The π-transportation problem: On the value of split transports for the Physical Internet concept

The Physical Internet (PI or π) is a design metaphor that applies the digital internet as an archetype to rethink freight logistics and transportation in a more sustainable, interoperable, and cooperative way. Analogously to the protocols of the digital internet, freight should be encapsulated into standardized π-containers and transported through an open network of cooperating π-hubs. Despite the inspiring analogy, parallels are not absolute. Digital data packages can be duplicated without cost, can be (re-)sent anywhere in short time, generate no return flows, and their routing decisions have to be taken in microseconds. In this paper, we focus on a characteristic of the digital internet that can be emulated by the PI but has received less attention yet: split transports. Analogously to the internet protocol, which forwards each data packet individually according to dynamically adapted routing tables, larger shipments can be split into multiple smaller π-containers, so that different containers with the same destination may be routed via different paths. To evaluate whether these split transports significantly promote the aims of the PI, we derive a basic scheduling problem, called the π-transportation problem, where a given set of (either split or unsplit) shipments aim to travel along a linear transport corridor with given π-hubs. Based on this problem, we derive analytical and computational results to quantify the impact of split transports on the success of the PI concept. Our results suggest that split transports are not among the important features when redesigning the transportation sector.