In this study, a new heuristic approach to the resource constrained project scheduling problem is introduced. This approach, which is called local constraint based analysis (LCBA), is more robust than the dispatching rules found in the literature, since it does not depend on an a priori insight as do the dispatching rules. LCBA consists of the application of local essential conditions which respect the current temporal and resource constraints to generate a necessary sequence of activities at a scheduling decison time point in a single-pass parallel scheduling algorithm. LCBA is a time efficient procedure due to the localized aspect with which the activities are handled. Only the activities which are schedulable at the current scheduling time are considered for the application of the essential conditions. LCBA is tested against well-known rules from the literature and some recently developed rules. This testing is done using a set of problems of a special design and also a set of optimally solved problems from a recent benchmark in the literature. It is observed that near optimal time efficient solutions are obtained by LCBA and the procedure’s performance is considerably better than that of the dispatching rules.