A note on "schedule of n jobs on two identical machines to minimize weighted mean flor time"

In a recent paper, Alidaee [Computers ind. Engng 24, 53-55 (1993)] notes the similarity between the scheduling problems of minimizing weighted mean flow time (WMFT) on two parallel machines and minimmizing weighted earliness/tardiness (WET) about a common due date on a single machine. Based on this similarity, Alidaee descirbes how a dynamic programming algorithm proposed by Hall and Posner [Opns Res. 39, 836-846 (1991)] 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 [Mgmt Sci. 12, 437-447 (1966)] as the originator of algorithm described in [Computers ind. Engng 24 53-55 (1993)].