Lead-time-based freight routing in multi-modal networks considering the Physical Internet

This paper addresses the problem of optimizing the transport of goods in the Physical Internet (PI) framework in a multi-modal setting using a multi-objective mixed-integer linear programming (MILP) approach. The model is specifically designed to meet the requirements related to modular shipments and PI-hubs, and in particular, determines the allocation of modular shipments to each transport mode in an intermodal setting. In doing so, parallel direct connection via road, the delivery times and the transportation costs are minimized. The model is applied to a numerical case study, to test its effectiveness to enhance freight transport efficiency within the PI framework, by exploiting, in particular, all the capacities of the available vehicles. In addition, a sensitivity analysis is conducted on some model parameters, to test its reaction to changes in the supply system and in the objective priorities. Results show that all the shipments are effectively transported between the origin and the destination terminals, they are divided into modules when necessary, and the selected transport modes, allocation strategy, and delivery times vary accordingly to the objective priorities.