A Linear Programming Model of Integrated Iron and Steel Production
A LINEAR PROGRAMMING MODEL OF INTEGRATED IRON AND STEEL PRODUCTION *t
TmOR FABIAN
University of California, Los Angeles
Integrated steel mills usually have a choice over the use of various materials and production procMses. Different ores may be used in the proiduction of iron; steel scrap and iron can be used in different proportions in the production of steel. The economical usage rate of all materials is a fimction of numerous variables, among which the market price of some materials, notably of various grades of steel scrap, fiuctuates and therefore requires a periodic determination of the economical usage rate. This is a typical problem for programming. The paper presents a mathematical formulation of the stages of iron and steel production to determine the optimal 0east cost) rate of input of materials. The modeb of the various stages of production are connected to form a "master model" of an integrated steel mill. 1. Technological Background The production of iron and steel is dominated by integrated plants. Such plants are results of the economy of the immediate utilization of the byproducts of certain processes and the possibility of moving the output of one stage of the production process to the next stage with the minimum of heat loss. The structure of the production process in an integrated steel plant and the opportunity for economizing by the above-mentioned two characteristics of such plant may best be observed in a schematic flowchart of the production (Figure 1). Coal, iron ore of various kinds, limestone, and steel scrap are supplied to the plant from the outside; coking byproducts, iron and steel castings, and finished steel products are sold by the plant. Sometimes slag of the blast and open hearth furnaces is also sold,' but mostly it is a waste product after its metal content has been extracted. The various stages of the production are interrelated through input-output relationships. Coke ovens supply coke to the blast furnaces; oven gas
TmOR FABIAN
University of California, Los Angeles
Integrated steel mills usually have a choice over the use of various materials and production procMses. Different ores may be used in the proiduction of iron; steel scrap and iron can be used in different proportions in the production of steel. The economical usage rate of all materials is a fimction of numerous variables, among which the market price of some materials, notably of various grades of steel scrap, fiuctuates and therefore requires a periodic determination of the economical usage rate. This is a typical problem for programming. The paper presents a mathematical formulation of the stages of iron and steel production to determine the optimal 0east cost) rate of input of materials. The modeb of the various stages of production are connected to form a "master model" of an integrated steel mill. 1. Technological Background The production of iron and steel is dominated by integrated plants. Such plants are results of the economy of the immediate utilization of the byproducts of certain processes and the possibility of moving the output of one stage of the production process to the next stage with the minimum of heat loss. The structure of the production process in an integrated steel plant and the opportunity for economizing by the above-mentioned two characteristics of such plant may best be observed in a schematic flowchart of the production (Figure 1). Coal, iron ore of various kinds, limestone, and steel scrap are supplied to the plant from the outside; coking byproducts, iron and steel castings, and finished steel products are sold by the plant. Sometimes slag of the blast and open hearth furnaces is also sold,' but mostly it is a waste product after its metal content has been extracted. The various stages of the production are interrelated through input-output relationships. Coke ovens supply coke to the blast furnaces; oven gas