A branch-and-cut algorithm for the Winner Determination Problem

The Winner Determination Problem is the problem of maximizing the benefit when bids can be made on a group of items. In this paper, we consider the set packing formulation of the problem, study its polyhedral structure and then propose a new and tighter formulation. We also present new valid inequalities which are generated by exploiting combinatorial auctions peculiarities. Finally, we implement a branch-and-cut algorithm which shows its efficiency in a big number of instances.

[1]  Arne Andersson,et al.  Integer programming for combinatorial auction winner determination , 2000, Proceedings Fourth International Conference on MultiAgent Systems.

[2]  Michel Gendreau,et al.  A new bidding framework for combinatorial e-auctions , 2004, Comput. Oper. Res..

[3]  Mercedes Landete,et al.  New facets for the set packing polytope , 2000, Oper. Res. Lett..

[4]  Rudolf Müller,et al.  Optimization in electronic markets: examples in combinatorial auctions , 2001 .

[5]  Jyrki Wallenius,et al.  Decision support for multi-unit combinatorial bundle auctions , 2007, Decis. Support Syst..

[6]  L. Lovász,et al.  Geometric Algorithms and Combinatorial Optimization , 1981 .

[7]  Tuomas Sandholm,et al.  Approaches to winner determination in combinatorial auctions , 2000, Decis. Support Syst..

[8]  G. Nemhauser,et al.  A Strong Cutting Plane/Branch-and-Bound Algorithm for Node Packing , 1992 .

[9]  Egon Balas,et al.  Critical Cutsets of Graphs and Canonical Facets of Set Packing Polytopes , 1998 .

[10]  Zizhuo Wang,et al.  A unified framework for dynamic pari-mutuel information market design , 2009, EC '09.

[11]  Yoav Shoham,et al.  Towards a universal test suite for combinatorial auction algorithms , 2000, EC '00.

[12]  Robert W. Day.  CAMBO : Combinatorial Auctions using Matrix Bids with Order , 2003 .

[13]  M. Padberg,et al.  Solving airline crew scheduling problems by branch-and-cut , 1993 .

[14]  Laurence A. Wolsey,et al.  Integer and Combinatorial Optimization , 1988 .

[15]  Alessandro Avenali,et al.  Simulating combinatorial auctions with dominance requirement and loll bids through automated agents , 2007, Decis. Support Syst..

[16]  Andrew B. Whinston,et al.  Optimal Investment in Knowledge within a Firm Using a Market Mechanism , 2001, Manag. Sci..

[17]  Harvey M. Salkin,et al.  Integer Programming , 2019, Engineering Optimization Theory and Practice.

[18]  Bert Gerards,et al.  Matrices with the edmonds—Johnson property , 1986, Comb..

[19]  Manfred W. Padberg,et al.  On the facial structure of set packing polyhedra , 1973, Math. Program..

[20]  Andrew B. Whinston,et al.  Solving the combinatorial double auction problem , 2005, Eur. J. Oper. Res..

[21]  Michael H. Rothkopf,et al.  Combinatorial Auction Design , 2003, Manag. Sci..

[22]  Yoav Shoham,et al.  Combinatorial Auctions , 2005, Encyclopedia of Wireless Networks.

[23]  Sven de Vries,et al.  Combinatorial Auctions: A Survey , 2003, INFORMS J. Comput..

[24]  David Levine,et al.  CABOB: A Fast Optimal Algorithm for Winner Determination in Combinatorial Auctions , 2005, Manag. Sci..

[25]  Ronald M. Harstad,et al.  Computationally Manageable Combinational Auctions , 1998 .

[26]  Yossi Sheffi,et al.  Combinatorial Auctions in the Procurement of Transportation Services , 2004, Interfaces.

[27]  Gary J. Koehler,et al.  Combinatorial auctions using rule-based bids , 2002, Decis. Support Syst..