Optimal Inventory Policies When Sales are through Internet Auctions

We study the problem for a seller who uses an auction mechanism for selling a replenishment product. The number of bidders in each period as well as the individual bidders´ valuations are random. The seller purchases his good from an outside suppler at the ordering cost including both a fixed ordering cost and a variable cost proportional to the amount ordered. There is a holding cost for inventory and no lead times for replenishment. The seller must decide on how to replenish his stock over time to maximize his profits. We address both the finite and infinite horizon discounted profit criterion. We prove the optimality of inventory replenishment policies for both the finite and infinite horizon discounted profit criterion by using the unifying condition in Huh and Janakiraman (2006).