Disregarding duration uncertainty in partial order schedules? Yes, we can!

Abstract

In the context of Scheduling under uncertainty, Partial Order Schedules (POS) provide a convenient way to build flexible solutions. A POS is obtained from a Project Graph by adding precedence constraints so that no resource conflict can arise, for any possible assignment of the activity durations. In this paper, we use a simulation approach to evaluate the expected makespan of a number of POSs, obtained by solving scheduling benchmarks via multiple approaches. Our evaluation leads us to the discovery of a striking correlation between the expected makespan and the makespan obtained by simply fixing all durations to their average. The strength of the correlation is such that it is possible to disregard completely the uncertainty during the schedule construction and yet obtain a very accurate estimation of the expected makespan. We provide a thorough empirical and theoretical analysis of this result, showing the existence of solid ground for finding a similarly strong relation on a broad class of scheduling problems of practical importance. © 2014 Springer International Publishing.