A robust optimization approach to steel grade design problem subject to uncertain yield and demand

This work formulates and investigates a steel grade design problem (SGDP) arising from a production process of steelmaking continuous casting. For the first time, we consider uncertain yield and demand in SGDP and construct a two-stage robust optimisation model accordingly. Then, we propose an enhanced column-and-constraint generation algorithm to obtain high-quality solutions. By exploiting the problem characteristics, we first use a Lagrangian relaxation method to decompose SGDP into multiple subproblems and then apply a standard column-and-constraint generation algorithm to solve the latter. At last, we test the proposed algorithm by extensive instances constructed based on actual production rules of a steelmaking shop. Numerical results show that it can effectively solve large-scale SGDPs. The obtained plan is better than those obtained by a commonly-used and standard column-and-constraint generation algorithm.