Economic reorder point for fuzzy backorder quantity

In this paper we consider the backorder inventory problem with fuzzy backorder such that the backorder quantity is a triangular fuzzy number (S) over tilde = (s(1), s(0), s(2)). Suppose s* and q*, denote the crisp economic backorder and order quantities respectively in the classical inventory with backorder model. According to four order relations of s*, and s(1), s(0), s(2) (s(1) < s(0) < s(2)) we find the membership function mu(Gq((S) over bar))(z) Of the fuzzy cost function Gq((S) over tilde) and their centroid. We also obtain the economic order quantity q** and the economic backorder quantity s** in the fuzzy sense. We conclude that, after solving the model in the fuzzy sense, the total cost is slightly higher than that in the crisp model; however, it permits better use of the economic fuzzy quantities arising with changes in orders, deliveries, and sales. (C) 1998 Elsevier Science B.V.