A risk-averse approach to simulation optimization with multiple responses Ebru Angün Dept. of Industrial Engineering, Galatasaray University, Ortaköy 34357, _ Istanbul, Turkey article info Article history: Received 19 November 2009 Received in revised form 20 November 2010 Accepted 1 December 2010 Available online 15 December 2010 Keywords: Average Value-at-Risk Discrete-event dynamic simulation Taguchi’s robustness Multivariate robust parameter design Linear regression abstract This article considers risk-averse simulation optimization problems, where the risk mea- sure is the well-known Average Value-at-Risk (also known as Conditional Value-at-Risk). Furthermore, this article combines Taguchi’s robustness with Response Surface Methodol- ogy (RSM), which results in a novel, robust RSM to solve such risk-averse problems. In case the risk-averse problem is convex, the conic quadratic reformulation of the problem is pro- vided, which can be solved very efficiently. The proposed robust RSM is applied to both an inventory optimization problem with a service-level constraint and a call-center problem; the results obtained for the risk-averse problem and its benchmark problem, where the risk measure is the variance, are intuitively sound and interesting. Ó 2010 Elsevier B.V. All rights reserved. 1. Introduction Robust Parameter Design (RPD) has been successfully applied to improve the quality of products since the mid 1980s, particularly after the work of G. Taguchi in US companies; see Taguchi [30,31]. In his RPD, Taguchi focuses on physical exper- iments, and he distinguishes between two types of variables, namely decision and environmental variables, among those variables that contribute to the experiments. His technique consists of determining the levels of the decision variables that reduce the sensitivity of the process to variations in the environmental variables, thus increasing the robustness of the process. Although Taguchi’s approach to RPD has become popular, his statistical techniques have received considerable criticism from many statisticians including Nair [22] and Myers et al. [20]; in particular, Vining and Myers [32] show inefficiency of Taguchi’s signal-to-noise ratios under certain conditions; i.e., regression metamodels may provide statistically more rigorous alternatives to signal-to-noise ratios. Classic Response Surface Methodology (RSM) focuses on the optimization of the mean of a single random response of industrial processes; see, for example, Myers et al. [20]. This approach is known to be risk-neutral, since the mean perfor- mance measure is optimized on average without taking into account, for example, its estimated variance. In RSM, this risk-neutrality problem is first detected by Myers and Carter [19], who introduce the Dual Response Surface (DRS) approach. The DRS approach is further extended by Vining and Myers [32]. Basically, in the DRS approach, two regression metamodels are fitted for the mean and the variance of a single random response, and then the two fitted regression metamodels are optimized simultaneously in a region of interest. Furthermore, the DRS approach uses Lagrange multipliers to explore can- didate solutions in a manner similar to ridge regression. The DRS approach has received a great deal of attention from researchers. Fan and Del Castillo [7] present a methodology for building a so-called optimal region for the global optimal operating conditions to address the inherent sampling errors in DRS. Ross et al. [28] extend the DRS such that the decision-makers’ preferences can be incorporated into the selection of the 1569-190X/$ - see front matter Ó 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.simpat.2010.12.006 E-mail address: eangun@gsu.edu.tr Simulation Modelling Practice and Theory 19 (2011) 911–923 Contents lists available at ScienceDirect Simulation Modelling Practice and Theory journal homepage: www.elsevier.com/locate/simpat