Decomposable systems, decomposition and 0-1 integer programming techniques are reviewed relative to project selection problems. It is concluded that a heuristic procedure is a suitable way to handle such problems in organizational settings. A hierarchical multiperiod multidimensional model is proposed. Good results are obtained based on an existing heuristic algorithm by Toyoda, by means of a decomposable interactive formulation. Examples and discussions are included that show how the use of this model can improve management decisions. A major advantage of this formulation is its flexibility to handle many different R&D situations, a feature which should increase its usefulness over many other R&D Project Selection Models. The model can be used in a multihierarchy ambience, can use parametric budgeting, and can be used as a control tool. The interactive feature provides the means for improving organizational communications and integrating divergent viewpoints.