an epq model of exponential deterioration with fuzzy demand and production with shortages

in the fundamental production inventory model, in order to solve the economic production quantity (epq) we always fix both the demand quantity and the production quantity per day. but, in the real situation, both of them probably will have little disturbances every day. therefore, we should fuzzify both of them to solve the economic production quantity (q*) per cycle. using α-cut for defuzzification the total variable cost per unit time is derived. therefore the problem is reduced to crisp annual costs. the multi-objective model is solved by global criteria method with the help of grg (generalized reduced gradient) technique. in this model shortages are permitted and fully backordered. the purpose of this paper is to investigate a computing schema for the epq in the fuzzy sense. we find that, after defuzzification, the total cost in fuzzy model is less than in the crisp model. so it permits better use of the epq model in the fuzzy sense arising with little disturbances in the production, and demand.