This paper is a comprehensive review of the research conducted over the past four decades in the domain of time-dependent scheduling, where variable processing times of jobs depend on when the jobs start. The paper is divided into four parts. The first part recalls some definitions and notions, introduces terminology, and defines the main models of time-dependent job processing times and the notation that is used throughout the paper. The second part summarizes four decades of time-dependent scheduling research, focusing on the computational complexity of time-dependent scheduling problems, and algorithms solving these problems. The results are divided into groups with respect to the machine environment and illustrated by examples. The third part concentrates on new topics in time-dependent scheduling, such as two-agent time-dependent scheduling, mutually related time-dependent scheduling problems, and time-dependent scheduling games. The last part discusses the most important time-dependent scheduling problems which still await solution. The paper is completed by bibliographic notes and an extensive list of references.

中文翻译：

---

时间相关调度的四个十年回顾：主要结果、新主题和未解决的问题

这篇论文是对过去四十年来在时间相关调度领域进行的研究的全面回顾，其中作业的可变处理时间取决于作业的开始时间。论文分为四个部分。第一部分回顾了一些定义和概念，介绍了术语，并定义了与时间相关的作业处理时间的主要模型以及整篇论文中使用的符号。第二部分总结了时间相关调度研究的四个十年，重点关注时间相关调度问题的计算复杂度，以及解决这些问题的算法。结果根据机器环境进行分组，并通过示例进行说明。第三部分专注于时间相关调度中的新主题，例如双代理时间相关调度，相互关联的时间相关调度问题和时间相关调度博弈。最后一部分讨论仍在等待解决的最重要的时间相关调度问题。该论文由书目注释和广泛的参考文献列表完成。