LAUSR

In a recent study, Sun et al. (AOR 292:113–131, 2020) studied due-window proportionate flow shop scheduling problems with position-dependent weights. For common due-window (denoted by CONW) and slack due-window (denoted by SLKW) assignment methods, they proved that these two problems can be solved in $$O(n^2\log n)$$ O ( n 2 log n ) time respectively, where n is the number of jobs. In this paper, we consider the same problems, and our contribution is that the CONW problem can be optimally solved by a lower-order algorithm, which runs in $$O(n\log n)$$ O ( n log n ) time, implying an improvement of a factor of n .