An optimal decision policy for a single-vendor single-buyer production-inventory system with leaning effect, fuzzy demand and imperfect quality

This papers studies the optimization of an integrated SVSB (single-vendor single-buyer) production-inventory system consisted of a manufacturer and a retailer. Productivity learning effect, imperfect quality, fuzzy demand and backlogging are incorporated in the model to minimize the total cost of the retailer and the manufacturer. An algorithm is developed to solve the model to obtain the optimal order quantity of the retailer, optimal shipment number for one production cycle of the manufacturer and the optimal maximum backlogging of the retailer. Numerical examples show that the optimal shipment decreases with the increase of the learning coefficient. When the learning coefficient is small, the fluctuation of demand will have an important impact on the optimal cost. In the early phase of production, the learning effect is significant in reducing cost, but its role is limited in the latter phase.