Joint scheduling problems of quay cranes and yard trucks at container terminals considering real-world assumptions: non-crossing and safety margins of quay cranes

Document Type: Original Article


1 Industrial & Systems Engineering Dept. Tarbiat Modares University

2 Industrial & Systems Engineering Dept., Tarbiat Modares University, Tehran, Iran


A bi-objective mathematical model is developed to simultaneously consider the quay crane and yard truck scheduling problems at container terminals. Main real-world assumptions, such as quay cranes with non-crossing constraints, quay cranes’ safety margins and precedence constraints are considered in this model. This integrated approach leads to better efficiency and productivity at container terminals. Based on numerical experiments, the proposed mathematical model is effective for solving small-sized instances. Two versions of the simulated annealing algorithm are developed to heuristically solve the large-sized instances. Considering the allocation of trucks as a grouping problem, a grouping version of the simulated annealing algorithm is proposed. Effectiveness of the presented algorithms is compared to the optimal results of the mathematical model on small-sized problems. Moreover, the performances of the proposed algorithms on large-sized instances are compared with each other and the numerical results revealed that the grouping version of simulated annealing algorithm outperformed simulated annealing algorithm. Based on numerical investigations, there is a trade-off between the tasks’ completion time and the cost of utilizing more trucks. Moreover increasing the number of YTs leads to better outcomes than increasing the number of QCs. Besides two-cycle strategy and using dynamic assignment of yard truck to quay cranes leads to faster loading and unloading procedure.