Online scheduling with rearrangement on two related machines

In this paper, we consider an online non-preemptive scheduling problem on two related machines with rearrangement to minimize the completion time, called online scheduling with bounded rearrangement, which is a semi-online problem. Jobs arrive one by one over list. When a new job arrives at most K already scheduled jobs can be removed from the schedule, then all removed jobs and the new job must be assigned to the machines. The problem is a relaxation of the similar problem online scheduling with a buffer [4]. Assume machine M1 has speed 1 and M2 has speed s≥1. With respect to the worst case ratio, we obtain that (i) for or K≥2, the model of online scheduling with bounded rearrangement is equivalent to the model of online scheduling with a bounded buffer; (ii) the model of online scheduling with bounded rearrangement is more powerful than the model of online scheduling with a bounded buffer for and K=1; (iii) except for and K=1 there is an optimal algorithm for the online scheduling with bounded rearrangement; (iv) for s>1.618 the lower bound is improved.