Safety stock management in a two-stage supply chain with controllable lead time and batch shipments: a technical note

The joint economic lot size (JELS) model with stochastic demand and controllable lead time has received quite some attention in the literature. If a lot is shipped in batches from the vendor to the buyer, subsequent shipments may be subject to different lead times. Establishing a common safety stock for all batch shipments may lead to an inflated stockout risk for early batch shipments and an unnecessarily high inventory level for late batch shipments. To alleviate this shortcoming, a few authors proposed JELS models that adjust the safety stock level over the course of the inventory cycle. Existing works, however, do not always correctly establish the relationship between the vendor's and the buyer's inventory. This technical note adjusts the relationship between the buyer's and the vendor's inventory and numerically quantifies the error's impact on the expected average inventory as well as on the system's expected total cost.