A semi-online algorithm and its competitive analysis for parallel-machine scheduling problem with rejection

Abstract

Abstract In this paper, we focus on a semi-online scheduling problem with rejection on identical parallel machines, where “semi-online” means that the ratio of the longest processing time among all jobs to the shortest one is no more than γ with γ\xa0≥\xa01. In particular, in this setting, there are a coupling of independent jobs arriving online over time with the flexibility of rejection, which implies that each job will be either accepted and scheduled on one of identical machines or rejected at the cost of penalty cost. Our objective is minimizing the total completion time of the accepted jobs plus the total penalty cost of the rejected jobs. For this problem, we design a deterministic polynomial time semi-online algorithm entitled as α Delayed Shortest Processing Time with Rejection (ADSPTR). In competitive analysis, by adopting the approach “Improved Instance Reduction”, we obtain the competitive ratio of ADSPTR is at most 1 + 1 + γ ( γ − 1 ) − 1 γ .