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Journal of Applied Mathematics
Volume 2014, Article ID 957108, 8 pages
http://dx.doi.org/10.1155/2014/957108
Research Article

A Bicriteria Approach Identifying Nondominated Portfolios

1Escuela de Ingeniería Industrial, Universidad Diego Portales, 8370179 Santiago, Chile
2Pontificia Universidad Católica de Valparaíso, 2362807 Valparaíso, Chile
3Universidad Finis Terrae, 7500000 Santiago, Chile
4Universidad Autónoma de Chile, 7500000 Santiago, Chile

Received 27 February 2014; Accepted 18 June 2014; Published 3 July 2014

Academic Editor: Mohammad Khodabakhshi

Copyright © 2014 Javier Pereira et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We explore a portfolio constructive model, formulated in terms of satisfaction of a given set of technical requirements, with the minimum number of projects and minimum redundancy. An algorithm issued from robust portfolio modeling is adapted to a vector model, modifying the dominance condition as convenient, in order to find the set of nondominated portfolios, as solutions of a bicriteria integer linear programming problem. In order to improve the former algorithm, a process finding an optimal solution of a monocriteria version of this problem is proposed, which is further used as a first feasible solution aiding to find nondominated solutions more rapidly. Next, a sorting process is applied on the input data or information matrix, which is intended to prune nonfeasible solutions early in the constructive algorithm. Numerical examples show that the optimization and sorting processes both improve computational efficiency of the original algorithm. Their limits are also shown on certain complex instances.