The multi-commodity network flow problem (MCNF) consists in routing a set of commodities through a capacitated network at minimum cost and is relevant for routing containers in liner shipping networks. As commodity transit times are often a critical factor, the literature has introduced hard...

We present an integer programming based heuristic, a matheuristic, for the liner shipping network design problem. This problem consists of finding a set of container shipping routes defining a capacitated network for cargo transport. The objective is to maximize the revenue of cargo transport,...

The multi-commodity network flow problem is an important sub-problem in several heuristics and exact methods for designing route networks for container ships. The sub-problem decides how cargoes should be transported through the network provided by shipping routes. This paper studies the...

Global liner shipping is a competitive industry, requiring liner carriers to carefully deploy their vessels efficiently to construct a cost competitive network. This paper presents a novel compact formulation of the liner shipping network design problem (LSNDP) based on service flows. The...