In this paper the problem of scheduling to meet two performance criteria is considered. The first criteria relates to timeliness while the second relates to precedence (or technological) constraints. An ideal schedule is one that yeilds the best measure of timeliness without violating the precedence constraints. However in some systems, such as flexible manufacturing systems and real time scheduling systems, it is sometimes possible that all precedence constraints need not be met. Given deadlines by which all tasks must be completed, it may be desirable to perform an alternate set of tasks, perform tasks out of order or even omit some tasks given these deadlines. In this paper the case where it is permissible to violate some precedence constraints for a commensurate improvement in meeting timing constraints is considered. Thus, the precedence constraints are no longer inviolate constraints, but can be represented by another measure of performance. The problem of preparing task schedules is formulated such that a trade-off between timing and precedence constraints is made when both constraints cannot be met and procedures are developed to obtain solutions for arbitrary deadlines.