Scheduling is presented of N dependent tasks made up of unit execution time operations of M nonidentical machines. As a scheduling criterion the elapsed time for completing all tasks is considered. The paper demonstrates that the scheduling problem can be characterized as a special case of a discrete control problem with mixed-integer control variables, a fixed final state and free terminal time to be minimized. A single pass scheduling algorithm is provided in which implied due-dates are systematically updated until a feasible schedule is obtained. Solution results are included for a simple numerical example.