Comparing winner determination algorithms for mixed multi-unit combinatorial auctions

Mixed multi-unit combinatorial auctions are combinatorial auctions in which the auctioneer and the bidders negotiate over transformations rather than over simple goods. By proposing a transformation a bidder is offering to produce a certain set of output goods after having received the specified input goods. Solving such a mixed auction means choosing a sequence of transformations such that the auctioneer ends up with all the goods desired at the lowest possible cost. This is a generalisation of the winner determination problem in combinatorial auctions and cannot be solved using standard winner determination algorithms. In this paper we analyse the computational complexity of the winner determination problem for mixed auctions and compare the performance of two new algorithms and of the original algorithm proposed for the problem. We also discuss suitable ways of generating test sets for this comparison.