Tri-level decision-making for decentralized vendor-managed inventory

Vendor-managed inventory (VMI) is a common inventory management policy which allows the vendor to manage the buyer's inventory based on the information shared in the course of supply chain management. One challenge in VMI is that both the vendor and buyer are manufacturers who try to achieve an inventory as small as possible or even a zero inventory; it is therefore difficult to manage inventory coordination between them. This paper considers a decentralized VMI problem in a three-echelon supply chain network in which multiple distributors (third-party logistics companies) are selected to balance the inventory between a vendor (manufacturer) and multiple buyers (manufacturers). To handle this issue, this paper first proposes a tri-level decision model to describe the decentralized VMI problem, which allows us to examine how decision members coordinate with each other in respect of decentralized VMI decision-making in a predetermined sequence. We then turn our attention to the geometry of the solution space and present a vertex enumeration algorithm to solve the resulting tri-level decision model. Lastly, a computational study is developed to illustrate how the proposed tri-level decision model and solution approach can handle the decentralized VMI problem. The results indicate that the proposed tri-level decision-making techniques provide a practical way to design a novel manufacturer-manufacturer (vendor-buyer) VMI system where third-party logistics are involved.