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In this study, an optimal integrated vendor-buyer inventory model with defective items is proposed. Most researches for defective items assumed that an inspection process is carried out by the buyer. We consider that the vendor conducts the inspection process and disposes defective items in multiple batches. We prove that the function of annual cost is convex, and obtain closed-form expressions. A solution procedure is used to derive the optimal order quantity, the number of shipments and the number of defective item disposals. Numerical examples are provided to illustrate our model. Setting the fraction of defective items be zero, the numerical examples indicate that the proposed model can result in the solutions of the existing models without considering defective items. Moreover, a sensitivity analysis is used to reveal the effects of cost parameters on the optimal solution. When the disposal cost is relatively low, we show that a multiple disposals strategy may perform better than a single disposal strategy.

An integrated lot-sizing model for imperfect production with multiple disposals of defective items