Bounds in Tree-Based Approaches to Generate Project Portfolios in the Presence of Interactions

Portfolio decision models have become an important branch of decision analysis. Portfolio problems are inherently complex, because of the combinatorial explosion in the number of portfolios that can be constructed even from a small number of items. To efficiently construct a set of portfolios that provide good performance in multiple criteria, methods that guide the search process are needed. Such methods require the calculation of bounds to estimate the performance of portfolios that can be obtained from a given partial portfolio. The calculation of such bounds is particularly difficult if interactions between items in the portfolio are possible. In the paper, the authors introduce a method to represent such interactions and develop various bounds that can be used in the presence of interactions. These methods are then tested in a computational study, where they show that the bounds they propose frequently provide a good approximation of actual outcomes, and also analyze specific properties of the problem that influence the approximation quality of the proposed bounds.