Abstract: Auction houses play some important roles in gathering and releasing information about supply and demand, valuing commodity valuation, and supervising auction processes. As a result, more and more sellers tend to entrust a third-party auction house to replace themselves for organizing auction activities. This paper studies the coordination of a supply chain with a seller and an auction house. The seller consigns his homogeneous commodities to the auction house. The auction house sells the commodities by a discriminatory auction with a secret reservation price. We take centralized decision-making as the benchmark of the supply chain optimal strategy. Analytical results show that the optimal reservation price is independent of both the supply quantity and the buyers’ bids distribution. For a commodity, to auction it successfully is superior to hold it if its auction price larger than its salvage value. Furthermore, the seller should balance the single expected revenue of a commodity with the accumulated revenue of multiple commodities, as the buyers’ bids decrease with the commodity quantity. Thus, the seller should choose the optimal supply quantity to maximize his auction revenue. Then we investigate the supply chain coordination with the auction commission contract, in which the auction house charges the seller a commission for each successful transaction. If a commodity is unsold, it will return to the seller. The analysis shows that the seller submits his reservation price is not on the basis of the buyers’ real bids. The seller also takes his commission and the commission of the buyers into account. Thus, his reservation price is not optimal, and thereby the supply chain cannot be coordinated with the auction commission contract. We propose a new sales-subsidy contract to coordinate the supply chain. In the sales-subsidy contract, the seller gains fixed revenue return from the auction house if a commodity is auctioned successfully, and the seller is simultaneously subsidized by the auction house if a commodity is unsold. We discuss the supply chain optimal strategy in the case of noncooperative and cooperative games, respectively. In the noncooperative game, the seller offers the supply quantity, i.e. acts as a leader, and then the auction house submits reservation price, i.e. acts as a follower. In the cooperative game, the seller and the auction house make joint decisions of the supply quantity and the reservation price, i.e. they are cooperative partners. The analysis shows that the sales-subsidy contract cannot coordinate the supply chain in the noncooperative game, whereas can coordinate the supply chain in the cooperative game. On the linear frontier of the optimal contract parameters, the profit distribution between the seller and the auction house is determined by the bargaining strength and power. Adjusting the subsidy amount can balance the risk burden between the seller and the auction house. At the end of the paper, a numerical example is provided to verify the above conclusions. The contributions of this paper are as follows. First, the interaction and profit allocation between the seller and the auction house in a multi-unit consignment auction are discussed. Second, the optimal strategic responses between the seller and the auction house to the sales-subsidy contract are investigated in the case of noncooperative and cooperative games, respectively. Third, some useful managerial insights are obtained: the traditional auction commission contract distorts bidding information from the buyers to the seller, whereas the sales-subsidy mechanism promotes the communication and cooperation between the seller and the auction house, and then optimizes the performance of the whole supply chain.

Key words: multi-unit auction, supply chain coordination, noncooperative game, cooperative game