The Makespan Scheduling problem is an extensively studied NP-hard problem, and its simplest version looks for an allocation approach for a set of jobs with deterministic processing times to two identical machines such that the makespan is minimized. However, in real life scenarios, the actual processing time of each job may be stochastic around the expected value with a variance, under the influence of external factors, and the actual processing times of these jobs may be correlated with covariances. Thus within this paper, we propose a chance-constrained version of the Makespan Scheduling problem and investigate the theoretical performance of the classical Randomized Local Search and (1+1) EA for it. More specifically, we first study two variants of the Chance-constrained Makespan Scheduling problem and their computational complexities, then separately analyze the expected runtime of the two algorithms to obtain an optimal solution or almost optimal solution to the instances of the two variants. In addition, we investigate the experimental performance of the two algorithms for the two variants.

翻译：最大完工时间调度问题是一个被广泛研究的NP难问题，其最简单的版本是寻找一组具有确定加工时间的作业在两台同构机器上的分配方式，以最小化最大完工时间。然而，在实际场景中，受外部因素影响，每个作业的实际加工时间可能围绕期望值随机波动并存在方差，且这些作业的实际加工时间之间可能存在协方差相关关系。因此，本文提出机会约束版本的最大完工时间调度问题，并研究经典随机局部搜索算法和(1+1)进化算法在该问题上的理论性能。具体而言，我们首先研究机会约束最大完工时间调度问题的两个变体及其计算复杂度，随后分别分析两种算法在获得两个变体实例的最优解或近似最优解时的期望运行时。此外，我们还对这两个算法在两类变体上的实验性能进行探究。