Fuzzy mixture inventory model involving fuzzy random variable lead time demand and fuzzy total demand

This article considers the mixture inventory model involving variable lead time with backorders and lost sales. We first fuzzify the random lead-time demand to be a fuzzy random variable and obtain the total cost in the fuzzy sense. Then, we further fuzzify the total demand to be the triangular fuzzy number and derive the fuzzy total cost. By the centroid method of defuzzification, we derive the estimate of total cost in the fuzzy sense. Also, we find the optimal solution for order quantity and lead time in the fuzzy sense such that the total cost has a minimum value. A numerical example is provided to illustrate the results of proposed model.