Liner shipping network design with deadlines

It is crucial for a liner shipping company to design its container shipping network. Given a set of port‐to‐port container shipment demands with delivery deadlines, the liner shipping company aims to design itineraries of portcalls, deploy ships on these itineraries and determine how to transport containers with the deployed ships in order to maximize its total profit. In this paper we first demonstrate NP‐hardness of this problem and subsequently formulate it as a mixed‐integer non‐linear non‐convex programming model. A column generation based heuristic method is proposed for solving this problem. Numerical experiments for container shipping on the Asia–Europe trade lane show that the proposed solution algorithm is efficient to find good quality solutions.