Developing a two-echelon mathematical model for a vendor-managed inventory (VMI) system

Vendor-managed inventory (VMI) system is a mechanism where the supplier creates the purchase orders based on the demand information exchanged by the retailer/customer. In this paper, the performance of the traditional and VMI system is compared. Mathematical modeling is applied and total inventory cost in the supply chain is used as the performance measure. The supply chain is considered in two levels, i.e., buyer and supplier, with the assumption that the supplier faces only one buyer as the contract party. Since none of the previous works quantitatively directed the practitioners to select the traditional or VMI system, the extent point is introduced in which the difference in total cost of both systems is minimal. It is applied to investigate how increasing or reducing the related parameters changes total cost of two systems with respect to each other. A numerical example and sensitivity analysis are provided to illustrate the theory and derive the extent points and percentage of difference in total cost of the traditional and VMI system. The results show that VMI works better and delivers lower cost in all conditions including back order, and as one goes farther from the extent point, the application of VMI is more justified.