Optimal Solutions for Multi-Unit Combinatorial Auctions: Branch and Bound Heuristics

Finding optimal solutions for multi-unit combinatorial auc- tions is a hard problem and finding approximations to the optimal solution is also hard. We investigate the use of Branch-and-Bound techniques: they require both a way to bound from above the value of the best allocation and a good criterion to decide which bids are to be tried first. Different methods for e ciently bounding from above the value of the best allocation are considered. Theoretical original results characterize the best approximation ratio and the ordering criterion that provides it. We suggest to use this criterion.