Optimization for two-stage double-cycle operations in container terminals

• We minimized the total operation times of quay crane and yard crane in double-cycle operation.
• We designed a bi-level genetic algorithm to solve the proposed mixed integer programming model.
• We presented a novel chromosome representation.
• A lower bound was derived to evaluate the proposed algorithm.
• The result of the designed scheduling method did not exceed the lower bound by 8.04%.

The loading of ships while they are unloaded (double cycling) can significantly improve the efficiency of container terminal handling operations. This paper formulated a mixed integer programming model for two-stage double-cycle operation. The quay crane operating time is reduced by optimizing the loading and unloading sequence for the hatches and stacks in each ship-bay. Meanwhile, optimizing the stowage plan of outbound containers in container yards reduces yard crane operating time. A bi-level genetic algorithm was proposed to solve this model, and a lower bound was derived to evaluate the scheduling performance. The numerical experiments indicated that the model and algorithm presented in this paper are effective compared with the lower bound, the currently used method and the method raised in previous studies.