Abstract: This paper deals with two period inventory optimization problem for perishable items where the demand rate depends on the service-level of the previous replenishment cycle. Two scenarios are considered, namely, (1)the buyer order once and (2)the buyer order several times in the selling period. Two inventory models are proposed respectively by maximizing the average profit. In addition, we prove the existence and uniqueness of the optimal inventory service-level and ordering quantity. Finally, an example is presented and the sensitivity analyses on the parameters are conducted to illustrate the validity and the effectiveness of the proposed models. The results show that, in the first case, when the unit inventory holding cost or deteriorating rate increases, the average profit of the system will decrease. As the deteriorating rate increases, the ordering quantity will also increase. In the second case, when the unit inventory holding cost, the expected service-level of customers or the loss rate of order during the shortage increases, the inventory service-level and the average profit of the system will decrease. Only when the inventory holding cost is extremely small, is order once more profitable, so the buyer will usually choose to order several times to enhance the profit. The results also indicate that, service-level is an important factor that influence the inventory policy, and the enterprise should balance the service-level and profits.

Key words: operational management, inventory model, optimization, perishable items, service-level-dependent demand rate

摘要： 本文研究需求依赖于上一周期服务水平、缺货时订单部分损失的两周期易变质品库存问题。分别考虑一次订货和多次订货两种情况,以平均利润最大化为目标构建库存模型,证明了模型解的存在性和唯一性,得到了最优库存服务水平和最优补货策略。最后,通过算例给出两个模型的应用,对重要参数进行了灵敏度分析,并且将两种模型的结果进行了对比分析。结果表明:订单损失率的增加会提高服务水平,但会使得利润降低;顾客期望服务水平的提高会降低第一阶段的服务水平,同时使利润减少;单位库存持有成本或变质率的增加会降低服务水平和平均利润。通常情况,企业通过多次订货能获得更大的利润,而只有当库存持有成本极小时,一次订购才能够获得更大的利润。同时,结果也表明:服务水平对库存策略有较大的影响,因此在进行库存决策时考虑服务水平具有重要的作用。

关键词: 物流与供应链管理, 库存模型, 最优化, 易变质品, 需求依赖于服务水平