Optimal Lot Sizing Policies For Sequential Online Auctions

This study proposes methods for determining the optimal lot sizes for sequential auctions that are conducted to sell sizable quantities of an item. These auctions are fairly 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 non-stationary bid distributions. For stationary bid distribution, 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 non-stationary bid distribution captures the inter-auction 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.