Truthful auctions for e-market logistics services procurement with quantity discounts

Auctions are an important method for solving the logistics procurement problem in electronics markets. However, current 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. For a market with only one customer, we design a P-VCG auction with quantity discounts, and for a market with multiple customers, we construct a model for maximizing social welfare and propose a trade reduction with a quantity discount (TR-QD) double-auction mechanisms. We prove that both auction mechanisms ensure incentive compatibility, individual rationality, balanced budget, and asymptotical efficiency. Furthermore, compared with traditional truthful double-auctions, the TR-QD mechanism supports cooperative purchases—which allows more customers to enjoy discounts on large-scale logistics services—and bid time priority—which achieves the goal of meeting earlier requests earlier and improves auction efficiency. Numerical studies further show that the TR-QD auction mechanism can achieve an increase in customers’ total value, logistics companies’ total value, social welfare and total trading volume.