & Bard, J. F. (2006). Generating labor requirements and rosters for mail handlers using simulation and optimization. Computers & Operations Research, 33(9), 2645–2666.

    Article  Google Scholar 

  • Qu, R., & He, F. (2009). A hybrid constraint programming approach for nurse rostering problems. In 28th SGAI International Conference on Innovative Techniques and Applications of Artificial Intelligence (pp. 211–224).

  • Rong, A. Y. (2010). Monthly tour scheduling models with mixed skills considering weekend off requirements. Computers & Industrial Engineering, 59(2), 334–343.

    Article  Google Scholar 

  • Rönnberg, E., & Larsson, T. (2010). Automating the self-scheduling process of nurses in Swedish healthcare: A pilot study. Health Care Management Science, 13(1), 35–53.

    Article  Google Scholar 

  • Rosenbloom, E., & Goertzen, N. (1987). Cyclic nurse scheduling. European Journal of Operational Research, 31(1), 19–23. doi:10.1016/0377-2217(87)90131-7.

    Article  Google Scholar 

  • Sodhi, M. S., & Norris, S. (2004). A flexible, fast, and optimal modeling approach applied to crew rostering at London underground. Annals of Operations Research, 127(1), 259–281.

    Article  Google Scholar 

  • Syslo, M. M., Deo, N., & Kowalik, J. S. (1983). Discrete optimization algorithms: With Pascal programs. Englewood Cliffs, NJ: Prentice-Hall.

    Google Scholar 

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

  • Topaloglu, S. (2009). A shift scheduling model for employees with different seniority levels and an application in healthcare. European Journal of Operational Research, 198(3), 943–957.

  • Trilling, L., Guinet, A., & Le Magny, D. (2006). Nurse scheduling using integer linear programming and constraint programming. In Proceedings of the 12th IFAC International Symposium (Vol. 3, pp. 651–656).

  • Valouxis, C., & Housos, E. (2000). Hybrid optimization techniques for the workshift and rest assignment of nursing personnel. Artificial Intelligence in Medicine, 20(2), 155–175.

    Article  Google Scholar 

  • Valouxis, C., Gogos, C., Goulas, G., Alefragis, P., & Housos, E. (2012). A systematic two phase approach for the nurse rostering problem. European Journal of Operational Research, 219(2), 425–433.

    Article  Google Scholar 

  • Van den Bergh, J., Beliën, J., De Bruecker, P., Demeulemeester, E., & De Boeck, L. (2013). Personnel scheduling: A literature review. European Journal of Operational Research, 226(3), 367–385.

    Article  Google Scholar 

  • Veldman, B., Post, G., Winkelhuijzen, W., & Fijn van Draat, L. (2006). Harmonious personnel scheduling. Medium Econometrische Toepassingen, 14(1), 4–7.

    Google Scholar 

  • Versteegh, F. (2009). Let the weekend begin! A solution for solving the weekend scheduling problem for ORTEC Harmony. Master’s thesis, University of Twente, The Netherlands. Retrieved from http://essay.utwente.nl/60656.

  • Warner, D. M. (1976). Scheduling nursing personnel according to nursing preference: A mathematical programming approach. Operations Research, 24(5), 842–856.

    Article  Google Scholar 

  • White, C. A., Nano, E., Nguyen-Ngoc, D. H., & White, G. M. (2007). An evaluation of certain heuristic optimization algorithms in scheduling medical doctors and medical students. In Proceedings of the 6th International Conference on the Practice and Theory of Automated Timetabling (Vol. 3867, pp. 105–115).

  • Wright, P. D., & Bretthauer, K. M. (2010). Strategies for addressing the nursing shortage: Coordinated decision making and workforce flexibility. Decision Sciences, 41(2), 373–401.

    Article  Google Scholar 

  • Wright, P. D., Bretthauer, K. M., & Côté, M. J. (2006). Reexamining the nurse scheduling problem: Staffing ratios and nursing shortages. Decision Sciences, 37(1), 39–70.

    Article  Google Scholar 

  • Yunes, T. H., Moura, A. V., & de Souza, C. C. (2005). Hybrid column generation approaches for urban transit crew management problems. Transportation Science, 39(2), 273–288.

    Article  Google Scholar 

Download references

Acknowledgments

The authors would like to thank Frédérique Versteegh for initiating and taking the first steps in this research, and Monique Hoogstrate for helpful discussions. This research is supported by the Dutch Technology Foundation STW, applied science division of NWO and the Technology Program of the Ministry of Economic Affairs.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Egbert van der Veen.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

van der Veen, E., Hans, E.W., Post, G.F. et al. Shift rostering using decomposition: assign weekend shifts first. J Sched 18, 29–43 (2015). https://doi.org/10.1007/s10951-014-0385-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10951-014-0385-x

Keywords

Navigation