On solving the 1.5-dimensional cutting stock problem with heterogeneous slitting lines allocation in the steel industry

This paper presents a mathematical optimisation model to solve the slitting problem in a Spanish steel manufacturing company. In order to satisfy the demand for steel strip, coils are selected from the warehouse and cut lengthwise on the slitting lines. The main challenge in this problem is to determine a slitting plan, which involves defining a set of cutting patterns for the coils and selecting the slitting line where the coils will be cut. The cutting patterns must meet the customer's requirements and the ongoing operational constraints imposed by the slitting lines. The differences between the lines limit the allocation of coils - cutting pattern - slitting line, with a high impact on the company's productivity. It is therefore necessary to integrate the slitting line allocation into the coil selection and cutting pattern definition. The model is validated with real data and outperforms the results obtained without this integration, thus improving the company's performance without reducing the quality of the solutions. Three different objectives are taken into account (1) reducing the leftovers generated in the process, (2) maximising the productivity of the process and (3) reducing the difference between the quantity of product actually delivered and the quantity demanded by the customer.