An improved on-line algorithm for single parallel-batch machine scheduling with delivery times

We study an on-line single parallel-batch machine scheduling problem where each job has a processing time and a delivery time. Jobs arrive over time and the batch capacity is unbounded. Jobs can be processed in a common batch, and each job is delivered independently and immediately at its completion time on the machine. The objective is to minimize the time by which all the jobs are delivered. We provide an on-line algorithm with a competitive ratio 22−1≈1.828, which improves on a 2-competitive on-line algorithm for this problem in the literature.