Joint optimization of container slot planning and truck scheduling for tandem quay cranes

This paper examines the loading operations of a new type of quay crane, the tandem quay crane (TQC), which has been designed to increase the terminal productivity by lifting more containers simultaneously. Due to the special characteristics of the TQC, more than one truck is required to serve a tandem-lift of it, and the containers handled in a tandem-lift must be loaded into two neighboring rows in the same tier of the containership. Of particular importance in schedules at the terminal is to coordinate the truck scheduling and container stowage slot plan with the TQCs, which is a key challenge in practice. This paper is an attempt to tackle this issue by developing a mixed integer linear programming (MILP) model with an objective of minimizing the completion time of the loading operation under the full utilization of the TQC. Due to the complexity of the MILP model, we then propose a model to derive lower bounds of the problem, and a greedy randomized adaptive search procedure (GRASP) to solve the problem. Computational experiments are conducted with a variety of instances. The results derived by GRASP for solving small size problems are within 0.04% of the optimal results obtained by the Gurobi. For large scale instances, GRASP outperforms the Gurobi in terms of the solution quality and computation time. Additionally, on average results derived by GRASP are within 8.2% of the lower bound. Further experiments demonstrate the advantage of the integrated optimization of container slot planning and truck scheduling for TQCs.