Online Parallel-Machine Scheduling in KRT Environment to Minimize Total Weighted Completion Time

This paper studies online scheduling on m identical parallel machines under the KRT environment, where jobs arrive over time and “KRT” means that in the online setting no jobs can be released when all of the machines are busy. The goal is to determine a feasible schedule to minimize the total of weighted completion times. When m = 1, we prove that WSPT is an optimal online algorithm. When m ≥ 2, we first present a lower bound m2−2+m4 −4m+4 2m(m−1), and then show that WSPT is a 2-competitive online algorithm for the case m = 2. For the case in which m = 2 and all jobs have equal processing times, we provide a best possible online algorithm with a competitive ratio of 1+3 2.