We study a new service network design problem, where the number of available resources at each terminal is limited, and each commodity is delivered along a single path that prevents flow partition. Such a single-path constraint is motivated by currently emerging requirements in bulk transportation, express delivery, hazardous material transportation, etc. We model this problem with two mathematical formulations, i.e., node-arc and arc-cycle formulations, both of which lead to large-scale and computationally difficult mixed-integer programs. The node-arc formulation faces a significant computation burden. To that end, we develop a two-stage mathematical integer programming based heuristic for the arc-cycle formulation to produce high-quality solutions. In the first stage, a column generation procedure is executed to generate an optimal solution for the linear relaxation of the restricted master problem, and in the second stage, four heuristic strategies are designed to efficiently generate integer feasible solutions for the original problem. We conduct extensive experiments to verify the effectiveness of our proposed approach by comparing it with a commercial solver (CPLEX). We also examine the performance differences among four heuristic strategies, in terms of the frequency of finding integer feasible solutions and the quality of solutions.

我们研究了一个新的服务网络设计问题，其中每个终端的可用资源数量受到限制，并且每种商品都沿着防止流分配的单一路径进行传递。当前的散装运输，快递，危险材料运输等方面的新要求推动了这种单路径约束。我们使用两个数学公式（即节点弧和弧周期公式）对这个问题进行建模大型且计算困难的混合整数程序。节点弧公式面临巨大的计算负担。为此，我们针对弧周期公式开发了基于启发式的两阶段数学整数编程，以生成高质量的解决方案。在第一阶段 执行列生成过程以生成约束主问题的线性松弛的最佳解，在第二阶段，设计了四种启发式策略以有效地生成原始问题的整数可行解。我们进行了广泛的实验，通过将其与商业求解器（CPLEX）进行比较来验证我们提出的方法的有效性。我们还根据寻找整数可行解的频率和解的质量，检查了四种启发式策略之间的性能差异。我们进行了广泛的实验，通过将其与商业求解器（CPLEX）进行比较来验证我们提出的方法的有效性。我们还根据寻找整数可行解的频率和解的质量检查了四种启发式策略之间的性能差异。我们进行了广泛的实验，通过将其与商业求解器（CPLEX）进行比较来验证我们提出的方法的有效性。我们还根据寻找整数可行解的频率和解的质量，检查了四种启发式策略之间的性能差异。