1- Bi-Level VMI Mathematical Models
The first class of VMI, bi-level VMI mathematical model, includes two levels (or echelons) in a supply chain: vendor and retailer. There are three types of VMI mathematical models developed from this class, which are single-vendor single-retailer VMI model, single-vendor multi-retailer VMI model, and multi-vendor multi-retailer VMI model. This class has been significantly developing. For example, single-vendor single-retailer VMI model was extended for multi-product case, the consignment stock (CS), and discount.
2- Multi-Level VMI Mathematical ModelsThe second class is multi-level VMI mathematical model such as a single manufacturer-single vendor multi-retailer (SM-SV-MR) VMI model. Those studies fail to model replenishment frequencies cannot classified here. As replenishment frequencies play an important role in integrated inventory models to reduce the total cost of supply chains which many studies fail to model it in mathematical problems.