ferts.gms : Egypt - Static Fertilizer Model
A simple production and distribution model of the Egyptian fertilizer
sector for the year 1975. This model was mainly used for data and
model validation purposes.
Reference:
- Choksi, A M, Meeraus, A, and Stoutjesdijk, A J, The Planning of Investment Programs in the Fertilizer Industry. The John Hopkins University Press, Baltimore and London, 1980.
Large Model of Type: LP
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$Title EGYPT - Static Fertilizer Model (FERTS,SEQ=13)
$Stitle Set Definitions
$Ontext
A simple production and distribution model of the Egyptian fertilizer
sector for the year 1975. This model was mainly used for data and
model validation purposes.
Choksi, A M, Meeraus, A, and Stoutjesdijk, A, The Planning of Investment
Programs in the Fertilizer Industry. The John Hopkins University Press,
Baltimore and London, 1980.
$Offtext
Set i plant locations /
aswan
helwan
assiout
kafr-el-zt
abu-zaabal /
j demand regions /
alexandria alexandria
behera damanhur
gharbia tanta
kafr-el-sh kare el-sheikh
dakahlia el mansura
damietta damietta
sharkia zagazig
ismailia ismailia
suez suez
menoufia shibin el kom
kalubia benha
giza giza
beni-suef beni-suef
fayoum el-fayoum
minia el-minia
assiout assoiut
new-valley el kharga
sohag sohag
quena quena
aswan aswan /
m productive units /
sulf-a-s sulfuric acid: sulfur
sulf-a-p sulfuric acid: pyrites
nitr-acid nitric acid
amm-elec ammonia: water electrolysis
amm-c-gas ammonia: coke gas
c-amm-nitr calcium ammonium nitrate
amm-sulf ammonium sulfate
ssp single superphosphate /
p processes /
sulf-a-s sulfuric acid: sulfur
sulf-a-p sulfuric acid: pyrites
nitr-acid nitric acid
amm-elec ammonia: water electrolysis
amm-c-gas ammonia: coke gas
can-310 calcium ammonium nitrate: 31.0 %
can-335 calcium ammonium nitrate: 33.5 %
amm-sulf ammonium sulfate
ssp-155 single superphosphate: 15.5 % /
cq nutrients /
n nitrogen
p2o5 phosphorus /
c commodities /
urea
can-260 calcium ammonium nitrate: 26.0 %
can-310 calcium ammonium nitrate: 31.0 %
can-335 calcium ammonium nitrate: 33.5 %
amm-sulf ammonium phosphate
dap diammonium phosphate
ssp-155 single superphosphate: 15.5 %
c-250-55 compound 25-5.5-0
c-300-100 compound 30-10-0
ammonia
nitr-acid nitric acid
sulf-acid sulfuric acid
el-aswan electricity from aswan dam
coke-gas coke-oven gas
phos-rock phosphate rock
limestone
el-sulfur elemental sulfur
pyrites
electric electricity
bf-gas blast-furnace gas
water cooling water
steam
bags /
cf(c) final product / urea, can-260, can-310, can-335
dap, ssp-155, c-250-55, c-300-100, amm-sulf /
ci(c) intermediate products / ammonia, nitr-acid, sulf-acid /
cs(c) intermediates for shipment / ammonia, sulf-acid /
cr(c) domestic raw materials and miscellaneous inputs / el-aswan , coke-gas , phos-rock, limestone
el-sulfur, pyrites , electric , bf-gas
water , steam , bags , sulf-acid /
Alias (i,ip);
$Stitle Consumption and Demand Data
Table cf75(j,c) fertilizer consumption 1974-75 (1000 tpy)
amm-sulf urea can-260 can-310 can-335 dap ssp-155 c-250-55 c-300-100
alexandria 3.0 1.0 5.0 8.0
behera 90.0 35.0 1.0 25.0 .1 64.0 1.0 .1
