This study aims at presenting fuzzy optimal production  and shortage quantity  for fuzzy production inventory with backorder when setup, holding, and shortage costs are fuzzy. For this purpose, two different fuzzy models, one of which includes crisp production and crisp shortage quantity, and the other of which involves those that are fuzzy, have been presented by making use of trapezoidal fuzzy numbers. For each model, fuzzy total cost FTC has been attained via function principle. In order to defuzzify the FTC, graded mean integration method has been used, and as to solve inequality constrained problems, extension of the Lagrangean method has been applied.

inventory models, shortage, fuzzy set theory, fuzzy number.