Scheduling parallel machines to minimize total weighted and unweighted tardiness

This article considers the problem of scheduling a set of n jobs on m parallel machines to minimize total weighted and unweighted tardiness. A modified due date (MDD) algorithm will be presented. The MDD algorithm of Baker and Bertrand is a special case of our algorithm. When all the jobs have a common due date, a worst case bound for the MDD rule in single machine will be given. In this case, if the weight of jobs are proportional to the processing times, the largest processing time order is optimal for the single machine problem. Computational results for the identical machines are presented. The results show that MDD rule outperforms other existing rules by a large margin. Concepts in this article can be incorporated into other rules to improve their performances.