Optimal scrap combination for steel production

In steel production, scrap metal is used for cooling the enormous quantity of heat produced by blowing oxygen on hot metal. Scrap differs in regard to the content of iron and of some tramp elements. The price of the scrap depends on these attributes. Each melting bath unit of steel has its own material constraints for the amount of iron and tramp elements in order to guarantee the desired quality. In addition, the transportation of scrap is restricted because it needs time and space: the scrap is kept in some railroad cars in the scrap hall; empty cars must leave the hall, filled cars must be taken from several railroad tracks in the scrap yard and assembled to form a train before transportation to the hall. There are upper limits for the number of cars in the hall and in the train, also for the number of railroad tracks used for assembly. Our objective is to find a minimum cost scrap combination for each melting bath unit of steel that obeys the material and transportation constraints. We model the problem using a MIP (mixed integer linear programming) approach. Real-life situations are solved with the commercial MIP-solver CPLEX. We present computational results which show significant improvement compared to the strategy applied today.