Optimal ordering policy for a deteriorating item with imperfect quality and partial backordering

This study develops a production-inventory model considering a deteriorating item with imperfect quality and partial backordering. Such implicit assumptions are reasonable in view of the fact that poor-quality items do exist during production. Defective items are usually picked up during the screening process. Shortages are partially backordered since not all customers are willing to wait for new replenishments of stocks. The impatient customer will result in lost sale. The analysis shows that our model is a generalization of the models in current literatures. Also, a lower bound on the back-ordered ratio is obtained to ensure concave of the net expected profit function. An algorithm and numerical analysis are used to illustrate the solution procedure. Computational results indicate that our model leads to more realistic results.