A fair schedule helps in improving the competitiveness and attractiveness of sports tournaments and in turn contributes positively to the sports economy. Break minimization and carryover effects minimization are considered to be two important criteria of fairness in scheduling of compact round-robin tournaments, and most related research looks at these problems separately. Various studies have sought to minimize the carryover effects in tournaments so that the number of breaks per team does not exceed a specific level. This study, however, is the first effort to define an integrated problem that aims to minimize the carryover effects and the number of breaks simultaneously for round-robin tournaments. We first introduce the mathematical formulation for the problem, whose objective measures how well a schedule simultaneously performs with respect to the number of breaks and the carryover effects. We then develop a heuristic method for this computationally hard problem. Comparing our results with the previous literature and the current practices of some European leagues, we show that our method provides schedules with better objective function values.

公平的赛程有助于提高体育赛事的竞争力和吸引力，进而为体育经济做出积极贡献。中断最小化和结转效应最小化被认为是紧凑型循环锦标赛安排公平性的两个重要标准，大多数相关研究分别着眼于这些问题。各种研究都试图将锦标赛中的遗留效应降至最低，以便每支球队的休息次数不超过特定水平。然而，这项研究是第一次尝试定义一个综合问题，旨在最大限度地减少循环赛的遗留效应和同时中断的次数。我们首先介绍这个问题的数学公式，其目标是衡量一个时间表在休息次数和遗留效应方面的同时执行情况。然后，我们为这个计算困难的问题开发了一种启发式方法。将我们的结果与以前的文献和一些欧洲联赛的当前实践进行比较，我们表明我们的方法提供了具有更好目标函数值的时间表。