This paper investigates a transportation service procurement problem for truckload operations within a combinatorial auction framework. In practice, conventional clock auctions may suffer from slow convergence and inefficient allocation when the number of auction rounds is limited. To address this issue, we propose a two-phase combinatorial auction framework, in which supplementary bidding is introduced after the clock auction to improve allocation efficiency. The proposed framework integrates the bid generation problem, the winner determination problem, and the supplementary bidding process, all formulated as mixed-integer linear programming models. Two variants of the framework are developed, where supplementary bundles or bids are generated by the auctioneer or the carriers. Computational experiments show that the proposed framework improves allocation efficiency and reduces procurement costs within the tested settings compared with the standard clock auction. In addition, the supplementary bidding phase accelerates convergence and enables near-efficient allocations within a limited number of rounds. The results demonstrate that the framework can achieve reasonable allocation outcomes while accelerating convergence.
Lyu et al. (Thu,) studied this question.