This paper focuses on production planning and scheduling problems in an assembly system operating on a make-to-order basis. Due dates are considered as constraints in the problems, that is, tardiness is not allowed. Since the planning problem is a higher-level decision making than the scheduling problem, the scheduling problem is solved using a production plan obtained by solving the planning problem. We suggest heuristic procedures in which aggregated information is used when the production planning problem is solved while more detailed information is used when the scheduling problem is solved. Since a feasible schedule may not be obtained from a production plan, an iterative approach is employed in the two procedures to obtain a solution that is feasible for both the production planning and scheduling problems. Computational tests on randomly generated test problems are done to show the performance of these algorithms, and results are reported.