The collective schedules problem consists in computing a schedule of tasks shared between individuals. Tasks may have different duration, and individuals have preferences over the order of the shared tasks. This problem has numerous applications since tasks may model public infrastructure projects, events taking place in a shared room, or work done by co-workers. Our aim is, given the preferred schedules of individuals (voters), to return a consensus schedule. We propose an axiomatic study of the collective schedule problem, by using classic axioms in computational social choice and new axioms that take into account the duration of the tasks. We show that some axioms are incompatible, and we study the axioms fulfilled by three rules: one which has been studied in the seminal paper on collective schedules (Pascual et al. 2018), one which generalizes the Kemeny rule, and one which generalizes Spearman's footrule. From an algorithmic point of view, we show that these rules solve NP-hard problems, but that it is possible to solve optimally these problems for small but realistic size instances, and we give an efficient heuristic for large instances. We conclude this paper with experiments.

翻译：集体调度问题旨在计算个体间共享任务的调度方案。任务可能具有不同持续时间，且个体对共享任务的顺序存在偏好。该问题具有广泛的应用场景，因为任务可代表公共基础设施项目、共享空间举办的活动或同事协作完成的工作。我们的目标是根据个体（投票者）的偏好调度方案，生成共识调度。我们通过使用计算社会选择中的经典公理以及考虑任务持续时间的新公理，对集体调度问题进行了公理化研究。研究表明部分公理不可兼容，并分析了三条规则所满足的公理：一条源自集体调度开创性论文（Pascual et al. 2018）中研究的规则，一条是Kemeny规则的推广，另一条是Spearman footrule规则的推广。从算法角度而言，我们证明这些规则虽求解NP难问题，但能够在规模较小且符合现实的实例中实现最优求解，同时针对大规模实例提出高效启发式算法。最后通过实验对本文进行总结。