We study the Multiple Allocation Tree of Hubs Location Problem where a tree topology is required among the hubs and transportation cost of sending flows between OD pairs is minimized. Unlike most studies in the literature that assume a complete network with costs satisfying the triangle inequality to formulate the problem, we define the problem on non-complete networks and develop a modeling approach that does not require any specific cost and network structure. The proposed approach may provide more flexibility in modeling several characteristics of real-life hub networks. Moreover, the approach may produce better solutions than the classical approach, which may result from the differences in the selected hubs, the flow routes between origin–destination points, and the assignment of non-hub nodes to hub nodes. We solve the proposed model using CPLEX-based branch-and-bound algorithm and Gurobi-based branch-and-bound algorithm with Norel heuristic and develop Benders decomposition-based heuristic algorithms using two acceleration strategies, namely, strong cut generation and cut disaggregation. We conduct computational experiments using problem instances defined on non-complete networks with up to 500 nodes. The results indicate that the Benders-type heuristics are especially effective in finding good feasible solutions for large instances.

我们研究了集线器位置问题的多重分配树其中集线器之间需要树形拓扑结构，并且最小化 OD 对之间发送流的传输成本。与文献中的大多数研究假设一个具有满足三角不等式的成本的完整网络来制定问题不同，我们在非完整网络上定义问题并开发一种不需要任何特定成本和网络结构的建模方法。所提出的方法可以在建模现实生活中的集线器网络的几个特征时提供更大的灵活性。此外，该方法可能会产生比经典方法更好的解决方案，这可能是由于所选枢纽、起点-目的地之间的流动路线以及非枢纽节点到枢纽节点的分配的差异造成的。我们使用基于 CPLEX 的分支定界算法和基于 Gurobi 的基于 Norel 启发式的分支定界算法求解所提出的模型，并使用两种加速策略（即强切割生成和切割分解）开发基于 Benders 分解的启发式算法。我们使用在具有多达 500 个节点的非完整网络上定义的问题实例进行计算实验。结果表明，Benders 类型的启发式算法在为大型实例寻找良好可行的解决方案方面特别有效。