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, production is usually dependend on demand. This paper derives a production model for the lot-size inventory system with finite production rate, taking into consideration the effect of decay and the condition of permissible delay in payments. Usually no interest is charged if the outstanding amount is settled within the permitted fixed settlement period. Therefore, it makes economic sense for the customer to delay the settlement of the replenishment account up to the last moment of the permissible period allowed by the supplier. In this model shortages are permitted and fully backordered . The purpose of this paper is to investigate a computing schema for the EPQ. The model is illustrated with a numerical example. Keywords Economic production quantity, permissible delay, weibull distribution, deterioration
