The Physical Internet (PI) paradigm, which has gained attention in research and academia in recent years, leverages advanced logistics and interconnected networks to revolutionize the way goods are transported and delivered, thereby enhancing efficiency, reducing costs and delays, and minimizing environmental impact. Within this system, PI-hubs function similarly to cross-docks enabling the splitting of PI-containers into smaller modules to be delivered through a network of interconnected hubs, allowing dynamic routing optimization and efficient consolidation of PI-containers. Nevertheless, the impact of the system parameters and of the relevant uncertainties on the performance of this innovative logistics framework is still unclear. For this reason, this work proposes a robustness analysis to understand how the PI logistic framework is affected by how PI-containers are handled, consolidated, and processed at the PI-hubs. To this end, the considered PI logistic system is represented via a mathematical programming model that determines the best allocation of PI-containers in an intermodal setting with different transportation modes. In doing so, four Key Performance Indicators (KPIs) are separately considered to investigate different aspects of the PI system's performance and the relevant robustness is assessed with respect to the PI-hubs' processing times and the number of modules per PI-container. In particular, a Global Sensitivity Analysis (GSA) is considered to evaluate, by means of a case study, the individual relevance of each input parameter on the resulting performance.

翻译：近年来备受研究和学术界关注的物理互联网（PI）范式，通过利用先进的物流技术和互联网络，彻底改变了货物的运输和交付方式，从而提高了效率、降低了成本和延误，并减少了环境影响。在该系统中，PI枢纽的功能类似于交叉转运站，能够将PI集装箱拆分为更小的模块，通过互联的枢纽网络进行配送，从而实现动态路径优化和PI集装箱的高效整合。然而，系统参数及相关不确定性对这一创新物流框架性能的影响尚不明确。为此，本研究提出了一种鲁棒性分析，以理解PI物流框架如何受到PI集装箱在PI枢纽中的处理、整合和加工方式的影响。为此，我们通过一个数学规划模型来表示所考虑的PI物流系统，该模型确定了在不同运输模式的多式联运环境中PI集装箱的最佳分配方案。在此过程中，我们分别考虑了四个关键绩效指标（KPIs），以研究PI系统性能的不同方面，并针对PI枢纽的处理时间和每个PI集装箱的模块数量评估了相关的鲁棒性。特别地，我们采用全局敏感性分析（GSA），通过一个案例研究来评估每个输入参数对最终性能的个体相关性。