Portfolio Scenarios for Interrelated Projects

Most papers on the selection of portfolios of interrelated projects employ mixed-integer programming optimization, data envelopment analysis, and heuristics, along with a few other methods. Although optimizing models do allow the user to find both the optimal and other solutions through sensitivity analysis, they tend to exclude portfolios that might be more desirable because of a combination of quantitative and qualitative criteria. For all practical purposes, these methods do not consider the entire set of possible portfolios, which could be or is assumed to be large. These possible portfolios consist of two groups: those that are not feasible because of mutually exclusive relationships between projects and those that are feasible. Our focus in this article is to identify all feasible portfolios such that the resulting set does not include any portfolio that contains projects with mutually exclusive relationships. We deploy a compatibility matrix that incorporates both the complex interactions and the extent to which projects are mutually exclusive or mutually complementary. We then generate a complete and inclusive set of project portfolio scenarios in which no single portfolio contains mutually exclusive projects. The resulting set generally has a manageable number of project portfolios. We then analyze the complete spectrum of project interactions with mutual exclusivity at one end, complete complementarity at the other, and project independence at the midpoint. Our deceptively simple method can stand alone or be used in conjunction with almost any of the existing methods. This article describes our innovative conceptual framework, which we believe could exert broad influence over managerial practice.