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This paper considers the problem of scheduling a set of jobs on both a single machine and identical parallel machines with the objective of minimizing the makespan or maximum completion time of all jobs. Jobs are subject to release dates and there are sequence-dependent setup times. Since this problem is known to be strongly NP-hard even for the single machine case, this paper proposes a heuristic algorithm to solve it. The algorithm uses a strategy of random generation of various execution sequences, and then selects the best of such schedules. Experiments are performed using random-generated data. Results show that the heuristic performs very well compared against the optimal solution, and requiring short computational time.