Application of fuzzy set theory to economic production quantity model

A method for solving the production inventory control problem is presented here where the input data are described by fuzzy members. It is assumed that the imperfect products can be discounted instantaneously at the end of the production process in each cycle, and the shortage is permitted and replenished linearly in the next cycle. Using the graded mean integration representation technique for defuzzification, the defuzzified economic production quantity model is derived. According to the convex characteristic of the model, the optimal production quantity under a minimum of total inventory cost can be obtained. Finally, the numerical example and sensitivity analysis are made to explain the presented model.