On the optimal release time of jobs with random processing times, with extensions to other criteria

We treat the problem of the optimal release time of a set of n jobs en masse to satisfy individual due dates and confidence levels under various objective functions. We propose a dynamic programming approach that has general applicability to single and multiple processors. We provide some dominance relations that should alleviate the computing burden which, in the worst case, is of time complexity O( n2 n ). Three special cases (same confidence level for all jobs; same due date for all jobs; and the ‘hierarchical case’) are immediate consequences of our general model.