On-line Single Machine Scheduling with Release Dates and Submodular Rejection Penalties

Xiaofei Liu, Yaoyu Zhu, Weidong Li, Lei Ma

Abstract: In this paper, we consider the on-line single machine scheduling problem with release dates and submodular rejection penalties. We are given a single machine and a sequence of jobs that arrive on-line and must be immediately and irrevocably either assigned on the machine or rejected. The objective is to minimize the sum of the makespan of the accepted jobs and the penalty of the rejected jobs which is determined by a submodular function. We prove that there is no on-line algorithm with a constant competitive ratio if the penalty submodular function is nonmonotone. When the penalty submodular function is monotone, we present an on-line algorithm with a competitive ratio 3.