Fuzzy Flexibility and Product Variety in Lot-Sizing

In terms of flexibility and product variety in lot-sizing systems of crisp cases, the average demand of per unit of time (mj), the relative duration of setup (qj), and the unit cost of production (cj) are considered. Instead of using the usual method that the mj, qj, and cj in the total cost function are respectively fuzzified by the triangular fuzzy numbers to derive fuzzy total cost, in this paper, we construct three different intervals to include mj, qj, and cj, respectively, and then consider the fuzzification of the system from these three different intervals directly. And finally the fuzzy total cost is obtained. By applying respectively the signed distance and centroid method for defuzzification, two different total cost functions are obtained, and thus the respective optimal solutions are computed.