An Asymmetric Multi-Item Auction with Quantity Discounts Applied to Internet Service Procurement in Buenos Aires Public Schools

Abstract

This article studies a multi-item auction characterized by asymmetricbidders and quantity discounts. We report a practical application of thistype of auction in the procurement of Internet services to the 709 publicschools of Buenos Aires. The asymmetry in this application is due to firms?existing technology infrastructures, which affect their ability to providethe service in certain areas of the city. A single round first-price sealed-bidauction, it required each participating firm to bid a supply curve specifyinga price on predetermined graduated quantity intervals and to identify theindividual schools it would supply. The maximal intersections of the setsof schools each participant has bid on define regions we call competitionunits. A single unit price must be quoted for all schools supplied withinthe same quantity interval, so that firms cannot bid a high price wherecompetition is weak and a lower one where it is strong. Quantity discountsare allowed so that the bids can reflect returns-to-scale of the suppliers andthe auctioneer may benefit of awarding bundles of units instead of separateunits. The winner determination problem in this auction poses a challengeto the auctioneer. We present an exponential formulation and a polynomialformulation for this problem, both based on integer linear programming.The polynomial formulation proves to find the optimal set of bids in amatter of seconds. Results of the real-world implementation are reported.