Efficient heuristics for minimizing weighted sum of squared tardiness on identical parallel machines

Scheduling jobs on a set of identical parallel machines using efficient heuristics when the objective is to minimize total weighted squared tardiness is considered. Two efficient heuristics and an improvement procedure are presented for the problem. These heuristics and other heuristics are tested using problem sets that represent a variety of conditions. The results show that one of the heuristics consistently performs better than the other heuristics tested. It is also shown how these heuristics can be incorporated into other procedures such as the existing Lagrangian relaxation procedure or meta-heuristics to obtain improved solutions for medium sized problems.