Freight transport network design using particle swarm optimisation in supply chain–transport supernetwork equilibrium

•A discrete freight transport network design is modelled within the framework of MPEC.•The model incorporates a supply chain–multimodal transport supernetwork equilibrium.•New variants of particle swarm optimisation are proposed to solve the upper level.•Effective transport-related actions are explored to enhance supply chain efficiency.

This paper presents a discrete network design problem for optimally designing freight transport network in terms of the efficiency of supply chain. Modelling is undertaken within the framework of mathematical programmes with equilibrium constraints, which first incorporates both supply chain and transport networks explicitly. The upper level determines the best set of actions for transport network improvement, while the lower-level decision is based on a supply chain–multimodal transport supernetwork equilibrium. New variants of particle swarm optimisation are developed to approximately solve the upper level. Numerical tests reveal their superior performance and the effective freight transport-related actions.