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A Lagrangian approach to the winner determination problem in iterative combinatorial reverse auctions

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  • Mansouri, Bahareh
  • Hassini, Elkafi

Abstract

Combinatorial auctions allow allocation of bundles of items to the bidders who value them the most. The NP-hardness of the winner determination problem (WDP) has imposed serious computational challenges when designing efficient solution algorithms. This paper analytically studies the Lagrangian relaxation of WDP and expounds a novel technique for efficiently solving the relaxation problem. Moreover, we introduce a heuristic algorithm that adjusts any infeasibilities from the Lagrangian optimal solution to reach an optimal or a near optimal solution. Extensive numerical experiments illustrate the class of problems on which application of this technique provides near optimal solutions in much less time, as little as a fraction of a thousand, as compared to the CPLEX solver.

Suggested Citation

  • Mansouri, Bahareh & Hassini, Elkafi, 2015. "A Lagrangian approach to the winner determination problem in iterative combinatorial reverse auctions," European Journal of Operational Research, Elsevier, vol. 244(2), pages 565-575.
    • Handle: RePEc:eee:ejores:v:244:y:2015:i:2:p:565-575
    DOI: 10.1016/j.ejor.2015.01.053
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    1. Paul Milgrom, 2000. "Putting Auction Theory to Work: The Simultaneous Ascending Auction," Journal of Political Economy, University of Chicago Press, vol. 108(2), pages 245-272, April.
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    3. Michael H. Rothkopf & Aleksandar Pekev{c} & Ronald M. Harstad, 1998. "Computationally Manageable Combinational Auctions," Management Science, INFORMS, vol. 44(8), pages 1131-1147, August.
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    Cited by:

    1. Mansouri, Bahareh & Hassini, Elkafi, 2019. "Optimal pricing in iterative flexible combinatorial procurement auctions," European Journal of Operational Research, Elsevier, vol. 277(3), pages 1083-1097.
    2. Lorentziadis, Panos L., 2016. "Optimal bidding in auctions from a game theory perspective," European Journal of Operational Research, Elsevier, vol. 248(2), pages 347-371.
    3. Xiaohu Qian & Mingqiang Yin & Felix T. S. Chan & Kai Yue, 2023. "Winner Determination with Sustainable-Flexible Considerations Under Demand Uncertainty in Transportation Service Procurement Auctions," Networks and Spatial Economics, Springer, vol. 23(4), pages 953-984, December.
    4. Fadaei, Salman & Bichler, Martin, 2017. "Truthfulness with value-maximizing bidders: On the limits of approximation in combinatorial markets," European Journal of Operational Research, Elsevier, vol. 260(2), pages 767-777.
    5. Qian, Xiaohu & Fang, Shu-Cherng & Huang, Min & Wang, Xingwei, 2019. "Winner determination of loss-averse buyers with incomplete information in multiattribute reverse auctions for clean energy device procurement," Energy, Elsevier, vol. 177(C), pages 276-292.
    6. Omar Abbaas & Jose A. Ventura, 2024. "An Iterative Procurement Combinatorial Auction Mechanism for the Multi-Item, Multi-Sourcing Supplier-Selection and Order-Allocation Problem under a Flexible Bidding Language and Price-Sensitive Demand," Mathematics, MDPI, vol. 12(14), pages 1-30, July.

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