Modern parcel logistic networks are designed to ship demand between given origin, destination pairs of nodes in an underlying directed network. Efficiency dictates that volume needs to be consolidated at intermediate nodes in typical hub-and-spoke fashion. In practice, such consolidation requires parcel sortation. In this work, we propose a mathematical model for the physical requirements, and limitations of parcel sortation. We then show that it is NP-hard to determine whether a feasible sortation plan exists. We discuss several settings, where (near-)feasibility of a given sortation instance can be determined efficiently. The algorithms we propose are fast and build on combinatorial witness set type lower bounds that are reminiscent and extend those used in earlier work on degree-bounded spanning trees and arborescences.

翻译：现代包裹物流网络设计用于在有向网络中给定的起点-终点节点对之间运输需求。效率要求以典型的枢纽-辐射模式在中间节点进行货物整合，而实际中这种整合需要包裹分拣。本文建立了包裹分拣物理需求与限制的数学模型，并证明判定是否存在可行分拣计划是NP困难的。我们探讨了若干可高效判定给定分拣实例（近）可行性的场景。所提出的算法快速且基于组合性见证集类型下界，该下界借鉴并扩展了早期关于度约束生成树和树形图的研究工作。