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

Bahareh Mansouri and Elkafi Hassini

European Journal of Operational Research, 2015, vol. 244, issue 2, 565-575

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.

Keywords: Reverse multi-unit combinatorial auction; Lagrangian relaxation; Iterative auctions (search for similar items in EconPapers)
Date: 2015
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Citations: View citations in EconPapers (6)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:ejores:v:244:y:2015:i:2:p:565-575

DOI: 10.1016/j.ejor.2015.01.053

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