Stock replenishment and shipment scheduling for vendor-managed inventory systems

Vendor-managed inventory (VMI) is a supply-chain initiative where the supplier is authorized to manage inventories of agreed-upon stock-keeping units at retail locations. The benefits of VMI are well recognized by successful retail businesses such as Wal-Mart. In VMI, distortion of demand information (known as bullwhip effect) transferred from the downstream supply-chain member (e.g., retailer) to the upstream member (e.g., supplier) is minimized, stockout situations are less frequent, and inventory-carrying costs are reduced. Furthermore, a VMI supplier has the liberty of controlling the downstream resupply decisions rather than filling orders as they are placed. Thus, the approach offers a framework for synchronizing inventory and transportation decisions. In this paper, we present and analytical model for coordinating inventory and transportation decisions in VMI systems. Although the coordination of inventory and transportation has been addressed in the literature, our particular problem has not been explored previously. Specifically, we consider a vendor realizing a sequence of random demands from a group of retailers located in a given geographical region. Ideally, these demands should be shipped immediately. However, the vendor has the autonomy of holding small orders until an agreeable dispatch time with the expectation that an economical consolidated dispatch quantity accumulates. As a result, the actual inventory requirements at the vendor are partly dictated by the parameters of the shipment-release policy in use. We compute the optimum replenishment quantity and dispatch frequency simultaneously. We develop a renewal-theoretic model for the case of Poisson demands, and present analytical results.