Fuzzy economic production for production inventory

A production cycle is defined using both production and sale, for which to a certain point the production stops until all inventories are sold out. For the planning period of T days, the function of total cost is F(q) where q represents the production quantity of each cycle. The best production quantity in the Crisp sense is qi. Fuzzification of q changes to fuzzy number (Q) over tilde; then, how to determine the best production quantity in the light of (Q) over tilde is the subject of this paper. Suppose the membership function of (Q) over tilde is a trapezoidal fuzzy number set (q(1),q(2),q(3),q(4)) satisfying the condition of 0<q(1) <q2<q3<q4, the membership function of fuzzy cost F((Q) over tilde) is mu(F((Q) over tilde))(z): and its centroid, which is thought to be the estimated total cost and minimum for the condition of 0<q(1)(*)<q(2)(*)<q(3)(*)<q(4)(*). From trapezoidal fuzzy number set (q(1)(*),q(2)(*),q(3)(*),q(4)(*)) find out its centroid as the best production quantity. (C) 2000 Elsevier Science B.V. All rights reserved.