Emergency Shipment Decision in Newsvendor Model

Abstract

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.