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In steel production, an electric arc furnace (EAF) is most commonly used to melt raw material in order to produce liquid steel. Scrap is the main raw material which differs in regard to the content of iron and of some chemical elements. The price of scrap depends on these attributes. In order to obtain the desired quality and quantity, each melting bath unit of steel has either its own material constraints or the constraints for electric arc furnace such as the capacity of EAF. In addition, the availability and transportation of scrap are also restricted because they need space. This research is to create an optimization model which minimizes the cost of raw material The running speed of the model is reasonably guaranteed by properly designing the combinatorial structure with branch and bound rules. Simulation results show significant improvement compared to the : the cost of scrap steel is reduced by 2 to 6% and the time of charging buckets is 2 to 10 minutes faster.