Optimal Lot Sizing Policies for Sequential Online Auctions
This study proposes methods for determining the optimal lot sizes for sequential online auctions that are conducted to sell sizable quantities of an item. These auctions are common in business-to-consumer (B2C) auctions. In these auctions, the tradeoff for the auctioneer is between the alacrity with which funds are received and the amount of funds collected by the faster clearing of inventory using larger lot sizes. Observed bids in these auctions impact the auctioneer's decision on lot sizes in future auctions. We first present a goal programming approach for estimating the bid distribution for the bidder population from the observed bids, readily available in these auctions. We then develop models to compute optimal lot sizes for both stationary and nonstationary bid distributions. For stationary bid distributions, we present closed-form solutions and structural results. Our findings show that the optimal lot size increases with inventory holding costs and number of bidders. Our model for nonstationary bid distributions capture the interauction dynamics such as the number of bidders, their bids, past winning bids, and lot size. We use simulated data to test the robustness of our model.
lot sizing goal programming sequential auctions order statistics dynamic programming stochastic order