Resource-constrained project scheduling: from a lagrangian relaxation to competitive solutions

List scheduling belongs to the classical and widely used algorithms for scheduling problems, but for resource-constrained project scheduling problems most standard priority lists do not capture enough of the problem structure, often resulting in poor performance. We use a well-known Lagrangian relaxation to first compute schedules which do not necessarily respect the resource constraints. We then apply list scheduling in the order of so-called α-completion times of jobs. Embedded into a standard subgradient optimization, our computational results show that the schedules compare to those obtained by state-of-the-art local search algorithms. In contrast to purely primal heuristics, however, the Lagrangian relaxation also provides powerful lower bounds, thus the deviation between lower and upper bounds can be drastically reduced by this approach.