A Heuristic for Winner Determination in Rule-Based Combinatorial Auctions

Abstract Combinatorial auctions address the sale of materials where there exist complementarities between items. A major stumbling block to the widespread use of combinatorial auctions is the complexity of winner determination known to be NP-complete. We consider a rich version of combinatorial auctions, rule-based combinatorial auctions, where bids consist of rules that describe acceptable bundles rather than provide complete enumerations of acceptable bundles. This makes the winner determination problem even harder because the problem must find bundles meeting bid criteria as well as finding an optimal selection of winning bids. Our contribution is threefold. First, we give a general approach to providing good approximations to the winner determination problem for rule-based auctions. Although the approach requires adaptation for specific instances, it is conceptually tractable and implementable. Second, the approach is illustrated and tested with an artificial but realistic case proposing an auction format for selling prime time television advertising time formed from data and interviews with industry sources. Third, while some researchers have used commercial solvers that appeared to obviate the need for specialized solution approaches to the winner determination problem, we give evidence which, at least for the problem studied here, shows specialized approaches are necessary.