| Auctions are an important method for solving the logistics procurement problem in electronics markets.However,existing auction methods rarely consider the existence of quantity discounts.To fill this research gap,we introduce quantity discounts into the procurement Vickrey-Clark-Groves(P-VCG)and truthful double-auction mechanisms and apply them to the logistics services procurement market.First,for only one customer,we established a P-VCG mechanism based on the VCG and reverse auction mechanisms.In the proposed mechanism,we allow logistics companies to have a quantity discount on bids.Minimizing the total cost of the customer is the goal of this mechanism.For a logistics company,its best bid is a real one.The P-VCG mechanism also satisfies incentive compatibility(IC),individual rationality(IR),balanced budget(BB),and asymptotical efficiency(AsE).Second,when there are multiple customers,we applied quantity discounts,cooperative procurement,and bidding time to the double auction.Based on the trade reduction mechanism,we established two new auction mechanisms:trade reduction with a quantity discount(TR-QD)double-auction mechanism and Improved TR-QD(I-TR-QD)double-auction mechanism.Under the TR-QD mechanism,we allow logistics companies to have a quantity discount on bids and there is also a cooperative procurement between customers.The TR-QD mechanism satisfies IR,IC,BB,and AsE.Compared with the existing multi-unit trade reduction mechanism,the customer’s income,logistics company’s income,and total social welfare are improved.In our research,we chose a balanced market,in which the numbers of customers and transportation companies increase or decrease simultaneously.Obviously,logistics companies can add their own competitiveness through bidding with quantity discounts.For the buyer’s market(where the number of customers is small and the increase rate is far less than the number of logistics companies),it is clear that logistics companies also prefer to quantitative discount bids to improve their competitiveness.However,for the seller’s market(where the number of customers is large and the growth rate is much greater than that of logistics companies),logistics companies are in a dominant position in the market,and may thus abandon the strategy of quantity discounts.In summary,our auction mechanism is mainly used for balanced and buyer’s markets.Through the introduction of bidding time,we solved the deficiencies of the existing distribution schemes,while ensuring the compatibility of incentives.Furthermore,our auction mechanism reaches the goal that earlier requests are met earlier,and this bid-time priority idea can also encourage customers to quickly cast their own real bids and improve auction efficiency.Third,the I-TR-QD mechanism is the first truthful double-auction mechanism to achieve an SBB.Third-party auctioneers only play a role in determining the distribution of the auction.Third parties do not make a difference,and logistics companies and customers can have greater profits.More customers and logistics companies are attracted to our auction mechanism.In addition,the I-TR-QD mechanism is identical to the TR-QD mechanism in other respects.Our work researches the potentials of the logistics auction market by adding quantity discounts and cooperative procurement.The number of transactions and social welfare are improved.However,it should be pointed out that our mechanisms are more suitable for equilibrium market or buyer’s market.It is not applicable to the seller’s market for the seller in the seller’s market does not have the willingness to bid with quantity discounts. |
