Project portfolio selection and planning with fuzzy constraints

Selecting a project portfolio is a complex process involving many factors and considerations from the time it is proposed to the time the project portfolio is finally selected. Given that making a good selection is of crucial importance, it is essential to develop well-founded mathematical models to lead the organization to its final goal. To achieve this, such models have to reflect as closely as possible both the real situation of the organization as well as its targets and preferences. However, since the process of selecting and implementing project portfolios occurs in real environments and not in laboratories, uncertainty and a lack of knowledge regarding some data is always an important issue due to the strong interdependence between the projects and the political, economic, social, and legal conditions in which they are carried out. In this work, a mathematical model is proposed which extends the classical approach incorporating the inherent uncertainty to these problems. We have handled this uncertainty, vagueness and/or imprecision through the use of fuzzy parameters, which allow representation of information not fully known by the decision makers. The model combines selecting and planning project portfolios, specifies different relationships between projects (synergies, incompatibilities, time order, etc.) and other important constraints appearing in real situations. Moreover, a resolution procedure is developed which obtains, simultaneously, the optimal portfolio and the range for the confidence levels associated to it. An illustrative example and a real application are given in order to show the potentiality of the approach. The results are complemented with graphical tools, which show the usefulness of the proposed model to assist the decision makers.