A joint liner ship path, speed and deployment problem under emission reduction measures

This paper addresses a joint ship path, speed, and deployment problem in a liner shipping company considering three emission reduction measures, including sulfur emission regulations, carbon tax, and vessel speed reduction incentive programs (VSRIPs). Given a set of service routes and the total number of available ships, the proposed problem determines how many ships should be deployed on each route and how to design sailing path and speed for each leg. A mixed-integer non-linear programming model is presented for minimizing the total cost of all routes, i.e., fuel cost, carbon tax, and fixed cost, minus dockage refund. The different impacts of the three emission reduction measures on sailing path and speed complicate the problem. Some important properties are obtained by analyzing the proposed model. Combining these properties with a dynamic programming approach, a tailored method is developed to solve the problem. Based on real data, extensive numerical experiments are conducted to examine the validity of the proposed model and the efficiency of the solution method. The computational results demonstrate that the proposed model can contribute to significant cost savings for shipping companies.