We study the scheduling problem with calibrations and time slot costs. In this problem, the machine has to be calibrated to run a job and such a calibration only remains valid for a fixed time period of length T, after which it must be recalibrated in order to execute jobs. On the other hand, a certain cost will be incurred when the machine executes a job and such a cost is determined by the time slot that is occupied by the job in the schedule. We consider jobs with release times, deadlines and identical processing times. The objective is to schedule the jobs on a single machine and minimize the total cost while calibrating the machine at most K times.

We investigate the structure of the optimal schedule and based on that we propose dynamic programs for different scenarios of the problem. At last, for another variant of the problem without the consideration of machine calibration, a greedy algorithm is proposed, which is based on matroid theory.

我们用校准和时隙成本研究调度问题。在这个问题中，必须对机器进行校准以运行作业，并且这种校准仅在长度为T的固定时间段内保持有效，此后必须重新校准以执行作业。另一方面，当机器执行作业时，将产生一定的成本，并且该成本由时间表中该作业所占用的时隙确定。我们考虑具有发布时间，截止日期和相同处理时间的作业。目的是在单台机器上安排作业，并最大程度地降低总成本，同时最多校准K次。

我们研究最佳计划的结构，并在此基础上针对问题的不同情况提出动态程序。最后，针对不考虑机器校准的问题的另一变体，提出了一种基于拟阵理论的贪婪算法。