A Linear Programming Model of Integrated Iron and Steel Production

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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 and liquid fuel to the open hearth and reheating furnaces. The blast furnaces supply hot * Received September 1957. t This paper was prepared while the author was under contract with the Office of Naval Rraearch, Logistics Branch, and working on the Management Sciences Research Project, University of California, Los Angeles. Thanks are due to Dr. James R. Jackson, Director, Management Sciences Research Project, for his critical reading of this report. The author is indebted to Kaiser Steel Corporation for invaluable technical assistance. The responsibility for errors and omissicms is of course the author's. Reproduction in whole or in part is permitted for any purpose of the United States Government. The model developed here was applied in a process analysis study of the U. S. iron and steel industry. Results of this study will be reported at a later date. * For producing Portland cement, road building materials, insulating materials, soil conditions. CAMP AND FBANCIS, pp. 279-281. 416

416

TIBOB FABIAN

J

Coal Coke ^ Screening station Power steam blowing To furnaces, ovens, mills Gas Pitch tar mixture^ Gas Coke

Iron ore

Dust Sintering plant Blast furnaces H o •o

Coke ovens

Coal chemical dept.

Mixing

Purchased scrap Soaking pits and primary rolling
O

Byproducts

Reheating and second rolling

Finished products Fio. I. Flowchart of Production Processes in an Integrated Steel Plant Source: CAMP, J . M., AND C . B . FRANCIS, The Making, Shaping, and Treating of Steel. 6th ed., p. 189.

metal to the steel furnaces and to the casting of finished iron products. The gas of these furnaces is a mixture with oven gas for heat generation for the open hearth or reheating furnaces. The steel furnaces supply raw steel in the form of ingots for rolling. The open hearth slag may be charged back into the blast furnaces in order to extract some of the manganese, and at the same time, some steel. The rolling and finishing mills supply the main...
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