A two level heuristic for the resource constrained scheduling problem is presented. This heuristic is based on a combination of priority rules where utilization of resources by the operations, the critical path of operations in a job, and the due dates of the jobs are taken into account. The schedules that this heuristic generates have been compared with small problems for which optimal solutions are available and it is shown that these solutions are generally within 15% of the optimal. Also the polynomial time and space complexity of the heuristic is demonstrated.