Optimal semi‐online scheduling algorithms on two parallel identical machines under a grade of service provision

This paper investigates semi‐online scheduling problems on two parallel identical machines under a grade of service (GoS) provision. We consider two different semi‐online versions where the optimal offline value of the instance is known in advance or the largest processing time of all jobs is known in advance. Respectively for the two semi‐online models, two algorithms with competitive ratios of 3/2 and $(\sqrt{5}+1)/2$ are shown to be optimal.