Abstract
In this paper we consider the backorder inventory problem with fuzzy backorder such that the backorder quantity is a triangular fuzzy number S ̃ = (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 μ G q ( S ̃ ) (Z) of the fuzzy cost function G q ( S ̃ ) 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.
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