Bids submitted in auctions are usually treated as enforceable commitments in most bidding and auction theory literature. In reality bidders often withdraw winning bids before the transaction when it is in their best interests to do so. Given a bid withdrawal in a combinatorial auction, finding an alternative repair solution of adequate revenue without causing undue disturbance to the remaining winning bids in the original solution may be difficult or even impossible. We have called this the “Bid-taker’s Exposure Problem”. When faced with such unreliable bidders, it is preferable for the bid-taker to preempt such uncertainty by having a solution that is robust to bid withdrawal and provides a guarantee that possible withdrawals may be repaired easily with a bounded loss in revenue. In this paper, we propose an approach to addressing the Bidtaker’s Exposure Problem. Firstly, we use the Weighted Super Solutions framework [13], from the field of constraint programming, to solve...