🤖 AI Summary
This paper addresses the equitable assignment of periodic tasks—such as train maintenance and crew shifts—in railway operations, aiming to guarantee that each employee undertakes every task type with identical long-term frequency. The base model enforces mutual exclusivity among concurrent tasks; an extended variant incorporates practical constraints like working-hour limits. We formulate the problem for the first time as a fairness-optimization problem under periodic integer allocation and derive a necessary and sufficient condition for equilibrium, verifiable in polynomial time—establishing a theoretically complete fairness certification framework. Our methodology integrates combinatorial optimization, periodic sequence analysis, and graph-theoretic modeling, yielding an algorithm with O(n³) time complexity. Evaluated on real-world SNCF operational data, the approach supports real-time scheduling for instances with up to thousands of employees and achieves 100% theoretical fairness guarantee.
📝 Abstract
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.