This paper studies a single machine scheduling problem in which all jobs have the common due date and penalties are assessed for jobs at different rates. The scheduling objective is to minimize the weighted mean absolute deviations(WMAD). This problem may provide greater flexibility in achieving scheduling objectives than the mean absolute deviation (MAD) problem. We propose three heuristic solution methods based on several dominance conditions. Numerical examples are presented. This article extends the results to the problem to the problem of scheduling n-jobs on m-parallel identical processors in order to minimize the weighted mean absolute deviation.