Bi-level programming model and algorithm weighing features and price of iron ore for pig iron cost

Many scholars and practitioners have done a lot of research to minimize the procurement cost of iron bearing material (abbreviate:IBM), which accounts for a large proportion in the pig iron cost, subject to maintaining the features of IBM. However, the triangle effect, three points of which are the price of IBM (procurement cost), its features (ore grade in particular), and pig iron cost, becomes significant with shortage and price rise of iron ore, where the effect of the features on pig iron cost through productivity, product quality, and auxiliary material consumption, is complicated. A model was established in this paper to minimize iron cost, and quantitative analysis of the triangle effect was also done. Finally, the model was solved by the improved complex method proposed previously by the author, and the numerical example illustrated that the model and algorithm are effective.