Minimizing Total Weighted Flow Time with Calibrations

In sensitive applications, machines need to be periodically calibrated to ensure that they run to high standards. Creating an efficient schedule on these machines requires attention to two metrics: ensuring good throughput of the jobs, and ensuring that not too much cost is spent on machine calibration. In this paper we examine flow time as a metric for scheduling with calibrations. While previous papers guaranteed that jobs would meet a certain deadline, we relax that constraint to a tradeoff: we want to balance how long the average job waits with how many costly calibrations we need to perform. One advantage of this metric is that it allows for online schedules (where an algorithm is unaware of a job until it arrives). Thus we give two types of results. We give an efficient offline algorithm which gives the optimal schedule on a single machine for a set of jobs which are known ahead of time. We also give online algorithms which adapt to jobs as they come. Our online algorithms are constant competitive for unweighted jobs on single or multiple machines, and constant-competitive for weighted jobs on a single machine.