Hybrid dynamic modeling and receding horizon speed optimization for liner shipping operations from schedule reliability and energy efficiency perspectives

Uncertainties in port handling efficiency can cause port delays in the liner shipping system. Furthermore, policies on carbon emission reduction, such as EEXI standards, restrict the potential for speed optimization in liner shipping operations. Traditional tactical planning speed optimization is unsuitable for operational-level decision making, leading to unreliable schedules. From a schedule-reliability and energy-efficiency perspective, we propose a real-time speed optimization method based on discrete hybrid automaton (DHA) and decentered model predictive control (DMPC). We use a dynamic adjustment of sailing speed to offset the disturbance caused by port handling efficiency uncertainties. First, we establish a DHA model that describes each ship's hybrid dynamics of state switching between sailing and berthing; then, we develop a prediction model for the DMPC controller, which is analogous to the DHA model. The schedule is transferred into time-position coordinates as controller reference trajectories in the receding horizon speed optimization framework. We consider determining tracking errors, carbon emissions, and fuel consumption as our objectives, and we carry out engine power limitation (EPL) analysis for the sample ship, which turns the EEXI standards into constraints. We attain the recommended speed by solving a mixed-integer optimization. We carry out a case study, and our results indicate the effectiveness of our proposed DHA-DMPC scheme in lowering port delays and achieving the best trade-off between schedule reliability and energy efficiency. Additionally, we conduct further experiments to analyze the impacts of various carbon reduction policies on the performance levels of liner shipping operations.