The hub location problem (HLP) is a fundamental facility planning problem with various applications in transportation, logistics, and telecommunication systems. Due to strategic nature of the HLP, considering uncertainty and the associated risks is of high practical importance in designing hub networks. This paper addresses a risk-averse single allocation HLP, where the traffic volume between the origin–destination (OD) pairs is considered to be uncertain. The uncertainty in demands is captured by a finite set of scenarios, and a flow-dependent economies of scale scheme is used for transportation costs, modeled as a piece-wise concave function of flow on all network arcs. The problem is cast as a risk-averse two-stage stochastic problem using mean-CVaR as the risk measure, and a novel solution approach combining Benders decomposition and scenario grouping is proposed. An extensive set of computational experiments is conducted to study the effect of different input parameters on the optimal solution, and to evaluate the performance of the proposed solution algorithm. Managerial insights are derived and presented based on the obtained results.

枢纽位置问题 (HLP) 是一个基本的设施规划问题，在运输、物流和电信系统中有各种应用。由于 HLP 的战略性质，考虑不确定性和相关风险在设计枢纽网络时具有很高的实际意义。本文讨论了一个规避风险的单一分配 HLP，其中起点-终点 (OD) 对之间的交通量被认为是不确定的。需求的不确定性由一组有限的场景捕获，并且流量相关的规模经济方案用于运输成本，建模为所有网络弧上流量的分段凹函数。使用均值 CVaR 作为风险度量，将问题转化为规避风险的两阶段随机问题，并提出了一种结合 Benders 分解和场景分组的新解决方法。进行了大量的计算实验，以研究不同输入参数对最优解的影响，并评估所提出的求解算法的性能。管理见解是根据获得的结果得出和呈现的。