Strong valid inequalities for the resource-constrained scheduling problem with uniform resource requirements

We consider the resource-constrained scheduling problem when each job’s resource requirements remain constant over its processing time. We study a time-indexed formulation of the problem, providing facet-defining inequalities for a projection of the resulting polyhedron that exploit the resource limitations inherent in the problem. Lifting procedures are then provided for obtaining strong valid inequalities for the original polyhedron. Computational results are presented to demonstrate the strength of these inequalities.