Title
Exact algorithms for the matrix bid auction
Abstract
In a combinatorial auction, multiple items are for sale simultaneously to a set of buyers. These buyers are allowed to place bids on subsets of the available items. A special kind of combinatorial auction is the so-called matrix bid auction, which was developed by Day [Expressing preferences with price-vector agents in combinatorial auctions. PhD thesis, University of Maryland; 2004]. The matrix bid auction imposes restrictions on what a bidder can bid for a subsets of the items. This paper focusses on the winner determination problem, i.e. deciding which bidders should get what items. We discuss the computational complexity of the winner determination problem for a special case of the matrix bid auction. We present two mathematical programming formulations for the general matrix bid auction winner determination problem. Based on one of these formulations, we develop two branch-and-price algorithms to solve the winner determination problem. Finally, we present computational results for these algorithms and compare them with results from a branch-and-cut approach based on Day and Raghavan [Matrix bidding in combinatorial auctions. Manuscript; 2006].
Year
DOI
Venue
2009
10.1016/j.cor.2007.12.009
WEA
Keywords
DocType
Volume
branch and cut,mathematical programming,combinatorial auction,computational complexity,branch and price
Journal
36
Issue
ISSN
Citations 
4
0305-0548
3
PageRank 
References 
Authors
0.41
20
2
Name
Order
Citations
PageRank
Dries R. Goossens112915.88
Frits C. R. Spieksma259158.84