Emergency shipments are considered as an efficacious approach for mitigating the risk of shortages and increasing resilience in inventory systems. In this study, we develop a new newsvendor model where the retailer has a single opportunity to trigger an emergency shipment during the selling season. Due to demand uncertainty, it might not be possible to satisfy customer demands during the season. Provision for requesting an emergency shipment within the season can reduce the possibility of imminent shortages. As emergency shipments affect the dynamic of the system over time, the timing of emergency shipments in addition to their sizes is of particular interest. We use the time-weighted holding cost to compute the expected holding cost and assume that any unmet demand is lost. The goal is to determine the pre-season order quantity and both size and time of the emergency shipment such that the expected profit is maximized. We find that the newsvendor problem under time-weighted holding cost has a different structure and provide a different optimal order quantity. Our numerical experiences indicate that triggering an emergency shipment during the selling season can significantly improve cost savings. The results of a set of computational experiments demonstrate the superior performance of our proposed model when compared with the classical newsvendor problem. A sensitivity analysis is conducted showing that in the classical model, the unit lost sale cost is the most effective input parameter on the expected profit value. Moreover, the selling price and unit holding cost significantly affect the size and time of the emergency shipment.

紧急发货被认为是减轻短缺风险和提高库存系统弹性的有效方法。在这项研究中，我们开发了一种新的报童模型，其中零售商有一个机会在销售季节触发紧急发货。由于需求的不确定性，旺季可能无法满足客户的需求。在季节内要求紧急发货的规定可以减少即将发生短缺的可能性。由于紧急运输会随着时间的推移影响系统的动态，因此除了大小之外，紧急运输的时间安排特别重要。我们使用时间加权持有成本来计算预期持有成本，并假设任何未满足的需求都会丢失。目标是确定季前订单数量以及紧急发货的尺寸和时间，从而使预期利润最大化。我们发现时间加权持有成本下的报童问题具有不同的结构并提供不同的最优订货量。我们的数值经验表明，在销售季节触发紧急发货可以显着提高成本节约。与经典报童问题相比，一组计算实验的结果证明了我们提出的模型的优越性能。敏感性分析表明，在经典模型中，单位销售损失成本是对预期利润值最有效的输入参数。而且，