An asymmetric multi-item auction with quantity discounts applied to Internet service procurement in Buenos Aires public schools
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This article studies a multi-item auction characterized by asymmetric bidders and quantity discounts. We report a practical application of this type of auction in the procurement of Internet services to the 709 public schools of Buenos Aires. The asymmetry in this application is due to firms’ existing technology infrastructures, which affect their ability to provide the service in certain areas of the city. A single round first-price sealed-bid auction, it required each participating firm to bid a supply curve specifying a price on predetermined graduated quantity intervals and to identify the individual schools it would supply. The maximal intersections of the sets of schools each participant has bid on define regions we call competition units. A single unit price must be quoted for all schools supplied within the same quantity interval, so that firms cannot bid a high price where competition is weak and a lower one where it is strong. Quantity discounts are allowed so that the bids can reflect returns-to-scale of the suppliers and the auctioneer may benefit of awarding bundles of units instead of separate units. The winner determination problem in this auction poses a challenge to the auctioneer. We present an exponential formulation and a polynomial formulation for this problem, both based on integer linear programming. The polynomial formulation proves to find the optimal set of bids in a matter of seconds. Results of the real-world implementation are reported.
KeywordsMulti-item auction Asymmetric bidders Quantity discounts Integer linear programming
This study was partly financed by project nos. ANPCyT PICT-2012-1324, CONICET PIP 112-201201-00450CO, and UBACyT 20020130100808BA (Argentina), and by the Complex Engineering Systems Institute (Santiago, Chile). The third author was partly financed by FONDECYT project no. 1140787 (Chile). The fourth author was partly financed by FONDECYT project no. 1120475 (Chile). All of the authors are grateful to the Agencia en Sistemas de Información (ASI) of the city government of Buenos Aires, which organized the auction, and in particular to Julián Dunayevich and Eduardo Terada, both of whom were ASI officials during the implementation of this project, for their collaboration in making this study a reality. The authors would like to thank Nicolás Figueroa and Kenneth Rivkin for their interesting comments and to the anonymous referees whose suggestions helped to considerably improve the final version of this paper.
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