Abstract
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.