$TITLE MEXICO STEEL - SMALL STATIC (MEXSS,SEQ=15) $STITLE SET DEFINITIONS * A SIMPLIFIED REPRESENTATION OF THE MEXICAN STEEL SECTOR IS USED * TO INTRODUCE A PROCESS INDUSTRY PRODUCTION AND DISTRIBUTION * SCHEDULING PROBLEM. * * REFERENCE: KENDRICK D, MEERAUS A AND ALATORRE J, 1984, THE PLANNING OF * INVESTMENT PROGRAMS IN THE STEEL INDUSTRY, THE JOHNS HOPKINS * UNIVERSITY PRESS, BALTIMORE AND LONDON. SET I STEEL PLANTS / AHMSA ALTOS HORNOS - MONCLOVA FUNDIDORA MONTERREY SICARTSA LAZARO CARDENAS HYLSA MONTERREY HYLSAP PUEBLA / J MARKETS / MEXICO-DF, MONTERREY, GUADALAJA / C COMMODITIES / PELLETS IRON ORE PELLETS - TONS COKE TONS NAT-GAS NATURAL GAS - 1000 N CUBIC METERS ELECTRIC ELECTRICITY - MWH SCRAP TONS PIG-IRON MOLTEN PIG IRON - TONS SPONGE SPONGE IRON - TONS STEEL TONS / CF(C) FINAL PRODUCTS / STEEL / CI(C) INTERMEDIATE PRODUCTS / SPONGE, PIG-IRON / CR(C) RAW MATERIALS / PELLETS, COKE, NAT-GAS, ELECTRIC, SCRAP / P PROCESSES / PIG-IRON PIG IRON PRODUCTION FROM PELLETS SPONGE SPONGE IRON PRODUCTION STEEL-OH STEEL PRODUCTION: OPEN HEARTH STEEL-EL STEEL PRODUCTION: ELECTRIC FURNACE STEEL-BOF STEEL PRODUCTION: BOF / M PRODUCTIVE UNITS / BLAST-FURN BLAST FURNACES OPENHEARTH OPEN HEARTH FURNACES BOF BASIC OXYGEN CONVERTERS DIRECT-RED DIRECT REDUCTION UNITS ELEC-ARC ELECTRIC ARC FURNACES / $STITLE MODEL PARAMETERS TABLE A(C,P) INPUT-OUTPUT COEFFICIENTS PIG-IRON SPONGE STEEL-OH STEEL-EL STEEL-BOF PELLETS -1.58 -1.38 COKE -.63 NAT-GAS -.57 ELECTRIC -.58 SCRAP -.33 -.12 PIG-IRON 1.0 -.77 -.95 SPONGE 1.0 -1.09 STEEL 1.0 1.0 1.0 TABLE B(M,P) CAPACITY UTILIZATION PIG-IRON SPONGE STEEL-OH STEEL-EL STEEL-BOF BLAST-FURN 1.0 OPENHEARTH 1.0 BOF 1.0 DIRECT-RED 1.0 ELEC-ARC 1.0 TABLE K(M,I) CAPACITIES OF PRODUCTIVE UNITS (MILL TPY) AHMSA FUNDIDORA SICARTSA HYLSA HYLSAP BLAST-FURN 3.25 1.40 1.10 OPENHEARTH 1.50 .85 BOF 2.07 1.50 1.30 DIRECT-RED .98 1.00 ELEC-ARC 1.13 .56 SCALARS DT TOTAL DEMAND FOR FINAL GOODS IN 1979 (MILLION TONS) / 5.209 / RSE RAW STEEL EQUIVALENCE (PERCENT) / 40 / PARAMETERS D(C,J) DEMAND FOR STEEL IN 1979 (MILL TPY) DD(J) DISTRIBUTION OF DEMAND / MEXICO-DF 55, MONTERREY 30, GUADALAJA 15 /; D("STEEL",J) = DT * (1 + RSE/100) * DD(J)/100; $EJECT TABLE RD(*,*) RAIL DISTANCES FROM PLANTS TO MARKETS (KM) MEXICO-DF MONTERREY GUADALAJA EXPORT AHMSA 1204 218 1125 739 FUNDIDORA 1017 1030 521 SICARTSA 819 1305 704 