Robustness Evaluation of a Physical Internet-based Intermodal Logistic Network

TL;DR

The paper addresses the robustness of a Physical Internet (PI) intermodal logistics network to uncertainty in PI-hub processing times and the number of modules per PI-container. It develops a centralized optimization framework that routes PI-containers split into modules across trains, trucks, and hub links, and evaluates performance with four KPIs $J_1$–$J_4$ using variance-based Global Sensitivity Analysis (GSA). A case study with multiple origins, hubs, and destinations demonstrates deterministic performance and reveals that KPI2 (delivery time) is relatively robust, while KPI1 (direct trucks usage) and KPI3 (cost) are more sensitive to module counts; GSA indicates the average module count $n_s$ is a key driver of variability, with hub times $\tau_p$ having limited first-order impact. The findings suggest incorporating module splitting as a decision variable and pursuing dynamic, re-optimized routing to handle parameter uncertainty, with future work on scalable heuristics for larger instances.

Abstract

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.

Figures (8)

• Figure 1: Example of a PI-container split into different modules with different volumes (shahedi2023lead).
• Figure 2: A diagram depicting a generic PI network, along with an illustrative example of a PI-container breakdown and routing with trucks (in green), trains, and direct trucks from origin to destination terminals (in red).
• Figure 6: The assumed location of the terminals and PI-hubs in Europe - Black spots: distribution centers; Green spots: origin terminals; Blue spots: PI-hubs; Red spots: destination terminals.
• Figure 7: Modal split of the PI-containers when they leaves the origin terminal (a, b, c, d) and through the PI-hubs (e, f, g, h) for different objective functions. $\blacksquare$ Direct trucks; $\blacksquare$ Trucks to the PI-hubs; $\blacksquare$ Trains to the PI-hubs; $\blacksquare$ Trucks to destination terminals (from the PI-hubs); $\blacksquare$ Trains to destination terminals (from the PI-hubs).
• Figure 8: Ratio between the standard deviation and the mean (computed over 1000 samples) of the KPI values for the four considered configurations: $\blacksquare$ C1 $(\min J_1)$; $\blacksquare$ C2 $(\min J_2)$; $\blacksquare$ C3 $(\min J_3)$; $\blacksquare$ C4 $(\min J_4)$.