We address a single machine scheduling problem with the objective of minimizing the makespan considering position-based job eligibility where the position that each job can be assigned depends on the machine state. The machine deteriorates each time it processes a job and requires maintenance when there is no job that can be processed. This problem has been newly defined from the pressing operation of the battery manufacturing. We introduce a position limit for a job, which is defined as the maximum allowable position after the machine’s last maintenance. Additionally, we analyze special cases where a specific number of maintenance operations are needed, such as scenarios without any maintenance requirements or those with a single maintenance requirement, and propose optimal solutions. We then provide an optimal polynomial algorithm for the problem.

我们解决了单台机器调度问题，目标是考虑基于职位的作业资格来最小化完工时间，其中每个作业可以分配的职位取决于机器状态。机器每处理一项工作就会恶化，当没有可以处理的工作时就需要维护。这个问题是从电池制造的压制操作中重新定义的。我们引入了作业的位置限制，其定义为机器上次维护后的最大允许位置。此外，我们还会分析需要特定数量维护操作的特殊情况，例如没有任何维护需求或只有单一维护需求的场景，并提出最佳解决方案。然后我们为该问题提供最佳多项式算法。