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Service-oriented robust parallel machine scheduling

机译：面向服务的强大平行机器调度

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Stochastic scheduling optimisation is a hot and challenging research topic with wide applications. Most existing works on stochastic parallel machine scheduling address uncertain processing time, and assume that its probability distribution is known or can be correctly estimated. This paper investigates a stochastic parallel machine scheduling problem, and assumes that only the mean and covariance matrix of the processing times are known, due to the lack of historical data. The objective is to maximise the service level, which measures the probability of all jobs jointly completed before or at their due dates. For the problem, a new distributionally robust formulation is proposed, and two model-based approaches are developed: (1) a sample average approximation method is adapted, (2) a hierarchical approach based on mixed integer second-order cone programming (MI-SOCP) formulation is designed. To evaluate and compare the performance of the two approaches, randomly generated instances are tested. Computational results show that our proposed MI-SOCP-based hierarchical approach can obtain higher solution quality with less computational effect.
机译：随机调度优化是一种具有广泛应用的热点和具有挑战性的研究主题。随机并行机器调度地址不确定处理时间的大多数现有工作，并且假设其概率分布是已知的或可以正确估计。本文调查了随机平行机器调度问题，并且假设由于缺乏历史数据，仅知道处理时间的平均值和协方差矩阵。目标是最大限度地提高服务级别，这衡量了之前或在其截止日期之前联合完成的所有工作的概率。对于问题，提出了一种新的分布鲁棒制剂，开发了两种基于模型的方法：（1）示例性平均近似方法进行调整，（2）基于混合整数二阶锥编程的分层方法（Mi-设计了SOCP）制定。为了评估和比较两种方法的性能，测试了随机生成的实例。计算结果表明，我们提出的基于MI-SoCP的分层方法可以通过较少的计算效果获得更高的解决方案质量。

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