AI 中文总结
针对超连接城市包裹网络中的固定线路路由问题，提出带处理时间的线路网络路由模型，利用凸松弛和残差前沿框架高效求解，可显著提升配送效率。
AI 中文摘要
受超连接城市包裹网络用于同日和时效敏感配送的启发，我们研究了在评估一组重复性枢纽间车辆服务候选集时出现的固定线路路由问题。车辆遵循预定义的循环服务点序列，即线路，包裹可在线路之间转运。这种转运扩展了路径选择，但需要装卸操作，使车辆在服务点停留。由于处理量依赖于路由，停留时间变为内生变量，将路由决策与线路周期时间、有效服务频率和转运等待时间联系起来。我们提出了带处理时间的线路网络路由问题（RLN-HT），并将其建模为双线性广义容量-流量分配模型。我们刻画了作为处理工作量函数的最优停留时间和由此产生的频率，从而能够仅以商品流量进行重新表述。我们利用其凸子结构推导出两个二阶锥松弛，这些松弛保留了原始可行域，因此能产生可行的初始解以及有效的下界。我们还开发了一个残差前沿框架，刻画了凸松弛目标与剩余非凸残差之间的权衡，为构造下界证明提供了一种通用机制。计算实验表明，忽略处理时间可能导致路由质量差或不可行，而考虑内生停留时间可将平均包裹旅行时间最多提高26.5%。在多达257个节点和25条线路的实例中，松弛方法求解迅速，产生接近最优的路由，并获得较小的最优性间隙，而现成的空间分支定界法则难以产生有用的界。
英文摘要
Motivated by hyperconnected urban parcel networks for same-day and time-sensitive delivery, we study the fixed-line routing problem that arises when evaluating a candidate set of recurring inter-hub vehicle services. Vehicles follow predefined cyclic sequences of service points, or lines, and parcels may transfer between lines. Such transfers expand path choice but require loading and unloading operations that make vehicles dwell at service points. Because handled volumes are routing-dependent, dwell times become endogenous, linking routing decisions to line cycle times, effective service frequencies, and transfer waiting times. We introduce the Routing in Line Networks with Handling Times (RLN-HT) problem and formulate it as a bilinear generalized capacity-flow assignment model. We characterize optimal dwell times and the resulting frequencies as functions of handling workloads, enabling a reformulation solely in terms of commodity flows. We exploit its convex substructure to derive two second-order conic relaxations that preserve the original feasible region and therefore yield feasible incumbent solutions along with valid lower bounds. We also develop a residual-frontier framework that characterizes the tradeoff between the convex relaxation objective and the remaining nonconvex residual, yielding a general mechanism for constructing lower-bound certificates. Computational experiments show that ignoring handling times can yield poor or infeasible routing, whereas accounting for endogenous dwell times can improve average parcel travel times by up to 26.5%. In instances with up to 257 nodes and 25 lines, the relaxations solve quickly, yield near-optimal routing, and obtain small optimality gaps, whereas off-the-shelf spatial branch-and-bound struggles to produce useful bounds.
