The project scheduling problem has been widely studied given the practical importance it has and the complexity to find efficient solutions. In this work we address an extension of the same problem based on the Resource-Constrained Multi-Project Scheduling Problem, taking into account that each project has a set of own resources available for consumption. We propose a hybrid algorithm based on Ant Colony Optimization and a Local Search procedure based on Hill-Climbing First Improvement supported by an SMT Solver as a movement satisfaction verifier. Our approach was tested with a set of 12 instances belonging to the MPSPLIB datasets. We have obtained near-optimal solutions for several instances of the problem.