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Annals of Operations Research

, Volume 258, Issue 2, pp 569–585 | Cite as

An asymmetric multi-item auction with quantity discounts applied to Internet service procurement in Buenos Aires public schools

  • F. Bonomo
  • J. Catalán
  • G. Durán
  • R. Epstein
  • M. Guajardo
  • A. Jawtuschenko
  • J. Marenco
S.I. : CLAIO 2014
  • 233 Downloads

Abstract

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.

Keywords

Multi-item auction Asymmetric bidders Quantity discounts Integer linear programming 

Notes

Acknowledgments

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.

References

  1. Abrache, J., Crainic, T. G., Gendreau, M., & Rekik, M. (2007). Combinatorial auctions. Annals of Operations Research, 153(1), 131–164.CrossRefGoogle Scholar
  2. Aparicio, J., Ferrando, J. C., Meca, A., & Sancho, J. (2008). Strategic bidding in continuous electricity auctions: An application to the Spanish electricity market. Annals of Operations Research, 158(1), 229–241.CrossRefGoogle Scholar
  3. Ausubel, L. M., & Milgrom, P. R. (2002). Ascending auctions with package bidding. Advances in Theoretical Economics, 1(1), 1–42.CrossRefGoogle Scholar
  4. Campo, S., Perrigne, I., & Vuong, Q. (2003). Asymmetry in first-price auctions with affiliated private values. Journal of Applied Econometrics, 18(2), 179–207.CrossRefGoogle Scholar
  5. Cantillon, E., & Pesendorfer, M. (2013). Combination bidding in multi-unit auctions. The London School of Economics and Political Science: London, UK. http://eprints.lse.ac.uk/54289/.
  6. Catalán, J., Epstein, R., Guajardo, M., Yung, D., & Martínez, C. (2009). Solving multiple scenarios in a combinatorial auction. Computers & Operations Research, 36(10), 2752–2758.CrossRefGoogle Scholar
  7. Chernomaz, K., & Levin, D. (2012). Efficiency and synergy in a multi-unit auction with and without package bidding: An experimental study. Games and Economic Behavior, 76(2), 611–635.CrossRefGoogle Scholar
  8. Coatney, K. T., Shaffer, S. L., & Menkhaus, D. J. (2012). Auction prices, market share, and a common agent. Journal of Economic Behavior & Organization, 81(1), 61–73.CrossRefGoogle Scholar
  9. Cramton, P., Shoham, Y., & Steinberg, R. (2006). Combinatorial auctions. Cambridge: MIT Press.Google Scholar
  10. Davenport, A. J., & Kalagnanam, J. R. (2002). Price negotiations for procurement of direct inputs. Mathematics of the Internet: Auctions and Markets, 127, 27–43.CrossRefGoogle Scholar
  11. Demange, G., Gale, D., & Sotomayor, M. (1986). Multi-item auctions. The Journal of Political Economy, 94(4), 863–872.CrossRefGoogle Scholar
  12. Durán, G., Epstein, R., Martínez, C., & Zamorano, G. A. (2011). Quantitative methods for a new configuration of territorial units in a Chilean government agency tender process. Interfaces, 41(3), 263–277.CrossRefGoogle Scholar
  13. Epstein, R., Henríquez, L., Catalán, J., Weintraub, G. Y., & Martínez, C. (2002). A combinational auction improves school meals in Chile. Interfaces, 32(6), 1–14.CrossRefGoogle Scholar
  14. Flambard, V., & Perrigne, I. (2006). Asymmetry in procurement auctions: Evidence from snow removal contracts. The Economic Journal, 116(514), 1014–1036.CrossRefGoogle Scholar
  15. Glaister, S., & Beesley, M. (1991). Bidding for tendered bus routes in London. Transportation Planning and Technology, 15(2–4), 349–366.CrossRefGoogle Scholar
  16. Hohner, G., Rich, J., Ng, E., Reid, G., Davenport, A. J., Kalagnanam, J. R., et al. (2003). Combinatorial and quantity-discount procurement auctions benefit Mars, Incorporated and its suppliers. Interfaces, 33(1), 23–35.CrossRefGoogle Scholar
