# Simulated annealing approach to nurse rostering benchmark and real-world instances

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## Abstract

The nurse rostering problem, which addresses the task of assigning a given set of activities to nurses without violating any complex rules, has been studied extensively in the last 40 years. However, in a lot of hospitals the schedules are still created manually, as most of the research has not produced methods and software suitable for a practical application. This paper introduces a novel, flexible problem model, which can be categorized as ASBN|RVNTO|PLG. Two solution methods are implemented, including a MIP model to compute good bounds for the test instances and a heuristic method using the simulated annealing algorithm for practical use. Both methods are tested on the available benchmark instances and on the real-world data. The mathematical model and solution methods are integrated into a state-of-the-art duty rostering software, which is primarily used in Germany and Austria.

## Keywords

Nurse rostering problem Flexible model \(\alpha |\beta |\gamma \) notation Simulated annealing Mixed integer programming Real-world data Duty rostering software## Notes

### Acknowledgements

We would like to thank Connext Communication GmbH for providing us with the real-world instances and the use of their software, Vivendi PEP, to accomplish this paper.

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