Scheduling to minimize average completion time revisited: Deterministic on-line algorithms

We consider the scheduling problem of minimizing the average weighted completion time on identical parallel machines when jobs are arriving over time. For both the preemptive and the nonpreemptive setting, we show that straightforward extensions of Smith's ratio rule yield smaller competitive ratios compared to the previously best-known deterministic on-line algorithms, which are (4 + ε)-competitive in either case. Our preemptive algorithm is 2-competitive, which actually meets the competitive ratio of the currently best randomized on-line algorithm for this scenario. Our nonpreemptive algorithm has a competitive ratio of 3.28. Both results are characterized by a surprisingly simple analysis; moreover, the preemptive algorithm also works in the less clairvoyant environment in which only the ratio of weight to processing time of a job becomes known at its release date, but neither its actual weight nor its processing time. In the corresponding nonpreemptive situation, every on-line algorithm has an unbounded competitive ratio.