Optimizing the casting length of single diameter steel billets based on minimum cost

The hot rolling process uses, as raw material, round bars casted using continuous casting at the steel making plant. From here a limited number of casted billets, in terms of length, can be delivered. The supply order for the rolling process is unpredictable and imprecise, thus in this scenario the current paper intends to offer a solution to the industrial partner as to optimize the casting lengths of billets, considering the restrictions of the casting process, and to achieve minimum production cost. An order is converted into a number of billets that should be casted at an ideal length. Two different methods are proposed, an analytical one, designed by the authors, and the linear programming method, in order to generate an optimal solution to the stated problem based on minimizing a cost function. The analytical method's result is the optimal number of steel blocks that need to be casted at a single length, from the limited set. The linear programming method's result is the optimal number of blocks that need to be casted from each available length. The results obtained from both methods are compared based on a set of casting orders via successive simulations.