In this paper we consider an n-job non-preemptive and identical parallel machine scheduling problem of minimizing the sum of earliness and tardiness with different release times and due dates. In the real world this problem is more realistic than the problems that release times equal to zero or due dates are common. The problem is proved to be NP-complete. Thus a heuristic is developed to solve this problem To illustrate its suitability a proposed heuristic is compared with a genetic algorithm for a large number of randomly generated test problems. Computational results show the effectiveness and efficiency of proposed heuristic. In summary the proposed heuristic provides good solutions than genetic algorithm when the problem size is large.