Maximizing set function formulation of two scheduling problems

In this note two problems are considered: (1)Scheduling n jobs non-preemptively on a single machine to minimize total weighted earliness and tardiness (WET). (2)Scheduling n jobs non-preemptively on two parallel identical processors to minimize weighted mean flow time (WMFT). A new approach for these problems is presented. The approach is based on a problem of maximizing a submodular set function. Heuristic algorithm for the problems also is presented.