Abstract In this paper an ( r , Q ) stock policy is used to control an inventory system with deterministic demand and defective items. The fraction of defective items in a batch is a random variable whose variance maybe dependent and independent of the order quantity. Considering the numerous benefits of selling high quality items (noting the vital importance for firms like medical device companies), a full inspection of the order quantity is conducted. Although full inspection reduces returns, ensures high quality products and improves customer satisfaction, it requires a substantial inspection time. Consequently, during this time a non-zero probability of undesirable (unplanned) shortages exists. The dominant suggestion in the literature, is to set the reorder level equal to the total demand during inpection period. This paper suggests an alternative reorder level to prevent shortages during this period and to formulate the backlogging cost in the case that unplanned shortages are permitted. Then, theoretical results ensure the determination of the reorder level and the order quantity that minimize the average total cost of the inventory system. Comparisons, through numerical examples and simulation, demonstrate that the proposed model leads to significant reduction both in cost and probability of shortages (if allowed), in relation to other existing models.

中文翻译：

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具有缺陷物品的库存系统的最佳再订购水平和批量决策

摘要 在本文中，( r , Q ) 库存策略用于控制具有确定性需求和缺陷项目的库存系统。批次中缺陷品的比例是一个随机变量，其方差可能依赖于且独立于订单数量。考虑到销售高质量商品的众多好处（注意对医疗器械公司等公司至关重要），将对订单数量进行全面检查。虽然全检减少了退货，确保了高质量的产品并提高了客户满意度，但它需要大量的检验时间。因此，在此期间，存在不希望（计划外）短缺的非零概率。文献中的主要建议是将重新订购水平设置为等于检查期间的总需求。本文提出了一个替代的再订货水平，以防止在此期间出现短缺，并在允许计划外短缺的情况下制定积压成本。然后，理论结果保证了再订货水平和订货数量的确定，使库存系统的平均总成本最小。通过数值示例和模拟进行的比较表明，与其他现有模型相比，所提出的模型显着降低了成本和短缺概率（如果允许）。