A single-machine scheduling problem with deterioration and learning effect is studied in the present paper. The processing time and due date are considered uncertain variables due to lack of historical data. The aim is to minimize the makespan, total completion time, total weight completion time, and maximum lateness under an uncertain environment. To address the problem in an uncertain environment, the expected value model and pessimistic value model are developed. These models can be converted into equivalent models based on the inverse distribution method. It is proved that the corresponding dispatching rules can solve the problem optimally under different objective criteria. Finally, sensitivity analysis is used to illustrate the effectiveness of these rules.

中文翻译：

---

具有恶化和学习效果的不确定单机调度

研究了具有恶化和学习效果的单机调度问题。由于缺乏历史数据，处理时间和到期日被认为是不确定的变量。目的是在不确定的环境下，使制造期，总完成时间，总重量完成时间和最大延迟最小化。为了解决不确定环境中的问题，开发了期望值模型和悲观值模型。这些模型可以基于逆分布方法转换为等效模型。实践证明，在不同的客观标准下，相应的调度规则可以最优地解决问题。最后，使用敏感性分析来说明这些规则的有效性。