An integrated vendor–buyer cooperative inventory model in an imperfect production process with shortage backordering

In this paper, we develop an integrated inventory model for vendor–buyer coordination under an imperfect production process. The proportion of defective items in each production lot is assumed to be stochastic and follows a known probability density function. The vendor inspects the items while they are being produced and delivers good-quality items to the buyer in small lots over multiple shipments. We assume that shortages are permitted and are completely backordered. The expected annual integrated total cost is derived and a solution procedure is provided to find the optimal solution. Numerical examples show that the integrated model gives an impressive cost reduction in comparison to an independent decision by the buyer. The results also show that if back orders are permitted, the expected integrated annual cost is less than that when back orders are not permitted. Therefore, if customers are willing to wait for the next shipment when a shortage occurs, it is profitable for the company to allow back orders although the delay incurs a penalty cost.