The process of project portfolio selection is crucial in many organizations, especially R&D organizations. There is a need to make informed decisions on the investment in various projects or lack thereof. As the projects may continue over more than 1 year, and as there are connections between various projects, there is a need to not only decide which project to invest in but also when to invest. Since future benefits from projects are to be depreciated in comparison with near-future ones, and due to the interdependency among projects, the question of allocating the limited resources becomes quite complex. This research provides a novel heuristic method for allocating the limited resources over multi-annual planning horizons and examines its results in comparison with an exact branch and bound solution and various heuristic ones. This paper culminates with an efficient tool that can provide both practical and academic benefits.