The single machine coupled task scheduling problem includes a set of jobs, each with two separated tasks, and there is an exact delay between the tasks. We investigate the single machine coupled task scheduling problem with the objective of minimizing the makespan under identical processing time for the first task and identical delay period for all jobs, and the time-dependent processing time setting for the second task. Certain healthcare appointment scheduling problems can be modeled as the coupled task scheduling problem. Also, the incorporation of time-dependent processing time for the second task lets the human resource fatigue and the deteriorating health conditions be modeled. We provide optimal solution under certain conditions. In addition, we propose a dynamic program under the condition that the majority of jobs share the same time-dependent characteristic. We develop a heuristic for the general case and show that the heuristic performs well.

中文翻译：

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将任务调度与时间相关的处理时间相结合

单机耦合任务调度问题包括一组作业，每个作业有两个独立的任务，任务之间存在精确的延迟。我们研究了单机耦合任务调度问题，目标是在第一个任务的相同处理时间和所有作业的相同延迟时间下最小化完工时间，以及第二个任务的时间相关处理时间设置。某些医疗预约调度问题可以建模为耦合任务调度问题。此外，将与时间相关的处理时间纳入第二个任务可以模拟人力资源疲劳和不断恶化的健康状况。我们在特定条件下提供最佳解决方案。此外，在大多数工作具有相同的时间依赖性特征的情况下，我们提出了一个动态程序。我们为一般情况开发了一种启发式方法，并表明该启发式方法性能良好。