Parallel Genetic Algorithms (GAs) are developed to solve a single machine n-job scheduling problem which is to minimize the sum of absolute deviations of completion times from a common due date. (0, 1) binary scheme is employed to represent the n-job schedule. Two selection methods, best individual selection and simple selection are examined. The effect of crossover operator, due date adjustment mutation and due date adjustment reordering are discussed. The performance of the parallel genetic algorithm is illustrated with some example problems.