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Multiobjective project portfolio selection with fuzzy constraints

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Abstract

Decision makers usually have to face a budget and other type of constraints when they have to decide which projects are going to be undertaken (to satisfy their requirements and guarantee profitable growth). Our purpose is to assist them in the task of selecting project portfolios. We have approached this problem by proposing a general nonlinear binary multi-objective mathematical model, which takes into account all the most important factors mentioned in the literature related with Project Portfolio Selection and Scheduling. Due to the existence of uncertainty in different aspects involved in the aforementioned decision task, we have also incorporated into the model some fuzzy parameters, which allow us to represent information not fully known by the decision maker/s. The resulting problem is both fuzzy and multiobjective. The results are complemented with graphical tools, which show the usefulness of the proposed model to assist the decision maker/s.

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Notes

  1. In fact, it was in 1922 when Lukasiewicz questioned classic Boolean logic and proposed a logic of likely values in the interval unit as a generalisation of his three-valued logic. In the 1930s, several multi-valued logics were proposed for any given number of true likely values (equal to or greater than 2), and which were identified using rational numbers in the interval [0, 1]. Subsequently, in 1937, Max Black (1909−1989) published "Vagueness: An exercise in Logical Analysis" and in 1942 and 1950, Karl Menger (1902−1985) published two articles on indistinguishable fuzzy relationships in Statistical Metrics".

  2. By the "most likely value" we mean "the value that experts consider to be the most likely value".

  3. In this paper we prefer to use confidence level, since this term is familiar to those working in mathematical programming outside the domain of fuzzy logic. However, in Zimmermann (1996), for example, the α parameter is called the degree of truth or simply the degree of membership in a fuzzy set.

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Acknowledgements

This research has been partially funded by the Regional Government of Andalusia (Excellence Research Project P10-TIC-06618), and by the Regional Government of Andalusia Grants Programme for Teaching and Research Staff (2008).

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  1. Department of Applied Economics (Mathematics), Universidad de Málaga, Campus El Ejido s/n, 29071, Málaga, Spain

    F. Perez & T. Gomez

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Perez, F., Gomez, T. Multiobjective project portfolio selection with fuzzy constraints. Ann Oper Res 245, 7–29 (2016). https://doi.org/10.1007/s10479-014-1556-z

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