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Bender et al. (SPAA 2013) have proposed a theoretical framework for testingin contexts where safety mistakes must be avoided. Testing in such a context ismade by machines that need to be often calibrated. Given that calibrationcosts, it is important to study policies minimizing the calibration cost whileperforming all the necessary tests. We focus on the single-machine setting andwe extend the model proposed by Bender et al. by considering that the jobs havearbitrary processing times and that the preemption of jobs is allowed. For thiscase, we propose an optimal polynomial time algorithm. Then, we study the casewhere there are several types of calibrations with different lengths and costs.We first prove that the problem becomes NP-hard for arbitrary processing timeseven when the preemption of the jobs is allowed. Finally, we focus on the caseof unit-time jobs and we show that a more general problem, where therecalibration of the machine is not instantaneous but takes time, can be solvedin polynomial time.

Calibrations Scheduling Problem with Arbitrary Lengths and Activation Length