Models for a fuzzy inventory of two replaceable merchandises without backorder based on the signed distance of fuzzy sets

This paper investigates the inventory problems for two mutually complementary merchandises. We first consider the merchandises in a monopoly market, and then in a perfect competitive market. With the fuzzy sets concept, we discuss how to determine the optimal ordering policy for the aforementioned inventory problem such that the total related cost is minimum. Three results are obtained and the numerical examples are provided to illustrate these results. In contrast with the previous studies that employed the extension principle and centroid method to derive the estimate of the total cost in the fuzzy sense, we show that using the decomposition principle and the signed distance can attain it easier.