gharbia 60.0 28.0 17.0 .1 57.0 1.0 .2
kafr-el-sh 45.0 22.0 1.0 10.0 25.0 2.0 .1
dakahlia 60.0 20.0 1.0 26.0 52.0 1.0
damietta 15.0 8.0 2.0 5.0
sharkia 50.0 28.0 1.0 31.0 43.0 1.0 .1
ismailia 6.0 2.0 4.0 4.0
suez 1.0 1.0
menoufia 21.0 30.0 1.0 24.0 .1 33.0 2.0 .1
kalubia 16.0 7.0 25.0 .1 22.0 1.0
giza 6.0 2.0 40.0 14.0 1.0 .1
beni-suef 1.0 20.0 1.0 15.0 13.0 3.0
fayoum 6.0 20.0 1.0 20.0 17.0 1.0
minia 1.0 41.0 2.0 15.0 35.0 .1 50.0 3.0 .2
assiout 1.0 27.0 1.0 20.0 26.0 35.0 5.0 .1
new-valley 1.0 1.0
sohag 7.0 65.0 3.0 20.0 1.0
quena 3.0 95.0 2.0 8.0
aswan 40.0 8.0
Table alpha(c,cq) nutrient content
n p2o5
urea .46
can-260 .26
can-310 .31
can-335 .335
amm-sulf .206
dap .18 .46
ssp-155 .155
c-250-55 .25 .055
c-300-100 .30 .10
Parameters cn75(*,cq) consumption of nutrients 1974-75 (1000 tpy) ;
cn75(j,cq) = sum(cf, alpha(cf,cq)*cf75(j,cf));
cn75("total",cq) = sum(j, cn75(j,cq));
Display cn75;
$Stitle Transportation Data
Table road(j,*) road distances (km)
abu-kir kafr-el-zt talkha abu-zaabal helwan assiout aswan
alexandria 16 119 187 210 244 607 1135
behera 76 42 120 50 184 547 1065
gharbia 150 20 55 65 122 485 1003
kafr-el-sh 145 20 35 105 162 525 1043
dakahlia 208 58 3 138 152 515 1033
damietta 267 131 66 216 233 596 1114
sharkia 240 78 58 60 110 473 991
ismailia 365 241 146 142 173 536 1054
suez 370 246 298 224 178 541 1059
menoufia 157 33 90 154 109 472 990
kalubia 190 66 81 97 76 439 957
giza 287 133 146 48 9 372 890
beni-suef 359 248 261 163 105 257 775
fayoum 341 230 243 145 88 308 826
minia 384 372 386 288 230 132 650
assiout 616 504 518 420 362 518
new-valley 815 703 717 619 561 199 519
sohag 715 603 617 519 461 99 419
quena 858 746 760 662 604 242 276
aswan 1134 1022 1036 938 880 518
$Eject
Table rail(i,i) interplant rail distances (kms)
kafr-el-zt abu-zaabal helwan assiout aswan
abu-zaabal 85
helwan 142 57
assiout 504 420 362
aswan 1022 938 880 518
Table impd(i,*) import distances (kms)
barge road
kafr-el-zt 104 6
abu-zaabal 210 .1
helwan 183
assiout 583
aswan 1087 10
Parameters muf(i,j) transport cost (le per ton): final products
mufv(j) transport cost (le per ton): imported final products
mui(i,i) transport cost (le per ton): interplant shipment
mur(i) transport cost (le per ton): imported raw materials ;
rail(i,ip) = rail(i,ip) + rail(ip,i);
road(j,"import-pts") = road (j,"abu-kir");
muf(i,j) = ( .5 + .0144*road(j,i) )$road(j,i);
mufv(j) = ( .5 + .0144*road(j,"import-pts") )$road(j,"import-pts");
mui(i,ip) = (3.5 + .0300*rail(i,ip) )$rail(i,ip);
mur(i) = (1.0 + .0030*impd(i,"barge") )$impd(i,"barge")
+ ( .5 + .0144*impd(i,"road" ) )$impd(i,"road ");
Display muf,mufv,mui,mur;
$stitle technology data
Table a(c,p) input-output coefficients
sulf-a-s sulf-a-p nitr-acid amm-elec amm-c-gas
el-aswan -12.0
coke-gas -2.0
pyrites -.826
el-sulfur -.334
sulf-acid 1.0 1.0
ammonia -.292 1.0 1.0
nitr-acid 1.0
electric -50 -75 -231 -1960
bf-gas -609
water -20 -60 -.6 -700
steam -4
+ ssp-155 can-310 can-335 amm-sulf
phos-rock -.62
sulf-acid -.41 -.76
ammonia -.20 -.21 -.26
nitr-acid -.71 -.76
limestone -.12 -.04
ssp-155 1.0
can-310 1.0
can-335 1.0
amm-sulf 1.0
bags -22. -23. -23. -22.
