The ubiquitous nature of inventory: Vendor Managed Consignment Inventory in adverse market conditions

Inventories are ubiquitous in nature and inventory control is a crucial activity undertaken in the supply chain (SC) by a company’s management. The Vendor Managed Inventory (VMI) contract has become a common technique for supply chain management (SCM) since the 1980’s. In this technique, the decision about how much inventory to hold is made by the vendor. In the paper, we consider VMI with consignment (VMCI). Consignment is a frequently used form of business arrangement, in which the vendor retains the ownership of the inventory and gets paid by the retailer on actual units sold. Under VMCI, decisions are made in two steps. In the first step, the vendor specifies a consignment price and an order quantity with the objective to maximize the vendor’s expected profit. In the second step, the retailer chooses a retail price which maximizes the retailer’s expected profit. The customer demand is assumed to be stochastic, additive and price–sensitive. Additive uncertainty can produce negative demand realizations, which may occur in adverse market conditions. We prove that in this case an optimal and possibly non–unique solution to VMCI exists. We calculate closed–form formulas for optimal quantities for uniformly distributed demand. Finally, we demonstrate our approach through a numerical example and we show that the imposition of a non–negativity constraint can cause a higher vendor’s expected profit.