Calibrations scheduling with arbitrary lengths and activation length

Eric Angel (), Evripidis Bampis (), Vincent Chau () and Vassilis Zissimopoulos ()
Additional contact information
Eric Angel: University Paris Saclay
Evripidis Bampis: Sorbonne UniversitéCNRS
Vincent Chau: Southeast University
Vassilis Zissimopoulos: National and Kapodistrian University of Athens

Journal of Scheduling, 2021, vol. 24, issue 5, No 2, 459-467

Abstract: Abstract 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.

Keywords: Scheduling; Calibration; Dynamic programming (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1007/s10951-021-00688-5

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