A branch-and-price algorithm and new test problems for spectrum auctions

• 成果类型: Article
• 署名作者: Günlük, O; Ladányi, L; de Vries, S
• 署名单位: International Business Machines (IBM); IBM USA; Technical University of Munich
• 刊物名称: MANAGEMENT SCIENCE
• ISSN/ISSBN: 0025-1909
• DOI: 10.1287/mnsc.1040.0332
• 发表日期: 2005
• 页码: 391-406
• 关键词: Combinatorial auctions; branch-and-price; spectrum auctions; test problems

摘要

W hen combinatorial bidding is permitted in auctions, such as the proposed FCC Auction #31, the resulting full valuations and winner-determination problem can be computationally challenging. We present a branch-and-price algorithm based on a set-packing formulation originally proposed by Dietrich and Forrest (2002, A column generation approach for combinatorial auctions, in Mathematics of the Internet: E-Auction and Markets. The IMA, Volumes in Mathematics and Its Applications Vol. 127, Springer-Verlag, New York, 15-26). This formulation has a variable for, every possible combination of winning bids for. each bidder. Our algorithm exploits the structure of the XOR-of-OR bidding language used by the FCC. We also present a new methodology to produce realistic test problems based on the round-by-round results of FCC Auction #4. We generate 2,639 test problems, which involve 99 items and are substantially larger than most of the previously used benchmark problems. Because there are no real-life test problems for combinatorial spectrum auctions with the XOR-of-OR language, we used these test problems to observe the computational behavior of our algorithm. Our algorithm can solve all but one test problem within 10 minutes, appears to be very robust, and for difficult instances compares favorably to the natural formulation solved using a commercial optimization package with default settings. Although spectrum auctions are used as the guiding example to S describe the merits of branch and price for combinatorial. auctions, our approach applies to auctions of multiple goods in other scenarios similarly.