Generating the efficient frontier of a class of bicriteria generalized fractional programming

In this paper, a particular class of bicriteria maximization problems over a compact polyhedron is considered. The first component of the objective function is the ratio of powers of affine functions and the second one is linear. Several theoretical properties are provided, such as the pseudoconcavi...

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Bibliographic Details
Published in:Decisions in economics and finance 2017-11, Vol.40 (1-2), p.81-101
Main Authors: Cambini, Riccardo, Carosi, Laura, Martein, Laura
Format: Article
Language:English
Subjects:
Econometrics
Economic Theory/Quantitative Economics/Mathematical Methods
Economics
Economics and Finance
Efficiency
Finance
Management
Mathematical programming
Operations Research/Decision Theory
Public Finance
Set theory
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Summary:In this paper, a particular class of bicriteria maximization problems over a compact polyhedron is considered. The first component of the objective function is the ratio of powers of affine functions and the second one is linear. Several theoretical properties are provided, such as the pseudoconcavity of the first criterium of the objective function, the connectedness and compactness of both the efficient frontier and the set of efficient points. The obtained results allow us to propose a new simplex-like solution method for generating the whole efficient frontier; to better clarify the use of the suggested algorithm, several examples are described and the results of a computational test are presented.
ISSN:1593-8883
1129-6569
DOI:10.1007/s10203-017-0196-6