Optimal procurement mechanisms for divisible goods with capacitated suppliers

  • Garud Iyengar
  • Anuj KumarEmail author
Original Paper


Procurement auction literature typically assumes that the suppliers are uncapacitated [see, e.g. Dasgupta and Spulber in Inf Econ Policy 4:5–29, 1990 and Che in Rand J Econ 24(4):668–680, 1993]. Consequently, the auction mechanisms award the contract to a single supplier. We study mechanism design in a model where suppliers have limited production capacity, and both the marginal costs and the production capacities are private information. We provide a closed-form solution for the revenue maximizing direct mechanism when the distribution of the cost and production capacities satisfies a modified regularity condition [Myerson in Math Oper Res 6(1):58–73, 1981]. We also present a sealed low bid implementation of the optimal direct mechanism for the special case of identical suppliers. The results in this paper extend to other principle-agent mechanism design problems where the agents have a privately known upper bound on allocation.


Procurement auctions Optimal direct mechanism Capacity constraints Multiple sourcing 

JEL Classification

D24 D44 


  1. Ausubel LM (2004). An efficient ascending-bid auction for multiple objects. Amer Econ Rev 94(5): 1452–1475 CrossRefGoogle Scholar
  2. Ausubel LM, Cramton P (2002) Demand reduction and inefficiency in multi-unit auctions. Working Paper, University of MarylandGoogle Scholar
  3. Che YK (1993). Design competition through multidimensional auctions. Rand J Econ 24(4): 668–680 CrossRefGoogle Scholar
  4. Chen F (2004) Auctioning supply chain contracts. Technical report. Decisions risk and operations, Columbia Bussiness SchoolGoogle Scholar
  5. Dasgupta S and Spulber DF (1990). Managing procurement auctions. Inf Econ Policy 4: 5–29 CrossRefGoogle Scholar
  6. Harris M and Townsend R (1981). Resource allocation under asymmetric information. Econometrica 49(1): 33–64 CrossRefGoogle Scholar
  7. Iyengar G, Kumar A (2006a) Characterizing optimal adword auctions. Technical report. CORC tech report—TR-2006-04.
  8. Iyengar G, Kumar A (2006b) Optimal procurement auctions for divisible goods with capacitated suppliers. Technical report. CORC TR-2006-01, IEOR Department, Columbia UniversityGoogle Scholar
  9. Laffont JJ, Maskin ES and Rochet JC (1987). Optimal nonlinear pricing with two dimensional characteristics. In: Groves, T, Radner, R, and Reiter, S (eds) Information, Incentives and Economic Mechanisms; Essays in Honor of Leonid Hurwicz, Chap 8, pp 256–266. University of Minnesota Press, Minneapolis Google Scholar
  10. Milgrom P and Weber R (1982). A theory of auctions and competitive bidding. Econometrica 50(5): 1089–1122 CrossRefGoogle Scholar
  11. Myerson RB (1981). Optimal auction design. Math Oper Res 6(1): 58–73 CrossRefGoogle Scholar
  12. Naegelen F (2002). Implementing optimal procurement auctions with exogenous quality. Rev of Econ Des 7: 135–153 Google Scholar
  13. Parente DH, Venkataraman R, Fizel J, Millet I (2001) B2B online reverse auctions: what’s new? Decision Line, pp 13–15Google Scholar
  14. Rochet JC and Chone P (1998). Ironing, sweeping and multidimensional screening. Econometrica 4: 783–826 CrossRefGoogle Scholar
  15. Rochet JC and Stole LA (2003). The economics of multidimensional screening. In: Dewatripont, M, Hansen, LP and Turnovsky, SJ (eds) Advances in Economics and Econometrics: Theory and Applications—Eight world congress, Econometric Society Monographs, vol 36, pp. Cambridge University Press, Cambridge Google Scholar
  16. Rockafeller RT (1970). Convex Analysis. Princeton University Press, Princeton Google Scholar
  17. Vohra R, Malakhov A (2004) Single and multi-dimensional optimal auctions—a network approach. Working paper. Managerial Economics and Decision Sciences, Kellogg School of Management, Northwestern UniversityGoogle Scholar
  18. Vohra R, Malakhov A (2004) Optimal auction for capacitated bidders—a network approach. Working paper. Managerial Economics and Decision Sciences, Kellogg School of Management, Northwestern UniversityGoogle Scholar

Copyright information

© Springer-Verlag 2008

Authors and Affiliations

  1. 1.Industrial Engineering and Operations Research DepartmentColumbia UniversityNew YorkUSA
  2. 2.Lehman Brothers Inc.New YorkUSA

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