Minimal delaying alternatives and semi-active timetabling in resource-constrained project scheduling

Over the years numerous branch-and-bound procedures for solving the resource-constrained project scheduling problem have been developed. Enumerating delaying alternatives, extension alternatives, feasible posets, feasible sequences or feasible subsets, they all aim at finding as fast as possible a makespan minimal schedule among the resource and precedence feasible ones. The enumeration is oftenly reduced to the dominant set of semi-active schedules by checking feasibility of local left-shifts. In this paper we show that combining the concepts of minimal delaying alternatives and local left-shifts, if not properly done, does not, as claimed in the literature, reduce the enumeration to the set of semi-active schedules.