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∼} = (s1,s0,s2). 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 s1, s0, s2 (s1<s0<s2) we find the membership function μGq({S∼})(z) of the fuzzy cost function Gq({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.