The single machine scheduling problem which involves uncertain job due dates is one of the most important issues in the real make-to-order environment. To deal with the uncertainty, this paper establishes a robust optimization model by minimizing the maximum tardiness in the worst case scenario over all jobs. Unlike the traditional stochastic programming model which requires exact distributions, our model only needs the information of due date intervals. The worst case scenario for a given sequence that belongs to a set containing only n scenarios is proved, where n is the number of jobs. Then, the model is simplified and reformulated as an equivalent mixed 0–1 integer linear programming (MILP) problem. To solve the MILP problems efficiently, a heuristic approach is proposed based on a robust dominance rule. The experimental results show that the proposed method has the advantages of robustness and high calculating efficiency, and it is feasible for large-scale problems.

中文翻译：

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工业批量生产中具有不确定工作到期日期的鲁棒单机调度问题

涉及不确定工作到期日期的单机调度问题是实际按订单生产环境中最重要的问题之一。为了解决不确定性，本文通过在所有工作的最坏情况下最大程度地减少最大延迟来建立稳健的优化模型。与传统的随机编程模型需要精确的分布不同，我们的模型仅需要到期日期间隔的信息。证明了对于给定序列的最坏情况场景，该场景属于仅包含n个场景的集合，其中n是作业数。然后，将该模型简化并重新表述为等效的混合0-1整数线性规划（MILP）问题。为了有效地解决MILP问题，提出了一种基于鲁棒优势规则的启发式方法。