An Iterative Re-Optimization Framework for the Dynamic Scheduling of Crossover Yard Cranes with Uncertain Delivery Sequences

In yard-crane scheduling problems, as loading operations take priority over unloading, the delivery sequence of unloading from the quaysides to the yard is uncertain. The delivery sequence changes may make crane scheduling more difficult. As a result, the crane operations schedules developed statically become suboptimal or even infeasible. In this paper, we propose a dynamic scheduling problem considering uncertain delivery sequences. A mixed-integer linear program is developed to assign tasks to cranes and minimize the makespan of crane operations. We propose an iterative solution framework in which the schedules are re-optimized whenever the delivery sequence change is revealed. A genetic algorithm is proposed to solve the problem, and a greedy algorithm is designed to re-optimize and update the solution. To make the updated solution take effect as soon as possible, regarding batch-based task assignment, the tasks in the scheduling period are divided into several batches. In this case, the instant requests arising from the delivery sequence change are added to corresponding batch tasks and re-optimized together with the tasks of this batch. In addition, a relaxation model is formulated to derive a lower bound for demonstrating the performance of the proposed algorithm. Experimental results show that the average gap between the algorithm and the lower bound does not exceed 5%. The greedy insertion algorithm can re-optimize the instant requests in time. Therefore, the proposed iterative re-optimization framework is feasible and has the advantages (necessity) of batch-based task assignment.