Abstract: The EOQ inventory model for deteriorating item is considered. In a single item distribution channel, the supplier offers a fixed credit period to the retailer, while the retailer in turn provides customers a partially permissible delay in payments. Five distinct cases of the system are explored, and after analyzing the cost structure of the retailer under every scenario, the proper mathematical model is established to find the optimal ordering cycle, so that the total cost incurred per unit time has minimum value. Then the properties of the objective function are derived, and it is shown that there exists at most one minimum point under every situation within its feasible region. Upon this, several propositions are developed to efficiently determine the optimal ordering policy for the retailer. Finally, numerical examples are conducted to illustrate the effectiveness of the proposed model.

Key words: operational research, inventory management, optimization, two levels of trade credit, partially permissible delay in payments, deteriorating item

摘要： 针对易腐品的经济订货批量问题展开研究。在供应商给零售商提供延迟还款的同时,零售商也给顾客提供部分延期还款条件。分五种情况分别讨论零售商的成本构成,并由此建立数学模型以求解最优订货周期使得零售商单位时间总成本最小化。通过数学证明得到了目标函数的解析性质,结果显示每种情况下在可行域范围内至多存在一个极小值点。以此为基础给出了相应的命题以有效地确定零售商的最优决策。最后通过数值算例说明了模型的有效性。

关键词: 运筹学, 库存管理, 最优化, 两级商业信用, 部分延期付款, 易腐品