water -6. -49. -49. -17.
electric -14. -19.
steam -.4 -.4
Table b(m,p) capacity utilization coefficients
sulf-a-s sulf-a-p nitr-acid amm-elec amm-c-gas ssp-155 can-310 can-335 amm-sulf
sulf-a-s 1
sulf-a-p 1
nitr-acid 1
amm-elec 1
amm-c-gas 1
ssp 1
c-amm-nitr 1 1
amm-sulf 1
$Stitle prices
Parameter pv(c) import prices (cif us$ per ton 1975) /
pyrites 17.5
el-sulfur 55
urea 150
can-260 75
can-310 90
can-335 100
amm-sulf 75
dap 175
ssp-155 80
c-250-55 100
c-300-100 130
/
Table pd(i,c) domestic raw material prices
limestone coke-gas el-aswan phos-rock sulf-acid
* le/ton le/mncf le/mwh le/ton le/ton
kafr-el-zt 5.0
abu-zaabal 4.0
helwan 1.2 16 3
assiout 3.5
aswan 1.2 1
Parameter pmisc(c) miscellanous material costs /
$maxcol 17
electric .007 le/kwh
bf-gas .0075 le/cm
water .031 le/cm
steam 1.25 le/ton
bags .28 le/unit
$maxcol 120
/;
pd(i,cr)$pmisc(cr) = pmisc(cr);
Display pd;
Parameter nh3; nh3("ammonia","helwan") = 31;
$Stitle capacity data
$Eject
Table dcap(i,m) design capacity of plants (t per day)
sulf-a-s sulf-a-p nitr-acid amm-elec amm-c-gas ssp c-amm-nitr amm-sulf
aswan 800 450 1100
helwan 282 172 364 24
kafr-el-zt 200 50 600
assiout 250 600
abu-zaabal 242 227 600
Parameter k(m,i) initial capacity (1000 tpy); k(m,i) = .33*dcap(i,m);
Scalars er exchange rate / .4 /
util utilization / na /;
Sets mpos(m,i) productive units possibilities
ppos(p,i) process possibilities
cpos(c,i) commodity possibilities
cposp(c,i) commodity production possibilities
cposn(c,i) commodity consumption possibilities
cposi(c,i,i) commodity consumption and production possibilities: interplant
cposd(c,i) domestic raw material purchase possibilities
cposr(c,i) imported input commidity possibilities;
mpos (m,i) = yes$k(m,i);
ppos (p,i) = yes$(sum(m$(not mpos(m,i)), b(m,p) ne 0) eq 0) ;
ppos ("can-310","helwan") = no;
ppos ("can-335","aswan") = no;
cposp(c,i) = yes$sum(p$ppos(p,i), a(c,p) gt 0) ;
cposn(c,i) = yes$sum(p$ppos(p,i), a(c,p) lt 0) ;
cposi(cs,i,ip) = cposp(cs,i)*cposn(cs,ip);
cposd(cr,i) = yes$(cposn(cr,i)$pd(i,cr));
cposr(cr,i) = yes$(cposn(cr,i)$pv(cr));
cpos(c,i) = cposp(c,i) + cposn(c,i) ;
Display mpos, ppos, cposp, cposn, cpos , cposi, cposd, cposr;
$Stitle equations
Variables z(p,i) process level (1000 tpy)
xf(c,i,j) domestic shipment activity: final products (1000 tpy)
xi(c,i,i) domestic shipment activity: intermediates (1000 tpy)
vf(c,j) imports: final products (1000 tpy)
vr(c,i) imports: raw materials (1000 tpy)
