A Mathematical Model and Grouping Imperialist Competitive Algorithm for Integrated Quay Crane and Yard Truck Scheduling Problem with Non-crossing Constraint

Document Type : Original Article


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


In this research, an integrated approach is presented to simultaneously solve quay crane scheduling and yard truck scheduling problems. A mathematical model was proposed considering the main real-world assumptions such as quay crane non-crossing, precedence constraints and variable berthing times for vessels with the aim of minimizing vessels completion time. Based on the numerical results, this proposed mathematical model has suitable efficiency for solving small instances. Two versions of imperialist competitive algorithm (ICA) are presented to heuristically solve the problem. The grouping version of  algorithm (G-ICA) is used to solve the large-sized instances based on considering the allocation of trucks as a grouping problem. Effectiveness of the proposed metaheuristics on small-sized problems is compared with the optimal results of the mathematical model. In order to compare the efficiency of the proposed algorithms for large-sized instances, several instances were generated and solved, and the performance of algorithms has been compared with each other. Moreover, a simulated annealing (SA) algorithm is developed to solve the problem and evaluate the performance of the proposed ICA algorithms. Based on the experimental results, the G-ICA has a better performance compared to the ICA and SA. Also an instance of a container terminal in Iran has been investigated which shows that the proposed model and solution methods are applicable in real-world problems.