Study on proportionate flowshop scheduling with due-date assignment and position-dependent weights

In a recent paper, Jiang et al. (Eng Optim 52(1):37–52, 2020) considered proportionate flowshop scheduling with position-dependent weights. For common and slack due-date assignment problems, they proved that both of these two problems can be solved in $$O(n^{2} \log n)$$ time, where $$n$$ is the number of jobs. The contribution of this paper is that we show that these two problems can be optimally solved by a lower-order algorithm, i.e., in $$O(n\log n)$$ time.