Calibrations Scheduling Problem with Arbitrary Lengths and Activation Length

TL;DR

This paper investigates calibration scheduling for machines with arbitrary and unit processing times, providing optimal algorithms for some cases and proving NP-hardness for others, to minimize calibration costs in safety-critical testing.

Contribution

It extends existing models by considering arbitrary processing times and multiple calibration types, offering polynomial algorithms and NP-hardness proofs.

Findings

Optimal polynomial-time algorithm for single-machine calibration with arbitrary processing times and preemption.

NP-hardness of calibration scheduling with multiple calibration types and arbitrary processing times.

Polynomial-time solution for recalibration with non-instantaneous calibration in unit-time jobs.

Abstract

Bender et al. (SPAA 2013) have 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 often calibrated. Given that calibration costs, it is important to study policies minimizing the calibration cost while performing all the necessary tests. We focus on the single-machine setting and we extend the model proposed by Bender et al. by considering that the jobs have arbitrary processing times and that the preemption of jobs is allowed. For this case, we propose an optimal polynomial time algorithm. Then, we study the case where there are several types of calibrations with different lengths and costs. We first 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-time jobs and we show that a more general problem, where the recalibration of the machine is not instantaneous but takes time, can be solved in polynomial time.