In this paper, a class of single-allocation hub location problems is investigated from the perspective of upgrading. The latter is understood as an improvement of a set of edges to increase their individual performance, e.g., a decreased unit transportation cost. The goal is to obtain an improved optimal solution to the problem compared to that obtained if upgrading was not done. A budget constraint is assumed to limit the upgrading operations. A flow-based formulation is initially proposed that extends a classical model for uncapacitated single-allocation hub location with complete hub networks. Nevertheless, the fact that the unit costs after upgrading may violate the triangle inequality needs to be accounted for. Since the proposed formulation has a high computing burden, different possibilities are discussed for enhancing it. This leads to devising an efficient branch-and-cut algorithm with different variants. Additionally, a formulation based on the discrete ordered median function is also introduced that is also enhanced and embedded into a branch-and-cut algorithm again with several variants. All models and algorithms are also adapted to problems embedding hub network design decisions. Extensive computational tests were conducted to assess the methodological contributions proposed.

中文翻译：

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带边缘升级的无能力单分配中心中间位置：模型和精确解算法


本文从升级的角度研究一类单一分配枢纽选址问题。后者被理解为对一组边缘的改进，以提高其各自的性能，例如，降低单位运输成本。目标是获得与未进行升级时获得的问题相比改进的最佳解决方案。假设预算约束限制了升级操作。最初提出了基于流的公式，该公式扩展了具有完整枢纽网络的无能力单分配枢纽位置的经典模型。然而，需要考虑升级后的单位成本可能违反三角不等式的事实。由于所提出的公式具有很高的计算负担，因此讨论了增强它的不同可能性。这导致设计出具有不同变体的高效分支剪切算法。此外，还引入了基于离散有序中值函数的公式，该公式也经过增强并再次嵌入到具有多种变体的分支切割算法中。所有模型和算法也适用于嵌入中心网络设计决策的问题。进行了广泛的计算测试来评估所提出的方法论贡献。