Mathematical Model of Crane Scheduling for a Defined Slab Storage Locations Assignment in a Continuous Cast Billet Warehouse

An increasing number of steel factories around the world are integrating two processes: continuous casting and hot rolling. The slab warehouse is the link between these two processes. Slabs of certain sizes are cast on the continuous casting machine streams and then transported to the slab warehouse. In the warehouse, overhead cranes move the slabs to storage locations, into stacks. The sequence of slabs arriving at the slab warehouse plays an important role: slabs that arrive earlier should, as a rule, be stacked earlier. If several cranes may be operating in a warehouse in an adjacent space, the scheduling of cranes becomes much more difficult: a safe distance must be maintained between the cranes. This paper proposes a mathematical model of crane scheduling for a defined solution to the storage location assignment problem in a slab warehouse. This mathematical model considers a large number of constraints specific to the mentioned process, such as: orthogonality of crane movement; order of slab processing; minimum distance between cranes; maximum and minimum height of stacks; and many others. The developed mathematical model takes into account the space-time characteristics of the warehouse and crane trajectories, which allows its application to create a digital twin of the slab warehouse, which will allow to check the acceptability of the crane schedule for some solution of the problem of storage location assignment._