Containers transport and logistics models with Matrices of Sets: -enabling digital efficiency gains for freight transport & logistics

Extended Abstract Containerised transport is central to global commerce as shown by the recent traffic halt in the Suez Canal in March 2021, and the consequent threat to global freight transport, which our economies are used to rely upon. The new framework of Matrices of Sets considers matrices where each term at line i and column j is a set, instead of a number in classical matrices. A first exploration is reported here on how such a framework may suitably help model container based multimodal transport, with descriptive sets including numbers (data) and text (metadata) may efficiently gather in one matrix of sets, what might have been scattered in multiple matrices of numbers and added metadata. First benefits of embedding relational structures inherent to transport flows and modes, with varied granularity, will be discussed. Different views will be presented: from the bottom-up individual container and its content and intended routing, to the corridor-level from hub to hub, and further capillarity of upload or delivery, and of logistical tasks required, through the sea-vessel or road/rail vehicle and logistics centre perspective. In this paper, we focus on multimodal transport of containers from an origin to a destination using successively river, rail and road modes. The objective is to find all multimodal routes starting by river, then by rail and ending by road (Benantar et al. 2020). This order is justified by the fact that post-haulage is usually provided by road to deliver end clients. The multimodal transport will be designed as a multi-level network, each level corresponds to a transport network (river, rail, road). Each of the three networks will be represented by a matrix of sets that describes a graph whose vertices represent terminals (including predefined terminal transshipping points i.e. points of connection between modes of transport) and end clients and its edges represent the links between the vertices (as illustrated in Figure 1). The multimodal paths computation is carried out by multiplying the associated Matrices of Sets.