Weighted Throughput Maximization with Calibrations.

The scheduling problem with calibrations was introduced by Bender et al. (SPAA 2013). In sensitive applications, machines need to be periodically calibrated to ensure that they run correctly. Formally, we are given a set of n jobs with release times, deadlines and weights. Calibrating a machine requires a cost and remains calibrated for a period of T time units, after which it must be recalibrated before it can resume running jobs. Moreover, we are given a budget of K calibrations. The objective is to schedule a set of jobs such that the total weight is maximized on m identical machines with at most K calibrations. In this paper, we present a (1/3)-approximation polynomial time algorithm when jobs have unit processing time. For the arbitrary processing time case, we give a ((1 - epsilon)/3)-approximation pseudo-polynomial time algorithm and a ((1 - epsilon)/18)-approximation polynomial time algorithm.