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An algorithm is proposed for scheduling project networks having a single constraining resource and a constant level of available resources. The algorithm seeks to generate a minimum length schedule indirectly by maximizing the average resource utilization over the two time intervals represented by the current decision point and its successor. An attempt is made to schedule all of the activities whose predecessors have been completed; failing this, all feasible subsets are considered. Where possible, the algorithm considers only those subsets which introduce new activities at the subsequent decision point.