Fuzzy multi-objective truck scheduling in multi-modal rail–road Physical Internet hubs

The Physical Internet (PI) is an innovative concept that has the potential to significantly improve the efficiency, cost-effectiveness, and sustainability of the global supply chain industry, particularly in cross-docking operations. This paper addresses the truck-scheduling problem in rail–road PI-Hubs, taking into account simultaneously both uncertainty and multi-objective decision-making, which has not been fully explored in the literature, particularly for PI-structures. Our proposed approach defines a Multi-Objective Mixed-Integer Programming model (FMO-MIP) that incorporates fuzzy chance-constrained programming and ϵ-constraint to minimize both the total delay and the sum of PI-containers traveled distances, while considering the uncertainty on truck arrival times. This work takes into account the particularities of the Physical Internet and presents a novel decision-making solution to generate a robust Pareto front that aligns with decision-makers’ attitudes towards risk (optimistic/pessimistic) while balancing trade-offs between conflicting objectives.