A Study On Inventory Control Based On Internet Auctions

In recent years, with the rise of Internet and Information Technology, the study onthe intersection of auction theory and operations management is a relative new topic inOR/MS. In this paper, we study the combined optimal Internet auctions and inventorycontrol based on revenue/supply chain management.First, based on Revenue Equivalent Theory on homogeneous multi-object auctions,we obtain a single period revenue function on uniform price Internet auctions and its prop-erties, and generalize a type of optimal dynamic Internet auction for revenue managementto uniform price auctions. Second, we study an optimal inventory control with fixed or-dering costs and selling by Internet auctions by using Markov decision processes. Weaddress the total expected discounted criteria in both finite and infinite horizon and theaverage criterion in an infinite horizon. We show that the classic (j?,J?) policy is optimalfor each criterion. Moreover, we find simple algebraic expressions for the discounted andaverage criteria in an infinite horizon and thus the optimal (j?,J?) policy for these twocriteria can be computed by integer programming with bounded decision variables j? andJ?. Furthermore, numerical results and analysis are given. Third, we study the optimalinventory and allocation control for a sequential Internet auction systems by using Markovdecision processes. We address the total expected discounted criteria for both finite andinfinite horizon and the average criterion over an infinite horizon. We show that for eachcriterion the optimal replenishment and allocation policy is quite simple. That is, underthe optimal policy, the replenishing inventory follows an order-up-to (basestock) policyand all stocks are o?ered to the period auction. This policy is called base-stock-allocate-allpolicy. We obtain a simple optimization problem for the discounted and average criteriain an infinite horizon and thus it is easy to compute the optimal basestock levels for thesetwo criteria. Moreover, numerical results and analysis are given and show that under theoptimal reserve price our auction mechanism performs a little better than that in vanRyzin and Vulcano (2004).