u(c,i) domestic raw material purchases (units)
psi discounted total cost (1000 le)
psip domestic recurrent cost (1000 le per year)
psil transport cost (1000 le per year)
psii import cost (1000 le per year)
Positive Variables zl, xf, xi, vf, vr, u
Equations obj objective function (1000 le discounted)
mbd(cq,j) material balance on demand: nutrient (1000 tpy)
mbdb(c,j) material balance on demand: material (1000 tpy)
mb(c,i) material balance (1000 tpy)
cc(m,i) capacity constraint (1000 tpy)
ap accounting: domestic recurrent cost (1000 le per year)
al accounting: transport cost (1000 le per year)
ai accounting: import cost (1000 le per year);
$Double
mbd(cq,j).. sum(cf, alpha(cf,cq)*( sum(i$cposp(cf,i), xf(cf,i,j)) + vf(cf,j)$pv(cf))) =g= cn75(j,cq);
mbdb(cf,j)$cf75(j,cf).. sum(i$cposp(cf,i), xf(cf,i,j)) + vf(cf,j)$pv(cf) =g= cf75(j,cf);
mb(c,i).. sum(p$ppos(p,i), a(c,p)*z(p,i))
+ sum(ip, xi(c,ip,i)$cposi(c,ip,i) - xi(c,i,ip)$cposi(c,i,ip))
+ vr(c,i)$cposr(c,i) + u(c,i)$cposd(c,i)
- sum(j$cposp(c,i), xf(c,i,j))$cf(c) =g= 0 ;
cc(m,i)$mpos(m,i).. sum(p$ppos(p,i), b(m,p)*z(p,i)) =l= util*k(m,i) ;
obj.. psi =e= psip + psil + psii ;
ap.. psip =e= sum((cr,i)$cposd(cr,i), pd(i,cr)*u(cr,i));
al.. psil =e= sum(cf, sum((i,j)$cposp(cf,i), muf(i,j)*xf(cf,i,j)) + sum(j, mufv(j)*vf(cf,j)))
+ sum((cs,i,ip)$cposi(cs,i,ip), mui(i,ip)*xi(cs,i,ip))
+ sum((cr,i)$cposr(cr,i), mur(i)*vr(cr,i));
ai.. psii/er =e= sum((cf,j), pv(cf)*vf(cf,j)) + sum((cr,i)$cposr(cr,i), pv(cr)*vr(cr,i));
$single
Model stat2 / mbdb, mb, cc, obj, ap, al, ai /
stat4 / mbd, mb, cc, obj, ap, al, ai / ;
* define scenario for scenario 1 as stated in reference: no interplant shipments and capacity utilization of 85%
xi.fx(cs,i,ip) = 0;
util = .85;
Solve stat2 minimizing psi using lp ;
Parameters rxf(i,j,c) domestic shipment activity : final products (1000 tpy)
tds total domestic supply : final products (1000 tpy)
tif total import : final product (1000 tpy)
tl transportation load (1000 ton_km) ;
rxf(i,j,cf) = xf.l(cf,i,j) ;
tds = sum((cf,i,j), xf.l(cf,i,j));
tif = sum((cf,j), vf.l(cf,j));
tl("rail") = sum((cs,i,ip), rail(i,ip)*xi.l(cs,i,ip)) ;
tl("road") = sum((cr,i), vr.l(cr,i)*impd(i,"road"))
+ sum((cf,i,j), xf.l(cf,i,j)*road(j,i))
+ sum((cf,j), vf.l(cf,j)*road(j,"import-pts"));
tl("barge") = sum((cr,i), vr.l(cr,i)*impd(i,"barge")) ;
Display mbdb.lo, mbdb.m, mb.m, cc.up, cc.m, rxf, tds, tif, vf.l, z.l, vr.l, u.l, tl;
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