Optimal polices for queueing storage problem in steel slab yard

In most of iron and steel enterprises, slabs from a continuous casting stage are stored in a slab yard (as a buffer) for further processing in a hot rolling stage. In practice, the storage position of each slab is random. In this paper, we consider the slab storage problem to minimize the inventory cost of slabs, in which the storage positions of slabs are determined using a proposed method. We prove that the objective function of the problem is submodular and propose a dynamic programming algorithm for solving the problem optimally.