Semi-online Multiprocessor Scheduling with Nonsimultaneous Machine Available Times

This paper investigates scheduling problems on m parallel identical machines with non-simultaneous machine available times. Each machine M_i is not available until time r_i. Jobs arrive one by one, and we are required to schedule jobs irrevocably on machines as soon as they are given, without any knowledge of the successive jobs. We study semi-online version of the problem while we known the largest processing time of all jobs in advance, the objective is to minimize the makespan, i.e. the maximum completion time of the processors. A lower bound (√(33) + 3)/6 is showed when the number of machines is greater than 6, and a semi-online algorithm is presented with competitive ratio of at most 2-1/(m-1).