Since on-time delivery is becoming increasingly important in today's competitive markets, the development of effective scheduling methodologies to meet customer needs through on time delivery is of vital importance for the well-being of companies. The objective of this study is to develope a general heuristic algorithm for scheduling both the static and dynamic problems under certain on-time delivery criteria. For the problems with due-date related, we present insights for minimizing the number of tardy jobs and propose a heuristic scheduling algorithm. Experimental results show that the proposed algorithm performs significantly better than other dispatching rules within reasonable computation time, specially in the environment of strong competition for resources.