Modeling project interactions in multiattribute portfolio decision analysis : Axiomatic foundations and practical implications

A common approach to modeling project interactions in multiattribute project portfolio selection is to augment the additive portfolio utility function, in which portfolio utility is the sum of the included projects’ utilities, with additional terms representing the synergy/cannibalization effects triggered by selecting specific subsets of projects. In this paper we develop a set of sufficient and necessary assumptions for representing preferences among multiattribute project portfolios with a quasi-symmetric multilinear utility function and show how this function gives rise to interpreting interaction effects as additional terms in the additive portfolio utility function. To foster practical applicability of these theoretical contributions, we also develop techniques to elicit such portfolio utility functions as well as optimization models to identify the feasible portfolio that satisfies relevant resource and other constraints with the maximal expected utility. In recognition that incorporating project interactions necessitates increased involvement of decision makers in assessing the interaction effects and results in computationally more challenging portfolio optimization problems, we analyze the importance of modeling interactions through series of simulation studies based on randomly generated and real-world data sets. Specifically, we examine the impact that omitting project interactions has on the project-level decision recommendations and on the expected utility of the recommended portfolio.