In this paper, we study the single allocation hub location problem with capacity selection in the presence of congestion at hubs. Accounting for congestion at hubs leads to a non-linear mixed integer program, for which we propose 18 alternate mixed integer second order conic program (MISOCP) based reformulations. Based on our computational studies, we identify the best MISOCP-based reformulation, which turns out to be 20–60 times faster than the state-of-the-art. Using the best MISOCP-based reformulation, we are able to exactly solve instances up to 50 nodes in less than half-an-hour. We also theoretically examine the dimensionality of the second order cones associated with different formulations, based on which their computational performances can be predicted. Our computational results corroborate our theoretical findings. Such insights can be helpful in the generation of efficient MISOCPs for similar classes of problems.

在本文中，我们研究了在枢纽存在拥塞的情况下，容量选择的单个分配枢纽位置问题。考虑到枢纽处的拥塞会导致产生一个非线性混合整数程序，为此，我们提出了18种基于混合整数二阶二次曲线程序（MISOCP）的重新制定公式。根据我们的计算研究，我们确定了基于MISOCP的最佳重构，事实证明它比最新技术快20–60倍。使用基于MISOCP的最佳格式，我们可以在不到半小时的时间内准确地解决多达50个节点的实例。我们还从理论上检查了与不同公式相关联的二阶圆锥的维数，据此可以预测它们的计算性能。我们的计算结果证实了我们的理论发现。