A Lagrangian relaxation-based algorithm for the allocation of yard cranes for yard activities with different priorities

This paper proposes a mixed integer programming model for the allocation of rail mounted gantry cranes for four basic yard activities with different priorities. The model pays special attention to the typical features of this kind of gantry cranes, such as a restricted traveling range and a limited number of adjustments during loading and discharging operations. In contrast to most of the literature dealing with these four yard activities individually, this paper models them into an integrated problem, whose computational complexity is proved to be NP-hard. We are therefore motivated to develop a Lagrangian relaxation-based heuristic to solve the problem. We compare the proposed heuristic with the branch-and-bound method that uses commercial software packages. Extensive computational results show that the proposed heuristic achieves competitive solution qualities for solving the tested problems.