Congestions at loading docks can cause severe delays in logistics processes and cause increasing bottlenecks for truck routes. For warehouses, uncoordinated arrivals of trucks make appropriate staffing difficult and congestions can interfere with other processes at the facility. To mitigate congestions at loading docks, we propose package auctions to allocate time slots to trucks. \ \ The contribution of this research is the application of core-selecting package auctions to address the loading dock congestion problem. We propose a bidding language and a core-selecting package auction for this setting based on existing literature. Core-selecting payment rules can avoid drawbacks of the Vickrey–Clarke–Groves (VCG) mechanism with Clarke pivot rule, e.g., low perceived fairness of prices. \ \ We evaluate our proposal by means of simulation and assess (i) the potential for waiting time reduction compared to uncoordinated arrivals as well as sharing of historical waiting times, (ii) the empirical complexity of the computational problem for scenarios of varying complexity, and (iii) the relation of VCG and bidder-Pareto-optimal core payments. Our findings provide evidence that loading dock auctions can alleviate congestion substantially and that the core-pricing rule is well-suited to address the price fairness and low seller revenue problems in this setting.