Abstract
Nurse rostering is a complex task of practical relevance. Over the last years, researchers have been able to solve increasingly larger and more complex problems. In this paper, we describe the full procedure of running the First International Nurse Rostering Competition. The aim of the competition was to develop further interest in the area and to stimulate new solution approaches by bringing together researchers from different areas.
We describe the competition’s spirit and its rules, the problem description and evaluation of solutions. We also explain the selection process and the final results. In addition, we give a brief description of the algorithmic approaches undertaken by the participants. Finally, we discuss the lessons learned from the competition and future activities to undertake.
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Appendices
Appendix A: Unwanted patterns
An unwanted pattern is a sequence of assignments that a nurse does not want to work. We distinguish between patterns that are unwanted on specific days (e.g. a nurse does not want to work a night shift before a free weekend, a nurse wants to work on Friday before a working weekend, …) and patterns that are unwanted throughout the entire planning period (e.g. a nurse does not want to work a late shift before an early shift, …).
A pattern consists of a number of pattern entries X: [X]1…n . A pattern entry X can be one of the following:
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ST: a specific shift type
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W: any shift type on a day
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F: free (no shift type) on a day
A pattern entry X can occur on any day in the scheduling period or on a specific day. For patterns on fixed days, one numbering is sufficient. The other patterns need multiple numberings (see Appendix C).
We introduce the following pattern types:
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1.
{W,ST}−[F]2…n : Before a series of free days, it is prohibited to work either during the entire day or to work a specific shift type. E.g. an employee may not work a night shift before a free weekend.
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F−[W,ST]2…n : No free day can occur before working any of a number of consecutive days or shift types. E.g. if an employee works a shift in a weekend, the employee should also work on Friday.
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3.
[ST]2…n : Unwanted shift type successions. E.g. Late-Early-Late, Night-Early, …
Appendix B: Formal description of constraints
In Table 13, we give a sample numbering for each constraint introduced in Sect. 4.1. More formal definitions of the numberings can be found in the technical report describing the competition (Haspeslagh et al. 2010). We consider a planning horizon of two weeks. There are three shift types: an early (E), late (L) and night (N) shift type. A weekend consists of three days: Friday, Saturday and Sunday. Table 14 shows the mapping between a numbering and the constraints it can represent. Note that some constraints require multiple numberings (see Appendix C).
Appendix C: Constraints with multiple numberings
Some constraints cannot be expressed using only one numbering. Mostly constraints that do not occur on fixed days, need multiple numberings. The number of numberings needed is equal to the length of the pattern. For example consider the unwanted pattern, L-E-L, of length 3 and a scheduling period of 7 days. Since the pattern can start on any day, we need 3 numberings to achieve this. An example is shown in Table 15.
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Haspeslagh, S., De Causmaecker, P., Schaerf, A. et al. The first international nurse rostering competition 2010. Ann Oper Res 218, 221–236 (2014). https://doi.org/10.1007/s10479-012-1062-0
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DOI: https://doi.org/10.1007/s10479-012-1062-0