Calculating the benefits of vendor managed inventory in a manufacturer-retailer system

Firms such as Wal-Mart and Campbell's Soup have successfully implemented vendor managed inventory (VMI). Articles in the trade press and academic literature often begin with the premise that VMI is 'beneficial'; but beneficial to which party and under what conditions? We consider in this paper a vendor V that manufactures a particular product at a unique location. That item is sold to a single retailer, the customer C. Three cases are treated in detail: independent decision making (no agreement between the parties); VMI, whereby the supplier V initiates orders on behalf of C; and central decision making (both vendor and customer are controlled by the same corporate entity). Values of some cost parameters may vary between the three cases and each case may cause a different actor to be responsible for particular expenses. Under a constant demand rate, optimal solutions are obtained analytically for the customer's order quantity, the vendor's production quantity, hence the parties' individual and total costs in the three cases. Inequalities are obtained to delineate those situations in which VMI is beneficial.