The International Maritime Organization (IMO) has proposed to impose the carbon taxation on ports in the long term. The implementation of the carbon taxation policy will increase the operating cost and decrease its efficiency. Therefore, there is a trade-off between improving port operational efficiency and reducing carbon emission in ports. This study investigates the berth and quay cranes assignment planning, which aims at minimizing the total delay completion cost of all tasks, the total operating cost of quay cranes and the carbon taxation cost. In order to reflect the reality, some important uncertain factors are also considered. A recoverable robustness berth and quay crane assignment planning model is proposed. Numerical experiments are performed to demonstrate the applicability of the proposed model.