Abstract: With the development of the digital economy, logistics becomes an important part of people's everyday life. In recent days, disruption risks frequently happened, and would cause dire consequences for a logistics system. Due to the advantage of reverse auctions in reducing procurement and transaction costs, applying reverse auctions to logistics service procurement activities becomes a new trend. Yet, integrating disruption risks into the logistics services procurement auctions has not been sufficiently investigated. In this regard, this paper focuses on a winner determination problem of a logistics service procurement auction under disruption risks, aiming to improve the safety of a logistics system. A hybrid strategy that includes the fortification, reservation, and temporary outsourcing policies is proposed to mitigate disruption risks. Then, a two-stage stochastic winner determination model that integrates the hybrid strategy is constructed. Since the number of decision variables and constraints exponentially increases at the number of disruption scenarios, an approximation algorithm that integrates a reduced scenario method with a dual decomposition and Lagrangian relaxation method is designed.
The small- and medium-scale numerical instances will be generated randomly, while the large-scale numerical instances would be generated by an established tool called Combinatorial Auction Test Suite. Simulation experiments are conducted to compute the above numerical instances by using the proposed approximation algorithm and the CPLEX solver, respectively. We find that for small-scale problems, the proposed method can obtain optimal solutions as the CPLEX solver, but the computing time is much less. For medium- and large-scale problems, the proposed method can obtain near-optimal solutions, since the gap between the lower and upper bounds is very small, while the CPLEX solver cannot give a feasible solution in more than 90 hours when the number of disruption scenarios is sufficiently large. The simulation results verify the effectiveness and applicability of the proposed model and method. Sensitivity analysis is also conducted to provide managerial insights for the auctioneer. First, the proposed hybrid strategy outperforms other known strategies in mitigating disruption risks, since the auctioneer will pay a higher total cost if other known strategies would be employed. To achieve a lower total cost, the auctioneer shall make a trade-off between the fortification, reservation, and temporary outsourcing policies carefully. Second, a sufficient fortification budget can benefit the auctioneer. If the fortification budget is sufficient, then the temporary outsourcing policy becomes less important, while the fortification policy becomes more important, especially when the unit temporary outsourcing cost is relatively high. If the fortification budget is insufficient, then the auctioneer can only resort to the more expensive temporary outsourcing policy, and the total cost will increase. Third, when the auctioneer faces higher disruption risks or clients' demands, the fortification strategy is more significant, which can not only mitigate disruptions, but also expand bidders' capacities. If the unit temporary outsourcing cost is low and the disruption probability is high, then unsatisfied demands can be fulfilled by other suppliers out of the reverse auction with a relatively low total cost. If the unit temporary outsourcing cost is high and the disruption probability is high, then the total cost will increase by using other expensive suppliers out of the reverse auction to fulfill the unsatisfied demands, indicating the importance of the fortification strategy. If the disruption probability is low, then the fortification strategy would be more important only if the original capacity of the bidder that needs to be fortified is relatively low.
This paper not only extends the research field of reverse auction, but also provides methodological and technical support for logistics services procurement auctions.

Key words: logistics service procurement, winner determination, disruption risks, approximation algorithm

摘要： 中断风险会对物流系统造成严重的影响。为应对中断风险,重点研究物流服务采购拍卖中带有中断风险的胜者确定问题,构建了集成加固、保留及临时外包混合策略的两阶段随机胜者确定模型,并设计了集成降情景和对偶分解与拉格朗日松弛的近似算法。数值实验结果表明所提模型和方法的有效性和可用性。敏感性分析结果表明所提混合策略好于其他已知策略,且充足的加固预算对拍卖方更有利。当拍卖方面临较高中断风险或客户需求时,加固策略更加重要,不仅可以应对中断风险,还可以扩展竞标方的能力。本文不仅在理论上拓展了逆向拍卖的研究领域,而且为物流服务采购拍卖提供方法和技术支撑。

关键词: 物流服务采购, 胜者确定, 中断风险, 近似算法