Integrated optimisation of storage and pre-marshalling moves in a slab warehouse

In the slab warehouses of iron and steel enterprises, the slabs are stacked on top of others. Thus, some slabs will be blocked by others from being retrieved directly. In this study, we focus on optimising slab storage and pre-marshalling moves in advance so as to minimise the numbers of slabs which may block retrieval slab, the number of stacks occupied by slabs, and the number of required moves. We also address the practical concern of moving no more than two slabs together. To solve this problem, we present an integer linear programming model and further propose valid inequalities to enhance the model. Based on the labelled data from this modelling approach, a self-training technique is applied to train two functions which can predict the optimal following pre-marshalling move and storage move. By combining these functions, heuristics and branch-and-bound algorithm with the dominance rules, a multi-stage hybrid algorithm is proposed to solve practical problems. The experimental results show the effectiveness of the model, the valid inequalities, and the different components of hybrid algorithm which can produce high-quality solutions within seconds.