Optimal subsidy design for energy generation in ship berthing

Shipping, the backbone of economic development, poses a significant environmental threat. Many government agencies have implemented regulations to mitigate ship air pollution. Three commonly used methods for compliance during berthing are marine diesel oil, scrubber, and shore power. Scrubber and shore power have greater emission reduction potential but can be costlier than marine diesel oil. To encourage their adoption, we optimize the subsidy plan through a bi-level mixed integer programming model where the government at the upper level minimizes the total subsidy amount while ship operators at the lower level choose the most cost-effective energy supply. The problem's complexity arises from the interdependence in the bi-level structure and the nonlinearity in the model. We address this by first converting the model into an equivalent single-level form and then reformulating the model by linearization. Numerical experiments are conducted to assess the model's performance. Results suggest that the promotion of scrubber or shore power starts with large ships in the initial stage. Increasing the number of ships with these technologies reduces subsidies. Additionally, each subsidy corresponds to a specific utilization range, allowing the government to adjust amounts based on target utilization levels.