Restarts can help in the on-line minimization of the maximum delivery time on a single machine

We consider a single-machine on-line scheduling problem where jobs arrive over time. A set of independent jobs has to be scheduled on a single machine. Each job becomes available at its release date, which is not known in advance, and its characteristics, i.e. processing requirement and delivery time, become known at its arrival. The objective is to minimize the time by which all jobs have been delivered. In our model preemption is not allowed, but we are allowed to restart a job, that is, the processing of a job can be broken off to have the machine available to process an urgent job, but the time already spent on processing this interrupted job is considered to be lost. We propose an on-line algorithm and show that its performance bound is equal to 1.5, which matches a known lower bound due to Vestjens. For the same problem without restarts the optimal worst-case bound is known to be equal to (√(5) + 1)/2 ≈ 1.61803; this is the first example of a situation in which the possibility of applying restarts reduces the worst-case performance bound, even though the processing times are known.