Optimal inventory model for items with imperfect quality and shortage backordering

In this study, we develop an optimal inventory model for items with imperfect quality and shortage backordering. Such implicit assumption is reasonable in view of the fact that poor-quality items do exist during production. They are usually picked up during the screening process and are withdrawn from stock instantaneously. It is assumed that all customers are willing to wait for new supply when there is a shortage. The analysis shows that our model is a generalization of the models in current literatures. An algorithm and numerical analysis developed show that our model always results in better performance.