Bender et al. (SPAA 2013) proposed a theoretical framework for testing in contexts where safety mistakes must be avoided. Testing in such a context is made by machines that need to be calibrated on a regular basis. Since calibrations have a non-negligible cost, it is important to study policies minimizing the total calibration cost while performing all the necessary tests. We focus on the single-machine setting, and we study the complexity status of different variants of the problem. First, we extend the model by considering that the jobs have arbitrary processing times, and we propose an optimal polynomial-time algorithm when the preemption of jobs is allowed. Then, we study the case where there are many types of calibrations with their corresponding lengths and costs. We prove that the problem becomes NP-hard for arbitrary processing times even when the preemption of the jobs is allowed. Finally, we focus on the case of unit processing time jobs, and we show that a more general problem, where the recalibration of the machine is not instantaneous, can be solved in polynomial time via dynamic programming.

本德尔等人。(SPAA 2013) 提出了一个理论框架，用于在必须避免安全错误的情况下进行测试。在这种情况下的测试是由需要定期校准的机器进行的。由于校准具有不可忽视的成本，因此在执行所有必要测试的同时研究将总校准成本最小化的策略非常重要。我们专注于单机设置，并研究问题的不同变体的复杂性状态。首先，我们通过考虑作业具有任意处理时间来扩展模型，并在允许作业抢占时提出最优多项式时间算法。然后，我们研究了存在多种校准类型及其相应长度和成本的情况。我们证明即使在允许抢占作业的情况下，该问题对于任意处理时间也变得 NP-hard。最后，我们关注单元处理时间作业的情况，我们展示了一个更一般的问题，即机器的重新校准不是即时的，可以通过动态规划在多项式时间内解决。