We study approximation algorithms for the problem of minimizing the makespan on a set of machines with uncertainty on the processing times of jobs. In the model we consider, which goes back to Bertsimas et al. (Math. Program. 98(1-3), 49–71 2003), once the schedule is defined an adversary can pick a scenario where deviation is added to some of the jobs’ processing times. Given only the maximal cardinality of these jobs, and the magnitude of potential deviation for each job, the goal is to optimize the worst-case scenario. We consider both the cases of identical and unrelated machines. Our main result is an EPTAS for the case of identical machines. We also provide a 3-approximation algorithm and an inapproximability ratio of 2 − 𝜖 for the case of unrelated machines.

我们研究了在一组机器上最小化完工时间问题的近似算法，这些机器的处理时间不确定。在我们考虑的模型中，这可以追溯到 Bertsimas 等人。（Math. Program. 98 (1-3), 49–71 2003），一旦定义了时间表，对手就可以选择一个场景，在该场景中，某些作业的处理时间会增加偏差。仅考虑这些作业的最大基数，以及每个作业的潜在偏差幅度，目标是优化最坏情况。我们考虑相同和不相关机器的情况。我们的主要结果是针对相同机器的 EPTAS。对于不相关的机器，我们还提供了一个 3-近似算法和一个 2 - 𝜖的不可逼近比。