A Hierarchical Pricing Strategy for Shore-to-Ship Power Services Considering Ship Behaviors

Shore-to-ship power (SSP) technology is an effective way for developing sustainable maritime transportation systems. Its implementation requires attractive pricing and incentive policies. This paper proposes a time-of-use (TOU)-based pricing strategy for SSP services considering the ship behaviors. A hierarchical pricing framework is first proposed to characterize the interactions among government regulators (GR), seaport authorities (SA) and ships, which is formulated as a tri-level two-loop Stackelberg game model. On the ship-side, each ship is treated as an independent stakeholder and the queuing process caused by limited number of berths is considered. Correspondingly, a coupled voyaging-berthing-queuing (CVBQ) model is established for each individual ship to accurately formulate their voyage scheduling, berth selection, queuing behaviors and power dispatch. The optimal CVBQ decision of each ship depends on its queuing time, which cannot be known before all ships make their decisions. To this end, a first-come-first-serve (FCFS)-based ship queuing algorithm is developed to chronologically derive the optimal decisions of all ships. The proposed hierarchical pricing model is solved iteratively by combining heuristics and commercial solvers. Case studies demonstrate the effectiveness of the proposed method.