Stochastic programming methods in the response surface methodology

  • Authors:

  • José A. Díaz-García;Rogelio Ramos-Quiroga;Enrique Cabrera-Vicencio

  • Affiliations:

  • Department of Statistics and Computation, Universidad Autónoma Agraria Antonio Narro, 25350 Buenavista, Saltillo, Coahuila, México;Centro de Investigación en Matemáticas AC, Callejón de Jalisco s/n, 36240 Guanajuato, México;Department of Statistics, Universidad de Valparaíso, Valparaíso, Chile

  • Venue:
  • Computational Statistics & Data Analysis
  • Year:
  • 2005

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Abstract

Considering the minimisation of an estimated second degree polynomial response surface model as a problem of stochastic programming, this article establishes the equivalent deterministic programs applying the so called E-model, V-model, P-model and minimax methods. Similarly, after observing that some of the solutions by the techniques of stochastic programming coincide with the solution of a multiobjective optimisation problem, this paper proposes two alternative methods for the solution of the stochastic optimisation of a second degree polynomial response surface model: (i) A lexicographic method, and (ii) A method based on distances. An example is solved by means of the described techniques.