HYLSA 1017 1030 521 HYLSAP 185 1085 760 315 IMPORT 428 521 300 PARAMETER MUF(I,J) TRANSPORT RATE: FINAL PRODUCTS(US$ PER TON) MUV(J) TRANSPORT RATE: IMPORTS (US$ PER TON) MUE(I) TRANSPORT RATE: EXPORTS (US$ PER TON) ; MUF(I,J) = ( 2.48 + .0084*RD(I,J)) $RD(I,J); MUV(J) = ( 2.48 + .0084*RD("IMPORT",J))$RD("IMPORT",J); MUE(I) = ( 2.48 + .0084*RD(I,"EXPORT"))$RD(I,"EXPORT"); TABLE PRICES(C,*) PRODUCT PRICES (US$ PER UNIT) DOMESTIC IMPORT EXPORT PELLETS 18.7 COKE 52.17 NAT-GAS 14.0 ELECTRIC 24.0 SCRAP 105.0 STEEL 150. 140. PARAMETERS PD(C) DOMESTIC PRICES(US$ PER UNIT) PV(C) IMPORT PRICES (US$ PER UNIT) PE(C) EXPORT PRICES (US$ PER UNIT) EB EXPORT BOUND (MILL TPY) ; PD(C) = PRICES(C,"DOMESTIC"); PV(C) = PRICES(C,"IMPORT"); PE(C) = PRICES(C,"EXPORT"); EB = 1.0; $STITLE MODEL DEFINITION VARIABLES Z(P,I) PROCESS LEVEL (MILL TPY) X(C,I,J) SHIPMENT OF FINAL PRODUCTS (MILL TPY) U(C,I) PURCHASE OF DOMESTIC MATERIALS (MILL UNITS PER YEAR) V(C,J) IMPORTS (MILL TPY) E(C,I) EXPORTS (MILL TPY) PHI TOTAL COST (MILL US$) PHIPSI RAW MATERIAL COST (MILL US$) PHILAM TRANSPORT COST (MILL US$) PHIPI IMPORT COST (MILL US$) PHIEPS EXPORT REVENUE (MILL US$) POSITIVE VARIABLES Z, X, U, V, E EQUATIONS MBF(C,I) MATERIAL BALANCES: FINAL PRODUCTS (MILL TPY) MBI(C,I) MATERIAL BALANCES: INTERMEDIATES (MILL TPY) MBR(C,I) MATERIAL BALANCES: RAW MATERIALS (MILL TPY) CC(M,I) CAPACITY CONSTRAINT (MILL TPY) MR(C,J) MARKET REQUIREMENTS (MILL TPY) ME(C) MAXIMUM EXPORT (MILL TPY) OBJ ACCOUNTING: TOTAL COST (MILL US$) APSI ACCOUNTING: RAW MATERIAL COST (MILL US$) ALAM ACCOUNTING: TRANSPORT COST (MILL US$) API ACCOUNTING: IMPORT COST (MILL US$) AEPS ACCOUNTING: EXPORT COST (MILL US$); MBF(CF,I).. SUM(P, A(CF,P)*Z(P,I)) =G= SUM(J, X(CF,I,J)) + E(CF,I); MBI(CI,I).. SUM(P, A(CI,P)*Z(P,I)) =G= 0 ; MBR(CR,I).. SUM(P, A(CR,P)*Z(P,I)) + U(CR,I) =G= 0 ; CC(M,I).. SUM(P, B(M,P)*Z(P,I)) =L= K(M,I); MR(CF,J).. SUM(I, X(CF,I,J)) + V(CF,J) =G= D(CF,J); ME(CF).. SUM(I, E(CF,I)) =L= EB ; OBJ.. PHI =E= PHIPSI + PHILAM + PHIPI - PHIEPS ; APSI.. PHIPSI =E= SUM((CR,I), PD(CR)*U(CR,I)) ; ALAM.. PHILAM =E= SUM((CF,I,J), MUF(I,J)*X(CF,I,J)) + SUM((CF,J), MUV(J)*V(CF,J)) + SUM((CF,I), MUE(I)*E(CF,I)) ; API.. PHIPI =E= SUM((CF,J), PV(CF)*V(CF,J)) ; AEPS.. PHIEPS =E= SUM((CF,I), PE(CF)*E(CF,I)) ; MODEL MEXSS SMALL STATIC PROBLEM / ALL / ; SOLVE MEXSS USING LP MINIMIZING PHI ;