Reducing the feasible region to a scheduling problem

A special class of scheduling problems is considered. We consider cycle-free sets of fronts correspond to the orderings of a network. If the project is recourse-constrained, the same cycle-free set of fronts can correspond to different orderings. Some cycle-free sets of fronts can be subsets of others. The goal of the paper is to characterize maximal cycle-free sets of fronts because only those are essential for obtaining an optimal schedule.