The Project scheduling with resource constraints problem can be formulated as follows: given a graph G with node set N, a set H of directed arcs corresponding to precedence relations, and a set H' of disjunctive arcs reflecting the resource incompatibilities, find among the subsets of H' satisfying the resource constraints the set S that minimizes the longest path in graph (N,HℝS). The authors define the project scheduling polyhedron QS as the convex hull of the feasible solutions. They investigate several classes of inequalities with respect to their facet-defining properties for the associated polyhedron. The dimension of QS is calculated and several inequalities are shown to define facets. For the inequalities that do not define facets, the authors derive some general lifting theorems and apply them to obtain in general stronger inequalities and facets in some special cases.
