Binary decision diagrams for generating and storing non-dominated project portfolios with interval-valued project scores

When selecting a portfolio (i.e., set of) projects, the projects are often evaluated by additive scores with respect to multiple attributes. Uncertainty or incomplete information about projects’ scores can be modeled with plausible lower and upper bounds on the projects’ scores. It is recommended to select a non-dominated (ND) portfolio, that is a portfolio such that it is not possible to select another portfolio which has (i) at least as high value with respect to every attribute for all plausible scores, (ii) and has strictly higher value with respect to at least one attribute for some plausible scores. In this paper, we lay a foundation on computing (ND) project portfolios. We also present an algorithm based on binary decision diagrams (BDDs) for generating the ND portfolios. We show that our algorithms can provide significant computational advantages over previous algorithms. We also explore how BDDs can be used for storing large numbers of ND portfolios and how such BDDs can be efficiently generated.