Fuzzy mixture inventory model with variable lead-time based on probabilistic fuzzy set and triangular fuzzy number

This article considers the fuzzy problems for the mixture inventory model involving variable lead-time with backorders and lost sales. `Ve first use the probabilistic fuzzy set to construct a new random variable for lead-time demand, and derive the total expected annual cost in the fuzzy sense. Then, the average demand per year is fuzzified as the triangular fuzzy number. For this case, two methods of defuzzification, namely signed distance and centroid, are employed to find the value of total expected annual cost in the fuzzy sense. Next, the backorder rate of the demand during the stock-out period is also fuzzified as the triangular fuzzy number, and the value of total expected annual cost in the fuzzy sense is derived using the signed distance. For the proposed models, we provide a solution procedure to find the optimal lead-time and the optimal order quantity such that the total expected annual cost in the fuzzy sense has a minimum value.