Table of Contents Author Guidelines Submit a Manuscript
Journal of Applied Mathematics
Volume 2013 (2013), Article ID 801734, 9 pages
http://dx.doi.org/10.1155/2013/801734
Research Article

Pareto Optimal Solutions for Stochastic Dynamic Programming Problems via Monte Carlo Simulation

1Departamento de Física e Matemática, Centro Federal de Educaçäo Tecnológica de Minas Gerais, 30510-000 Belo Horizonte, MG, Brazil
2Departamento de Matemática, Universidade Federal de Minas Gerais, 31270-901 Belo Horizonte, MG, Brazil
3Departamento de Estatística, Universidade Federal de Minas Gerais, 31270-901 Belo Horizonte, MG, Brazil

Received 30 May 2013; Accepted 28 September 2013

Academic Editor: Lotfollah Najjar

Copyright © 2013 R. T. N. Cardoso 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

A heuristic algorithm is proposed for a class of stochastic discrete-time continuous-variable dynamic programming problems submitted to non-Gaussian disturbances. Instead of using the expected values of the objective function, the randomness nature of the decision variables is kept along the process, while Pareto fronts weighted by all quantiles of the objective function are determined. Thus, decision makers are able to choose any quantile they wish. This new idea is carried out by using Monte Carlo simulations embedded in an approximate algorithm proposed to deterministic dynamic programming problems. The new method is tested in instances of the classical inventory control problem. The results obtained attest for the efficiency and efficacy of the algorithm in solving these important stochastic optimization problems.