Online lazy bureaucrat scheduling with a machine deadline

The lazy bureaucrat scheduling problem was first introduced by Arkin et al. (Inf Comput 184:129–146, 2003). Since then, a number of variants have been addressed. However, very little is known on the online version. In this note we focus on the scenario of online scheduling, in which the jobs arrive over time. The bureaucrat (machine) has a working time interval. Namely, he has a deadline by which all scheduled jobs must be completed. A decision is only based on released jobs without any information on the future. We consider two objective functions of min-makespan] and min-time-spent]. Both admit best possible online algorithms with competitive ratio of \(\frac{\sqrt{5}+1}{2}\approx 1.618\).