Abstract
Given a set of predefined duties and groups of drivers, the duty assignment problem with group-based driver preferences (DAPGDP) aims at building rosters that cover all the duties over a predetermined cyclic horizon while respecting a set of rules (hard constraints), balancing the workload between the drivers and satisfying as much as possible the driver preferences (soft constraints). In this paper, we first model the DAPGDP as a mixed-integer linear program that minimizes the number of preference violations while maintaining the workload balance of the solutions within a certain margin relative to the optimal one. Since this model is hard to solve for large instances, we propose two new matheuristics. The first one restricts the search space by preassigning duties to rosters based on an optimal solution to the duty assignment problem with fixed days off. The second algorithm makes use of a set partitioning problem to decompose rosters consisting of a large number of positions into subrosters of smaller sizes. In a series of computational experiments conducted on real-world instances, we show that these matheuristics can be used to produce high-quality solutions for large instances of the DAPGDP (i.e., with up to 333 drivers and 1509 duties) within relatively short computational times.
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References
Bard JF, Purnomo HW (2005a) A column generation-based approach to solve the preference scheduling problem for nurses with downgrading. Socio Econ Plan Sci 39(3):193–213
Bard JF, Purnomo HW (2005b) Preference scheduling for nurses using column generation. Eur J Oper Res 164(2):510–534
Bard JF, Purnomo HW (2007) Cyclic preference scheduling of nurses using a Lagrangian-based heuristic. J Sched 10(1):5–23
Van den Bergh J, Beliën J, De Bruecker P, Demeulemeester E, De Boeck L (2013) Personnel scheduling: a literature review. Eur J Oper Res 226(3):367–385
Borndörfer R, Reuther M, Schlechte T, Schulz C, Swarat E, Weider S (2015) Duty rostering in public transport—facing preferences, fairness, and fatigue. Tech. Rep. 15-44, ZIB, Berlin
Desaulniers G, Hickman MD (2007) Public transit. In: Barnhart C, Gilbert L (eds) Handbooks in operations research and management science, vol 14. Elsevier, pp 69–127
Er-Rbib S, Desaulniers G, Elhallaoui I, Bani A (2020) Integrated and sequential solution methods for the cyclic bus driver rostering problem. J Oper Res Soc. https://doi.org/10.1080/01605682.2019.1700187
Erhard M, Schoenfelder J, Fügener A, Brunner JO (2018) State of the art in physician scheduling. Eur J Oper Res 265(1):1–18
Ernst AT, Jiang H, Krishnamoorthy M, Owens B, Sier D (2004a) An annotated bibliography of personnel scheduling and rostering. Ann Oper Res 127(1–4):21–144
Ernst AT, Jiang H, Krishnamoorthy M, Sier D (2004b) Staff scheduling and rostering: a review of applications, methods and models. Eur J Oper Res 153(1):3–27
Hanne T, Dornberger R, Frey L (2009) Multiobjective and preference-based decision support for rail crew rostering. In: 2009 IEEE congress on evolutionary computation, Trondheim. IEEE, pp 990–996
Hartog A, Huisman D, Abbink EJ, Kroon LG (2009) Decision support for crew rostering at NS. Public Transport 1(2):121–133. https://doi.org/10.1007/s12469-009-0009-6
Jütte S, Müller D, Thonemann UW (2017) Optimizing railway crew schedules with fairness preferences. J Sched 20(1):43–55
Kisielewski P, Dańda M, Bauer M (2019) Optimization of rosters in public transport. In: 6th international conference on models and technologies for intelligent transportation systems, Cracow. IEEE, pp 1–8
Knust F, Xie L (2019) Simulated annealing approach to nurse rostering benchmark and real-world instances. Ann Oper Res 272(1):187–216
Lezaun M, Pérez G, Sáinz de la Maza E (2006) Crew rostering problem in a public transport company. J Oper Res Soc 57(10):1173–1179
Mesquita M, Moz M, Paias A, Pato M (2015) A decompose-and-fix heuristic based on multi-commodity flow models for driver rostering with days-off pattern. Eur J Oper Res 245(2):423–437
Moz M, Respício A, Pato MV (2009) Bi-objective evolutionary heuristics for bus driver rostering. Public Transport 1(3):189–210. https://doi.org/10.1007/s12469-009-0013-x
Nurmi K, Kyngas J, Post G (2011) Driver rostering for bus transit companies. Eng Lett 19(2):125–132
Purnomo HW, Bard JF (2007) Cyclic preference scheduling for nurses using branch and price. Nav Res Logist 54(2):200–220
Sodhi MS, Norris S (2004) A flexible, fast, and optimal modeling approach applied to crew rostering at London underground. Ann Oper Res 127(1–4):259–281
Wong T, Xu M, Chin KS (2014) A two-stage heuristic approach for nurse scheduling problem: a case study in an emergency department. Comput Oper Res 51:99–110
Xie L (2014) Decision support for crew rostering in public transit: web-based optimization system for cyclic and non-cyclic rostering. PhD thesis, University of Paderborn
Xie L, Suhl L (2015) Cyclic and non-cyclic crew rostering problems in public bus transit. OR Spectr 37(1):99–136
Xie L, Kliewer N, Suhl L (2012) Integrated driver rostering problem in public bus transit. Proc Soc Behav Sci 54:656–665
Acknowledgements
We would like to thank the personnel of Giro Inc. for providing real-world datasets. We are also grateful to the Natural Sciences and Engineering Research Council of Canada for their financial support (Grant 2017-05683).
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G. Desaulniers has received a research grant from the company Giro Inc., but not for this project.
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Er-Rbib, S., Desaulniers, G., Elhallaoui, I. et al. Preference-based and cyclic bus driver rostering problem with fixed days off. Public Transp 13, 251–286 (2021). https://doi.org/10.1007/s12469-021-00268-y
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DOI: https://doi.org/10.1007/s12469-021-00268-y