Several countries and regions have announced sulphur emission control areas (SECAs) to regulate sulphur emissions from ships. Incorporating environmental benefits and economic impacts, a bi-level programming model following the Stackelberg game regime is proposed to capture the SECA design problem for a given coastal area, in which the irregular polygon of the SECA is assumed to be a convex hull and described by a system of linear constraints. The government, as the leader, minimizes total sulphur emissions of ships over the entire coastal area with the voyage cost constraint. The ships, as followers, minimize individual voyage costs by jointly choosing the sailing trajectories and speed profile inside and outside the SECA between the associated port pairs with the given geometric configuration of the SECA. We first derive the optimal trajectory and speed profile for each ship, which can be simplified to a shortest path problem. Subsequently, a heuristic algorithm based on the steepest descent method is proposed to obtain the Pareto optimal solution in the sense of simultaneous minimization of total emissions and voyage costs. Finally, two announced SECAs are adopted to illustrate the validity of the proposed model and algorithm.

一些国家和地区已经宣布设立硫排放控制区（SECAs）来规范船舶的硫排放。结合环境效益和经济影响，提出了一个遵循 Stackelberg 博弈机制的双层规划模型来捕获给定沿海地区的 SECA 设计问题，其中 SECA 的不规则多边形被假定为凸包并描述为线性约束系统。政府作为主导，在航次成本约束下，将整个沿海地区的船舶总硫排放量降至最低。作为追随者的船只通过在具有给定 SECA 几何配置的相关港口对之间共同选择 SECA 内外的航行轨迹和速度剖面，最大限度地减少个人航行成本。我们首先推导出每艘船的最佳轨迹和速度曲线，这可以简化为最短路径问题。随后，提出了一种基于最速下降法的启发式算法，从总排放量和航次成本同时最小化的意义上获得帕累托最优解。最后，采用两个已公布的 SECA 来说明所提出的模型和算法的有效性。