This study formulates an inventory model with limited storage capacity under the condition of order-size dependent trade credit. Shortages are allowed and partially backlogged. The objective of this study is to determine the optimal replenishment cycle length, the optimal fraction of no shortage, and whether retailers should choose to rent an extra warehouse to store more items, such that retailers’ total annual profit is maximized. We prove the global optimally of objective functions and derive the closed-form optimal solution. Some numerical examples are presented to illustrate the applicability of the proposed model. Sensitivity analysis is carried out and managerial insights are obtained. We find that if retailers’ own warehouse capacity is relatively small, they always benefit from enlarging order quantity and renting an extra warehouse; meanwhile, suppliers further prolong the credit period is beneficial for both parties. On the contrary, as retailers’ own warehouse capacity increases and exceeds the optimal order quantity under that of without capacity constraints, adopting the same replenishment strategy as that without capacity constraints is profitable for retailers. Our results also reveal that other model parameters (e.g., ordering cost, inventory holding cost, shortages cost, backordering rate, etc.) have a significant impact on retailers’ optimal decisions.

中文翻译：

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订单大小依赖贸易信用下存储容量有限的部分延期交货库存模型

本研究建立了在订单大小依赖贸易信用条件下存储容量有限的库存模型。允许短缺并部分积压。本研究的目的是确定最佳补货周期长度、最佳不缺货比例以及零售商是否应该选择租用额外的仓库来存放更多物品，从而使零售商的年总利润最大化。我们证明了目标函数的全局最优，并推导出了封闭形式的最优解。给出了一些数值例子来说明所提出模型的适用性。进行敏感性分析并获得管理洞察力。我们发现，如果零售商自己的仓库容量较小，他们总是受益于扩大订单数量和租用额外的仓库；同时，供应商进一步延长信用期对双方都有利。相反，随着零售商自身仓库容量的增加并超过无产能限制下的最优订货量，采用与无产能限制相同的补货策略对零售商来说是有利可图的。我们的结果还表明，其他模型参数（例如，订购成本、库存持有成本、短缺成本、延期交货率等）对零售商的最优决策有重大影响。采用与没有产能限制相同的补货策略对零售商来说是有利可图的。我们的结果还表明，其他模型参数（例如，订购成本、库存持有成本、短缺成本、延期交货率等）对零售商的最优决策有重大影响。采用与没有产能限制相同的补货策略对零售商来说是有利可图的。我们的结果还表明，其他模型参数（例如，订购成本、库存持有成本、短缺成本、延期交货率等）对零售商的最优决策有重大影响。