Low-emission berth allocation by optimizing sailing speed and mooring time - Hu, Zhi-Hua (Transport, 2020)
To investigate the relations among delay times (weighted by vessels’ handling times), the emissions during the vessels’ sailing and mooring in a Berth Allocation Problem (BAP) where the berth times and sailing speeds are formulated as decision variables. The vessels’ delay times are computed comparing to the vessels’ Expected Departure Times (EDTs); the sailing emission is determined by the sailing speed and distance; the mooring emission is positive to the mooring time at terminal. Multi-objective mixed-integer programs are established, and the nonlinear functions between emissions and sailing speeds are transferred to linear ones by the Second-Order Cone Programming (SOCP) method. Solution methods are further developed based on e-constraint and stage-based methods by considering the preferences of objectives. Four groups of experiments are conducted to demonstrate the formulations, effects of vessels’ handling times and EDTs on the solutions, and the reduced emissions affected by the number of vessels in the schedules. Experimental results demonstrated that the efficiency purpose is not absolutely conflict with the environment purposes for some instances, and so they can be pursued at the same time; improving the vessels’ handling efficiency help expand the ranges of berth times and sailing speeds, resulting in reducing the delay times and emissions; advancing the EDTs can improve the terminal operators’ service quality to shipping companies, while the weighted delay times and emission may be increased.