Project portfolio optimization is one of the most important strategic-decision problems faced by any organization. The construction of the best portfolio that accomplishes a certain balance among the selected projects can be defined as follows:
(1)
where RF is the space of feasible portfolios, and represents the functions zi that characterize the impact of a portfolio x over the considered criteria.
Although typical, Problem (1) is not the unique way in which decision makers (DMs) are concerned with project portfolio selection. Several papers (Fernandez 2009, Fernandez 2013, Bastiani 2015 and Fernandez 2017) have approached a problem with a distinctive feature, which is that the only information available about the projects is their rank, (they are ordered according to the DM’s preferences) and their budgetary requirements. This situation is related to the fact that sometimes a DM may i) prefer simpler decision methods; ii) agree easily on a priority ranking, or when the DM is a complex collective entity for which is very hard to evaluate the project objectives and to solve a multi-criteria optimization problem like (1).
Bastiani et al. (2015) y Fernández et al. (2017) proposed an optimization approach based on maximizing the cardinality and minimizing the discrepancies in a portfolio; cardinality refers to the total number of supported projects; the term discrepancy is a concept that reflects the negative effect that is applied over the DM's thinking because one of the projects, when it is compared against others, seems to have merits that belong to the portfolio but it is not in it.
Synergic effects in subsets of projects are not considered by the works from Bastiani et al. (2015) and Fernández et al. (2017), what is perhaps their most important limitation. The purpose of this contribution is in incorporating synergy in the proposal of Fernández et al. (2017). Synergy is related to the existence of complex interdependencies among projects. They compete for resources, but some can share them, becoming more advantageous when they are supported together. Likewise, it is very common for synergy to be manifested in subsets of projects and that, therefore, the combined contribution of them to the impact of the portfolio is greater than the sum of their separate contributions. We propose here to use a strategy based on creating artificial projects that represent synergic coalitions, with their own budgetary requirements (usually less than the sum of their components), and their specific rank (better than the rank of their component projects). Such strategy would need a re-definition of the objectives in the optimization problem. The objectives related to discrepancies may keep their original meaning, but those related to cardinality should be modified through some way to take into account the impact increased by synergy.
[Bastiani et al., 2015] Bastiani, S. Samantha, et al. "Portfolio Optimization From a Set of Preference Ordered Projects Using an Ant Colony Based Multi-objective Approach." International Journal of Computational Intelligence Systems 8.sup2 (2015): 41-53.
[Fernandez, 2009] E. Fernandez, L. F. Felix and G. Mazcorro, “Multiobjective Optimisation of an Outranking Model for Public Resources Allocation on Competing Projects”, International Journal of Operational Research, Vol. 5, No. 2, pp. 190-210, 2009.
[Fernandez, 2013] E. Fernandez and R. Olmedo, “Public Project Portfolio Optimization under a Participatory Paradigm”, Applied Computational Intelligence and Soft Computing, 2013, doi: 10.1155/2013/891781.
[Fernandez, 2017]Eduardo Fernandez, Claudia Gómez-Santillán, Laura Cruz-Reyes, Nelson Rangel-Valdez, and Shulamith Bastiani, “Design and Solution of a Surrogate Model for Portfolio Optimization Based on Project Ranking,” Scientific Programming, vol. 2017, Article ID 1083062, 10 pages, 2017.
