A Semi-Online Algorithm For Single Machine Scheduling With Rejection

In this paper, a single-machine semi-online scheduling problem with rejection is addressed. In this model, "semi-online" implies that p(max)/p(min) <= gamma, where p(max) and p(min) are the maximum processing time and the minimum one among all jobs, respectively, gamma >= 1. In this setting, each job arrives online over time, and rejection is allowable. Our goal is minimizing the total penalty cost of rejected jobs plus the total completion time of processed jobs. The seminal result of this study is that we offer an algorithm with competitive ratio 1 + root 1+gamma(gamma-1)-1/gamma, which matches the result of the problem without rejection.