Optimal Pricing and Scheduling of Seaport-Ships Coordination System: A Game Theoretic Approach

Owing to extensive seaport electrification and growing concerns about maritime carbon emissions, efficient coordination of logistics services and energy services among the seaport authorities and the shipowners has become crucial to maximize potential operational flexibility and to improve energy efficiency. However, existing studies rely on centralized models and overlook the logistics characteristics in maritime microgrids, which yields impractical operation strategies. To address this gap, we propose a hybrid hierarchical competitive game-based optimal pricing and service scheduling model with a single-leader-multiple-followers scheme for seaport-ships coordination systems. Specifically, the interaction between the port and the shipowners is represented as a hierarchical Stackelberg game, while the followers' subgame is formulated as a generalized Nash game with coupling constraints. To guarantee the optimal strategies for all participants, the existence and uniqueness of the proposed hierarchical game equilibrium are proven. Furthermore, an accelerated distributed augmented lagrangian (ADAL)-based distributed algorithm is developed for the global Stackelberg equilibrium to protect the privacy of each entity. Numerical results verify the necessity and efficiency of the proposed method.