On-line and Semi-online Scheduling Problems on m Parallel Machines with Non-simultaneous Machine Available Times

This paper investigates online and semi-online scheduling problems on m identical parallel machines with non-simultaneous machine available times.The objective function is to maximize the minimum machine completion time.In the online version we prove that the competitive ratio of algorithm LS is m.In the semi-online version,two problems are studied,where the total processing time of all jobs and the largest processing time of all jobs being known in advance.For each problem,we analyze its lower bound and give optimal algorithm with the competitive ratio m-1.