This work deals with a problem of assigning periodic tasks to employees in such a way that each employee performs each task with the same frequency in the long term. The motivation comes from a collaboration with the SNCF, the main French railway company. An almost complete solution is provided under the form of a necessary and sufficient condition that can be checked in polynomial time. A complementary discussion about possible extensions is also proposed.

翻译：本研究探讨如何将周期性任务分配给员工，使得长期内每位员工执行每项任务的频率相同。该问题的研究动机源于与法国主要铁路公司SNCF的合作。我们以多项式时间可验证的充分必要条件形式，给出了该问题近乎完整的解决方案。此外，本文还对可能的扩展方向进行了补充讨论。