This paper proposes a novel method to select an experimental design for interpolation in simulation. Although the paper focuses on Kriging in deterministic simulation, the method also applies to other types of metamodels (besides Kriging), and to stochastic simulation. The paper focuses on simulations that require much computer time, so it is important to select a design with a small number of observations. The proposed method is therefore sequential. The novelty of the method is that it accounts for the specific input/output function of the particular simulation model at hand; that is, the method is application-driven or customized. This customization is achieved through cross-validation and jackknifing. The new method is tested through two academic applications, which demonstrate that the method indeed gives better results than either sequential designs based on an approximate Kriging prediction variance formula or designs with prefixed sample sizes.

Whenever simulation requires much computer time, interpolation is needed. There are several interpolation techniques in use (for example, linear regression), but this paper focuses on Kriging. This technique was originally developed in geostatistics by D. G. Krige, and has recently been widely applied in deterministic simulation. This paper, however, focuses on random or stochastic simulation. Essentially, Kriging gives more weight to 'neighbouring' observations. There are several types of Kriging; this paper discusses -besides Ordinary Kriging -a novel type, which 'detrends' data through the use of linear regression. Results are presented for two examples of input/output behaviour of the underlying random simulation model: A perfectly specified detrending function gives the best predictions, but Ordinary Kriging gives quite acceptable results; traditional linear regression gives the worst predictions.

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This article presents a novel heuristic for constrained optimization of computationally expensive random simulation models. One output is selected as objective to be minimized, while other outputs must satisfy given theshold values. Moreover, the simulation inputs must be integer and satisfy linear or nonlinear constraints. The heuristic combines (i) sequentialized experimental designs to specify the simulation input combinations, (ii) Kriging (or Gaussian process or spatial correlation modeling) to analyze the global simulation input/output data resulting from these designs, and (iii) integer nonlinear programming to estimate the optimal solution from the Kriging metamodels. The heuristic is applied to an (s, S) inventory system and a call-center simulation, and compared with the popular commercial heuristic OptQuest embedded in the Arena versions 11 and 12. In these two applications the novel heuristic outperforms OptQuest in terms of number of simulated input combinations and quality of the estimated optimum.

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