On the Mathematical Theory of Schedules

The elapsed time to complete a scheduled task is expressed as a function of the completion times of the component tasks and the path matrix of the scheddule graph. The schedule function is interpreted geometrically as a polyhedron. If the scheduled activities have random completion times, the probability distribution of the time to complete the entire task is found by integrating over the contours of the polyhedron. Composite schedule functions are represented by algebraic formulae which are applicable in both the probabilistic and non-probabilistic cases. A method for joint control of cost and schedule is presented.