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“Double-Line Ship Mooring” (DLSM) mode has been applied as an initiative operation mode for solving berth allocation problems (BAP) in certain giant container terminals in China. In this study, a continuous berth scheduling problem with the DLSM model is illustrated and solved with exact and heuristic methods with an objective to minimize the total operation cost, including both the additional transportation cost for vessels not located at their minimum-cost berthing position and the penalties for vessels not being able to leave as planned. First of all, this problem is formulated as a mixed-integer programming model and solved by the CPLEX solver for small-size instances. Afterwards, a particle swarm optimization (PSO) algorithm is developed to obtain good quality solutions within reasonable execution time for large-scale problems. Experimental results show that DLSM mode can not only greatly reduce the total operation cost but also significantly improve the efficiency of berth scheduling in comparison with the widely used single-line ship mooring (SLSM) mode. The comparison made between the results obtained by the proposed PSO algorithm and that obtained by the CPLEX solver for both small-size and large-scale instances are also quite encouraging. To sum up, this study can not only validate the effectiveness of DLSM mode for heavy-loaded ports but also provide a powerful decision support tool for the port operators to make good quality berth schedules with the DLSM mode.

Optimization of Continuous Berth Scheduling by Taking into Account Double-Line Ship Mooring