Optimal Inventory Control and Allocation for Sequential Internet Auctions

We study an optimal inventory control and allocation for a seller who uses sequential Internet auctions to sell replenishment products. This problem is faced not only by retailers/distributors in the retail industry but also by manufacturers who use sequential Internet auctions to sell products that can be replenished. We consider the total expected discounted profit criterion in a finite horizon and both the discounted and average profit criteria over an infinite horizon, and show the optimality of the so-called base-stock-allocate-all (BSAA) policies. Then, we simplify the problem of computing the optimal policies and profits for either the discounted or average profit criterion in an infinite horizon to an optimization problem with only one integer decision variable. We show these results for the list price case, and also for the case where the reserve price is a decision variable. Finally, numerical results are given, where the effects of several model parameters on the optimal policies and profits are numerically analyzed.