隨機克利金法(Stochastic Kriging)是一種開發已久，用於模型化(metamodeling)隨機模擬模型的方法。隨機克利金法是將克利金法(Kriging)進行改良後的一種方法，相較於克利金法忽略了各模擬試驗中的每個重複試驗中輸出值的變異數，隨機克利金法加入了重複試驗中的內部變異數視為隨機模擬中固有的不確定性，進而使得隨機克利金法能夠更好的運用在隨機模擬上。
本研究主要為研究隨機克利金法在受限制式下進行估計設計點的模擬值，建立一個能夠快速得出總成本的模型，在該模型下找出最佳的訂貨政策。實驗研究了在( s , S )存貨系統下，目標為找到s和S的最佳解，使其總成本最小化；使用隨機克利金法之後所得到的元模型(metamodel)，將我們給定的設計點帶入元模型中，篩選出服從限制式條件下的設計點，最後篩選出最小成本的s和S值。

This paper demonstrated an experiment exploring the potential of the Stochastic Kriging methodology for constrained simulation optimization. The experiment study an ( s , S ) inventory system with the objective of finding the optimal values of s&S and the minimize total cost. The goal function and constraints in these experiment, did the approach to determine the optimum combination predicted by the Stochastic Kriging prediction model. The results of this experiment indicate that Stochastic Kriging offers opportunities for solving constrained optimization problems in stochastic simulation

[1]. Andradóttir, S.,“A review of simulation optimization techniques”,Proceedings of the 1998 Winter Simulation Conference, pp.151–158, 1998
[2]. Ankenman, B., B. L. Nelson, and J. Staum., “Stochastic kriging for simulation metamodeling”, Operations Research, 2008.
[3]. Bastos, L. S., and A. O’Hagan., “Diagnostics for Gaussian process emulators”Vol. 51, No. 4, Special Issue on Computer Modeling, pp. 425-438 ,2008.
[4]. Barton, R. R., and M. Meckesheimer., ”Metamodel-based simulation optimization. In Simulation”, Vol.3, Handbooks in Operations Research and Management Science, Chapter 18, pp.535–574,2006.
[5]. Bashyam,S. & Fu. M.C., “Optimization of (s,S) inventory systems with random lead timesand service level constraint”, Management Science,44(12-part-2), pp.243-255,1998.
[6]. Box, G.E.P.,“The exploration and exploitation of response surfaces”, pp.16–60,1954
[7]. Cressie, N.A.C., ”Statistics for spatial data”,1993.
[8]. Fang, K.T., R. Li, and A. Sudjianto, “Design and modeling for computer experiments”, 2006.
[9]. Fabian,T., Fisher,J., Sasieni,M.,& Yardeni.A., ”Purchasing raw material on a fluctuating market”,Operations Research,7,pp.107-122,1959.
[10]. Gramacy, R. B., and H. K. H. Lee.,“Bayesian treed Gaussian process models with an application to computer modeling, ”Journal of the American Statistical Association, pp.1119–1130, 2008.
[11]. Staum. Jeremy,“Better Simulation Metamodeling: The Why, What, and How of Sochastic kriging”, Winter Simulation Conference.,2009.
[12]. Kroese, D. P., Brereton, T., Taimre, T., Botev, Z. I.,“Why the Monte Carlo method is so important today”,WIREs Comput Stat6, pp. 386–392,2014.
[13]. Kleijnen, J.P.C.,“A comment on Blanning’s metamodel for sensitivity analysis: The regressionmetamodel in simulation”,Interfaces .Vol.5,pp.21–23.,1975
[14]. Kleijnen, J. P.C., “Kriging metamodeling in simulation: a review”. European Journal of Operational Research, Vol.192,pp.707–716,2009.
[15]. Santner. T. J., B. J. Williams, and W. I. Notz., ”Design and analysis of computer experiments”,New York: Springer-Verlag,2003.
[16]. Stein, M. L.,“Interpolation of spatial data: Some theory for kriging”, Springer Series in Statistics, 1999.
[17]. Tijms.H. C. &Groenevelt. H., ”Simple approximations for the recorder point in periodic and continuous review (s,S) inventory systems with service level constraints”,European journal of operational research,17(2), pp.175-180,1984.
[18]. van Beers & Kleijnen, J.P.C., ”Kriging for interpolation in random simulation”, Journal of the Operational Research Society,54,pp.255–262,2003.
[19]. William E.B., Jack P. C., Kleijnen., Wim C. M. van Beers., Inneke van Nieuwenhuyse, “Kriging metamodeling in constrained simulation optimization:an explorative study”, IEEE, 2008