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

Rodrigo T. N. Cardoso | Zendy; Ricardo H. C. Takahashi | Zendy; F.R.B. Cruz | Zendy

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

Author(s) -

Rodrigo T. N. Cardoso,

Ricardo H. C. Takahashi,

F.R.B. Cruz

Publication year - 2013

Publication title -

journal of applied mathematics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.307

H-Index - 43

eISSN - 1687-0042

pISSN - 1110-757X

DOI - 10.1155/2013/801734

Subject(s) - mathematical optimization , quantile , randomness , monte carlo method , heuristic , dynamic programming , computer science , pareto principle , stochastic programming , quantile function , random variable , mathematics , econometrics , statistics , moment generating function

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

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