  Resource Constrained Project Scheduling Problems (RCPSPs) without preemption
are well-known NP-hard combinatorial optimization problems. A feasible RCPSP
solution consists of a time-ordered schedule of jobs with corresponding
execution modes, respecting precedence and resources constraints. In this
paper, we propose a cutting plane algorithm to separate five different cut
families, as well as a new preprocessing routine to strengthen resource-related
constraints. New lifted versions of the well-known precedence and cover
inequalities are employed. At each iteration, a dense conflict graph is built
considering feasibility and optimality conditions to separate cliques,
odd-holes and strengthened Chv\'atal-Gomory cuts. The proposed strategies
considerably improve the linear relaxation bounds, allowing a state-of-the-art
mixed-integer linear programming solver to find provably optimal solutions for
754 previously open instances of different variants of the RCPSPs, which was
not possible using the original linear programming formulations.
