This paper considers a parallel-machine scheduling problem with dedicated and common processing machines using GA (Genetic Algorithm). Non-identical setup times, processing times and order lot size are assumed for each machine. The GA is proposed to minimize the total-tardiness objective measure. In this paper, heuristic algorithms including EDD (Earliest Due-Date), SPT (Shortest Processing Time) and LPT (Longest Processing Time) are compared with GA. The effectiveness and suitability of the GA are derived and tested through computational experiments.