A note on scheduling on two identical machines with early work maximization

Abstract This paper considers the problem of scheduling on two identical machines to maximize the total early work with a common due date of all the jobs. Chen et al. (2020) showed that the worst-case ratio of the classical LPT algorithm for the problem is at most 10/9 and provided an instance to show that the bound of LPT is at least 12/11. In this note we show that the tight bound of LPT is exactly 12/11.