Online scheduling of simple linear deteriorating jobs to minimize the total general completion time

Traditional scheduling assumes that the processing time of a job is fixed. Yet there are numerous situations in which the processing time increases (deteriorates) as the start time increases. In particular, lots of work has been devoted to jobs with simple linear deterioration. The processing time pj of job Jj is a simple linear function of its start time sj, precisely, pj=bjsj, where bj is the deteriorating rate. In this paper, we study the problem of online non-preemptive scheduling of jobs with arbitrary release times and simple linear deteriorating rates on a single machine to minimize the total general completion time. We present an algorithm DSDR (Delayed Smallest Deteriorating Rate) and prove that it achieves the best-possible competitive ratio for all deterministic online algorithms, where α is the general index of completion time and α>0.