A note on schedule of n-jobs on two identical machines to minimize weighted mean flow time

In a recent paper, Alidaee notes the similarity between the scheduling problems of minimizing weighted mean flow time (WMFT) on two parallel machines and minimizing weighted earliness/tardiness (WET) about a common due date on a single machine. Based on this similarity, Aldaee describes how a dynamic programming algorithm proposed by Hall and Posner for the WET problem can be modified and applied to the WMFT problem. The work is an important extension of earlier results on an equivalence relationship between the WMFT and WET problems. This note helps consolidate the literature by recognizing Rothkopf as the originator of the algorithm described by Alidaee.