Completion Time Scheduling and the WSRPT Algorithm

We consider the online scheduling problem of minimizing the total weighted and unweighted completion time on identical parallel machines with preemptible jobs. We show a new general lower bound of 21/19 ≈ 1.105 on the competitive ratio of any deterministic online algorithm for the unweighted problem and 16− √ 14 11 ≈ 1.114 for the weighted problem. We then analyze the performance of the natural online algorithm WSRPT (Weighted Shortest Remaining Processing Time). We show that WSRPT is 2-competitive. We also prove that the lower bound on the competitive ratio of WSRPT for this problem is 1.215.