A class of on-line scheduling algorithms to minimize total completion time

We consider the problem of scheduling jobs on-line on a single machine and on identical machines with the objective to minimize total completion time. We assume that the jobs arrive over time. We give a general 2-competitive algorithm for the single machine problem. The algorithm is based on delaying the release time of the jobs, i.e., making the jobs artificially later available to the on-line scheduler than the actual release times. Our algorithm includes two known algorithms for this problem that apply delay of release times. The proposed algorithm is interesting since it gives the on-line scheduler a whole range of choices for the delays, each of which leading to 2-competitiveness. We also show that the algorithm is 2α competitive for the problem on identical machines where α is the performance ratio of the Shortest Remaining Processing Time first rule for the preemptive relaxation of the problem.