Constrained Multicriteria Sorting Method Applied to Portfolio Selection
The paper focuses on portfolio selection problems which aim at selecting a subset of alternatives considering not only the performance of the alternatives evaluated on multiple criteria, but also the performance of portfolio as a whole, on which balance o
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Abstract. The paper focuses on portfolio selection problems which aim at selecting a subset of alternatives considering not only the performance of the alternatives evaluated on multiple criteria, but also the performance of portfolio as a whole, on which balance over alternatives on specific attributes is required by the Decision Makers (DMs). We propose a two-level method to handle such decision situation. First, at the individual level, the alternatives are evaluated by the sorting model Electre Tri which assigns alternatives to predefined ordered categories by comparing alternatives to profiles separating the categories. The DMs’ preferences on alternatives are expressed by some assignment examples they can provide, which reduces the DMs’ cognitive efforts. Second, at the portfolio level, the DMs’ preferences express requirements on the composition of portfolio and are modeled as constraints on category size. The method proceeds through the resolution of a Mixed Integer Program (MIP) and selects a satisfactory portfolio as close as possible to the DMs’ preference. The usefulness of the proposed method is illustrated by an example which integrates a sorting model with assignment examples and constraints on the portfolio definition. The method can be used widely in portfolio selection situation where the decision should be made taking into account the performances of individual alternatives and portfolio simultaneously. Keywords: Multicriteria decision aiding, Portfolio selection, Preference elicitation.
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Introduction
Let us consider the student enrollment in universities every year. Universities want to select students with good performances on several criteria (such as GPAs, motivation, maturity, . . . ). At the same time, the selected students should satisfy some specific requirements at a collective level. For instance, the number of students in each department should be more or less balanced. Each department tries to achieve a gender (nationality, etc.) diversity. Moreover, the positions available are limited. Therefore, the universities face a decision which consists of selecting a certain number of students, designing a waiting list and rejecting R.I. Brafman, F. Roberts, and A. Tsouki` as (Eds.): ADT 2011, LNAI 6992, pp. 331–343, 2011. c Springer-Verlag Berlin Heidelberg 2011
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J. Zheng, O. Cailloux, and V. Mousseau
the other students (see similar example in universities [7], other examples are available in the book [28]). Another example of such portfolio selection problems concerns allocating grants to research proposals. The committee evaluates the merit of the proposal, including originality, novelty, rigor and the ability of the researchers to carry out the research individually. On a whole level, they try to balance the funding among disciplines, institutions and even regions. Therefore, a decision is to be made to select certain research proposals within limited budget. The two problems above share some characteristics. Firstly, they involve evaluating individual alternatives according to thei
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