  17. Hopcroft, J. E., & Ullman, J. D. (1973). Set merging algorithms. SIAM Journal on Computing, 2(4), 294–303.CrossRefGoogle Scholar
  18. Hubbard, T. P., Li, T., & Paarsch, H. J. (2012). Semiparametric estimation in models of first-price, sealed-bid auctions with affiliation. Journal of Econometrics, 168(1), 4–16.CrossRefGoogle Scholar
  19. Hubbard, T. P., & Paarsch, H. J. (2014). Chapter 2 - On the numerical solution of equilibria in auction models with asymmetries within the private-values paradigm. In K. Schmedders & K. L. Judd (Eds.), Handbook of computational economics (Vol. 3, pp. 37–115). North-Holland: Elsevier.CrossRefGoogle Scholar
  20. Jeroslow, R. G. (1974). Trivial integer programs unsolvable by branch-and-bound. Mathematical Programming, 6(1), 105–109.CrossRefGoogle Scholar
  21. Jofre-Bonet, M., & Pesendorfer, M. (2000). Bidding behavior in a repeated procurement auction: A summary. European Economic Review, 44(4), 1006–1020.CrossRefGoogle Scholar
  22. Kameshwaran, S., Narahari, Y., Rosa, C. H., Kulkarni, D. M., & Tew, J. D. (2007). Multiattribute electronic procurement using goal programming. European Journal of Operational Research, 179(2), 518–536.CrossRefGoogle Scholar
  23. Kaufman, L., & Rouseeuuw, P. (2005). Finding groups in data: An Introduction to cluster Analysis. Wiley Series in Probability and Statistics. Hoboken: Wiley.Google Scholar
  24. Kennedy, D. (1995). London bus tendering: An overview. Transport Reviews, 15(3), 253–264.CrossRefGoogle Scholar
  25. Klemperer, P. (2004). Auctions: Theory and practice. Princeton: Princeton University Press.Google Scholar
  26. Kwasnica, A. M., & Sherstyuk, K. (2013). Multiunit auctions. Journal of economic surveys, 27(3), 461–490.CrossRefGoogle Scholar
  27. Li, T., Perrigne, I., & Vuong, Q. (2002). Structural estimation of the affiliated private value auction model. RAND Journal of Economics, 33(2), 171–193.Google Scholar
  28. Lloyd, S. P. (1982). Least squares quantization in PCM. IEEE Transactions on information theory, 28(2), 129–137.CrossRefGoogle Scholar
  29. Margot, F. (2010). Symmetry in integer linear programming. In M. Jünger, Th. M. Liebling, D. Naddef, G. L. Nemhauser, W. R. Pulleyblank, G. Reinelt, G. Rinaldi & L. A. Wolsey (Eds.), 50 Years of Integer Programming 1958–2008 (pp. 647–686). Springer: Berlin, Heidelberg.Google Scholar
  30. Maskin, E., & Riley, J. (2000). Asymmetric auctions. Review of Economic studies, 67, 413–438.CrossRefGoogle Scholar
  31. Méndez-Díaz, I., & Zabala, P. (2006). A branch-and-cut algorithm for graph coloring. Discrete Applied Mathematics, 154(5), 826–847.CrossRefGoogle Scholar
  32. Rey, P. A. (2004). Eliminating redundant solutions of some symmetric combinatorial integer programs. Electronic Notes in Discrete Mathematics, 18, 201–206.CrossRefGoogle Scholar
  33. Samuelson, W. (2014). Auctions: Advances in Theory and Practice. Game Theory and Business Applications, International Series in Operations Research & Management Science 194 (pp. 323–366). US: Springer.Google Scholar
  34. Tarjan, R. E. (1975). Efficiency of a good but not linear set union algorithm. Journal of the ACM, 22(2), 215–225.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  1. 1.Departamento de Computación, FCENUBABuenos AiresArgentina
  2. 2.CONICETBuenos AiresArgentina
  3. 3.Instituto de Cálculo, FCENUBABuenos AiresArgentina
  4. 4.Departamento de Matemática, FCENUBABuenos AiresArgentina
  5. 5.Departamento de Ingeniería Industrial, FCFMUniversidad de ChileSantiagoChile
  6. 6.Department of Business and Management ScienceNHH Norwegian School of EconomicsBergenNorway
  7. 7.Instituto de CienciasUniversidad Nacional de General SarmientoBuenos AiresArgentina

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