Estimating inventory variance with the batch means method

Abstract

This paper presents a simulation experiment and an estimation method to analyze the inventory variance of a production-inventory system with production capacity constraint. We first construct a model of the production-inventory system with production capacity constraint. Next we clarify the problems of estimating inventory variance and propose an estimation method with applying the batch means method to the problems. Furthermore, comparing the proposed method with a previous method developed by Welch, we quantitatively evaluate the performances of the methods. As results, we clarified that the problems of autocorrelation and non-normality of the inventory variance's time series occur as the production capacity constraint becomes tight. In spite of the problems, the estimation method proposed in this paper can estimate inventory variance with satisfying the required confidence level. The Welch method can estimate inventory variance too, however, the proposed method is more suitable to this problem because the length of confidence interval is shorter than that of Welch's method.