This study develops a mathematical model for an integrated vendor-buyer inventory with defective items and inspection error. We assume an imperfect production process with a known of defective probability. The buyer conducts a 100% quality check. However, due to an imperfect inspection process, the quality-controller may reject a good item as a defective item (Type I error), or accept a defective item as a non-defective item (Type II error). Different from existing research, we incorporate freight cost (a function of shipping weight and the distance between the vendor and the buyer) and stochastic lead time (a function of production and transportation times). The objective of the study is to minimize the joint total expected cost. This study indicates that Type I error is more significant when it is compared with Type II error. We also illustrate how the joint total expected cost and the lead time are significantly influenced by the distance of the buyer and the vendor. The results of our analysis also show that lead time can be shortened if the vendors speed up their shipment with smaller production lot sizes. Numerical examples and sensitivity analysis are given to illustrate the results.

这项研究为带有缺陷项目和检查错误的集成卖方-买方库存开发了一个数学模型。我们假设生产过程不完善，并且已知缺陷概率。买方进行100％的质量检查。但是，由于检查过程不完善，质量控制人员可能会将良品拒绝为有缺陷的物品（I类错误），或者将有缺陷的物品视为无缺陷的物品（II类错误）。与现有研究不同，我们将货运成本（运输重量和卖方与买方之间的距离的函数）和随机提前期（生产和运输时间的函数）合并在一起。研究的目的是使联合的总预期成本最小化。这项研究表明，与II型错误相比，I型错误更为显着。我们还说明了联合总预期成本和交货时间如何受买主和卖主的距离的显着影响。我们的分析结果还显示，如果供应商以较小的生产批次数量加快发货速度，则可以缩短交货时间。数值例子和灵敏度分析说明了结果。