Integrated optimization of revenue management and heterogeneous fleet deployment with green technology upgrading

This paper explores an integrated decision problem for heterogeneous fleet deployment within emission control areas (ECAs) considering shipping revenue management. Three types of ships (i.e., non-upgraded ships, scrubber-installed ships, and liquefied natural gas (LNG)-retrofitted ships) are considered in the shipping network, with the container demand varying with the freight rate. We propose a nonlinear mixed-integer programming model to determine whether to retrofit a liner company's ship fleet with new technologies, how to deploy different types of ships, and how to set freight rates for each origin-destination (OD) pair. The proposed model aims to maximize the weekly profits of the liner company. A branch-and-price method is introduced to efficiently solve this problem. Numerical experiments are performed to evaluate the performance of the proposed approach. The computational results show that our algorithm can yield an optimal solution within a significantly shorter time than the CPLEX solver. The results from sensitivity experiments suggest that various green technology investments in ships differ in their sensitivity to market volatility. Specifically, retrofitting an LNG engine is a stable and long-term strategic investment, while installing a scrubber is a flexible and short-term tactical decision. Our study provides shipping companies with a powerful decision support tool to comply with ECAs.