In container liner shipping, bunker cost is an important component of the total operating cost, and bunker consumption increases dramatically when the sailing speed of containerships increases. A higher speed implies higher bunker consumption (higher bunker cost), shorter transit time (lower inventory cost), and larger shipping capacity per ship per year (lower ship cost). Therefore, a container shipping company aims to determine the optimal sailing speed of containerships in a shipping network to minimize the total cost. We derive analytical solutions for sailing speed optimization on a single ship route with a continuous number of ships. The advantage of analytical solutions lies in that it unveils the underlying structure and properties of the problem, from which a number of valuable managerial insights can be obtained. Based on the analytical solution and the properties of the problem, the optimal integer number of ships to deploy on a ship route can be obtained by solving two equations, each in one unknown, using a simple bi-section search method. The properties further enable us to identify an optimality condition for network containership sailing speed optimization. Based on this optimality condition, we propose a pseudo-polynomial-time solution algorithm that can efficiently obtain an epsilon-optimal solution for sailing speed of containerships in a liner shipping network. 
Fundamental properties and pseudo-polynomial-time algorithm for network containership sailing speed optimization