Abstract

This study addresses a two-echelon container drayage problem incorporating multiple transportation modes, and attempts to explore its potential application advantages. The problem concentrates on truckload transportation, and represents a variation of the classical two-echelon capacity-constrained vehicle routing problem. In the first echelon, a fleet of tractors, often employing long combination vehicles, transports trailers between a central depot and multiple satellites. In the second echelon, a fleet of tractors, restricted to a single-trailer stay-with mode, due to transportation regulations, executes multi-trip trailer transportation between satellites and customers. The tractor can perform two operations of dropping-off and pulling-up trailers (i.e., simultaneous delivery and collection of containers are involved). These characteristics make the routes of the two echelons couple tightly, and result in intertwined time interdependence within the entire network. A mathematical formulation is developed to address this two-echelon scheduling with time interdependence. To enhance computational efficiency, two groups of valid inequalities are provided. A two-stage matheuristic algorithm integrating the proposed mathematical model and heuristic techniques is developed. A route-string scheduling framework combined with a fixing and releasing mechanism is introduced to mitigate the complexity associated with the time-interdependence nature of the network. This algorithm, possessing fewer parameters than comparable (meta-) heuristics, offers a practical implementation. The mathematical model, along with the valid inequalities and the performance of the matheuristic algorithm, are validated through computational experiments using established instances from prior studies. Furthermore, experiments are undertaken to investigate the effects of customer distribution patterns and maximum permissible trailers count on operational efficiency.