Response Surface Methodology

CentER Discussion Paper Series No. 2014-013

26 Pages Posted: 15 Feb 2014

Date Written: February 14, 2014

Abstract

This chapter fi…rst summarizes Response Surface Methodology (RSM), which started with Box and Wilson’s article in 1951 on RSM for real, non-simulated systems. RSM is a stepwise heuristic that uses …first-order polynomials to approximate the response surface locally. An estimated polynomial metamodel gives an estimated local gradient, which RSM uses in steepest ascent (or descent) to decide on the next local experiment. When RSM approaches the optimum, the latest …rst-order polynomial is replaced by a second-order polynomial. The …fitted second-order polynomial enables the estimation of the optimum. Furthermore, this chapter focuses on simulated systems, which may violate the assumptions of constant variance and independence. The chapter also summarizes a variant of RSM that is proven to converge to the true optimum, under speci…c conditions. The chapter presents an adapted steepest ascent that is scale-independent. Moreover, the chapter generalizes RSM to multiple random responses, selecting one response as the goal variable and the other responses as the constrained variables. This generalized RSM is combined with mathematical programming to estimate a better search direction than the steepest ascent direction. To test whether the estimated solution is indeed optimal, bootstrapping may be used. Finally, the chapter discusses robust optimization of the decision variables, while accounting for uncertainties in the environmental variables.

Keywords: simulation; optimization; regression, robustness; risk

JEL Classification: C0, C1, C9

Suggested Citation

Kleijnen, Jack P.C., Response Surface Methodology (February 14, 2014). CentER Discussion Paper Series No. 2014-013, Available at SSRN: https://ssrn.com/abstract=2395836 or http://dx.doi.org/10.2139/ssrn.2395836

Jack P.C. Kleijnen (Contact Author)

Tilburg University, CentER ( email )

P.O. Box 90153
Tilburg, 5000 LE
Netherlands
+31 13 4662029 (Phone)
+31 13 4663377 (Fax)

HOME PAGE: http://https://sites.google.com/site/kleijnenjackpc/

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