A scatter search for an integrated train plan of coil consolidation and stowage

We consider an integrated train plan problem. The ordinary researches divided train plan problem into two subproblems: the consolidation planning and stowage planning problem, and discussed them separately. A common situation appears that not all the coils in consolidation plan can be loaded on trains according to the stowage plan, and the result is difficult to change. As this result, we propose an ideal integrated train plan problem. The proposed problem selects coils and locates these coils to a train simultaneously, and exchange the coils to ensure all the selected coils can be loaded into the train successfully. Comparing with container stowage problem, the size of coils is more irregular and the constraints for balance of wagons are more rigorous. In this paper a mixed integer programming model is established by the operation process of the integrated train plan problem. The NP hardness of the problem and the intractableness of optimally solving the model motivate us to develop a scatter search algorithm with two-stage heuristic to solve it approximately. Computational tests are performed on a set of instances collected in an advanced steel company, and the improvement of loading ratio of two-stage heuristic and SS are 2.81% and 3.26%.