Due to the advantages of higher efficiency over fixed-price trading and the ability to discover equilibrium prices quickly, auction is a popular way of trading goods. In business-to-business e-commerce (B2B), many goods with complementarities or substitutabilities are being traded using auctions. Combinatorial auctions can be applied to improve the efficiency of trading in B2B marketplaces. In combinatorial auctions, a bidder can bid on a combination of goods with one limit price for the total combination. This improves the efficiency when the procurement of one good is dependent on the acquisition of another. Most of the combinatorial auctions studied in the literature are one-sided: either multiple buyers compete for commodities sold by one seller, or, multiple sellers compete for the right to sell to one buyer. Combinatorial double auctions in which both sides submit demand or supply bids are much more efficient than several one-sided auctions combined. However, combinatorial double auctions are notoriously difficult to solve from computation point of view. In this paper, we formulate the combinatorial double auction problem and propose an algorithm for finding near optimal solutions. The algorithm is developed by decomposing the combinatorial double auction problem into several subproblems and applying the subgradient algorithm to iteratively adjust the shadow prices for the subproblems.
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