Ship routing and freight assignment problem for liner shipping: Application to the Northern Sea Route planning problem

In recent years, the Northern Sea Route (NSR) has attracted significant attention with respect to liner shipping. In this research, we propose a general time-space network-based mathematical formulation to analyze the ship routing and freight assignment problem in liner shipping and apply it to NSR planning problem. To solve the resulting program, we propose a Lagrangian relaxation-based decomposition algorithm that facilitates the network features. Empirical results show that navigation skill, bunker price, delay penalty and service commitment are the primary factors that affect the NSR's commercial practicability.