Description
A simple model of the cement sector for the Yemen Arab Republic can be used to explore expansion plans under various assumptions about domestic and world markets and cost structures.
Large Model of Type : MIP
Category : GAMS Model library
Main file : yemcem.gms
$title Y E M E N Cement Model (YEMCEM,SEQ=51)
$onText
A simple model of the cement sector for the Yemen Arab Republic
can be used to explore expansion plans under various assumptions
about domestic and world markets and cost structures.
World Bank, Yemen Arab Republic - Manufacturing Industry: Performance,
Policies and Prospectives. Tech. rep., The World Bank, 1982.
Kexwords: mixed integer linear programming, micro economics, cement industry
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$sTitle Set Definitions
Set
i 'plants' / amran, baijil, mafrak /
j 'markets' / sanaa, hodeideh, taizz, ibb, dhamar /
m 'productive units' / dry-kiln 'dry process kiln and ancillaries'
wet-kiln 'wet process kiln and ancillaries'
mills 'clinker-gypsum mills storage and packing' /
ms(m) 'productive units with economies of scale'
mp(m) 'productive units without economies of scale'
p 'process' / dry 'dry process clinker production'
wet 'wet process clinker production'
grind 'clinker grinding' /
ca 'all commodities' / limestone 'tons'
clay 'tons'
gypsum 'tons'
fuel '1000*liter'
petrol '1000*liter'
explosives 'kg'
grindparts 'kg'
refractory 'kg'
bags 'bag'
clinker 'tons'
cement 'tons' /
c(ca) 'commodities for material balance constraints' / cement,clinker,fuel /
cf(c) 'final products' / cement /
ci(c) 'imported intermediate products' / clinker, fuel /
cr(ca) 'local materials' / limestone, clay, gypsum, petrol, explosives
grindparts, refractory, bags /
t 'time periods' / 1983-85, 1986-88, 1989-91, 1992-94 /
te(t) 'expansion periods' / 1986-88, 1989-91, 1992-94 /
s 'kiln sizes' / small, medium, large /;
Alias (te,tp);
$sTitle Parameters and Data Modifications
Parameter
pd(cr) 'domestic prices (yr per unit)'
/ limestone 5.0, clay 2.0
gypsum 24.6, petrol 1175.0
explosives 4.0, grindparts 3.328
refractory 4.0, bags 1.31 /
pv(ca) 'import prices (yr per ton)'
pe(ca) 'export prices (yr per ton)'
ebu(t) 'upper bound on exports (1000 tpy)'
vbu(t) 'upper bound on imports (1000 tpy)'
vibu(t) 'bound on klinker import (1000 tpy)';
pv("cement ") = 280;
pv("clinker") = .8*pv("cement");
pv("fuel ") = 600;
pe(c) = .75*pv(c);
ebu(t) = 1000;
vbu(t) = 3000;
vibu(t) = na;
display pd, pv, pe;
Table a(ca,p) 'input-output coefficients'
dry wet grind
limestone -1.3 -1.3
clay -.3 -.3
gypsum -.04
petrol -.00147 -.00147
explosives -.192 -.192
grindparts -.385
refractory -.152 -.152
bags -20.0
fuel -.1127 -.1465
clinker .96 .96 -.96
cement 1.0 ;
Table b(m,p) 'capacity utilization'
dry wet grind
dry-kiln 1.0
wet-kiln 1.0
mills 1.0;
Table k(m,i) 'capacities as of 1982 (1000 tpy)'
amran baijil mafrak
dry-kiln 500.0
wet-kiln 320.0
mills 500.0 320.0 ;
Table inv(m,*) 'capital investment data'
* cost millions yr (1978)
* size 1000 tpy
* scale scale factor - cost = constant*size**scale
cost size scale
dry-kiln 526.296 500.0 .53
wet-kiln 447.352 500.0 .56
mills 105.259 500.0 1.00;
Parameter
site(i) 'site factor' / amran 1.2
baijil 1.15
mafrak 1.05 /
size(s) 'kiln size (1000 tpy)' / small 500
medium 750
large 1000 /
klim(i) 'limit of total kiln capacity (1000 tpy)'
ts(t,t) 'time summation matrix'
midyear(t)
delta(t) 'discount factor'
rc(p) 'recurrent cost (yr per process unit)'
fc(m) 'fixed cost (yr per ton)' / dry-kiln 55.8
wet-kiln 60 /;
Scalar
sigma 'capital recovery factor'
zeta 'life of productive units (years)'
rho 'discount rate';
ms(m)$(inv(m,"scale") <> 1) = yes;
mp(m) = not ms(m);
inv(ms,s) = inv(ms,"cost")*(size(s)/inv(ms,"size"))**inv(ms,"scale");
inv(mp,"prop") = inv(mp,"cost")/inv(mp,"size");
klim(i) = 2000;
midyear(t) = 1981 + 3*ord(t);
ts(te,tp)$(ord(te) >= ord(tp)) = 1;
zeta = 30;
rho = .1;
sigma = rho/(1 - (1 + rho)**(-zeta));
delta(t) = (1 + rho)**(1982 - midyear(t));
rc(p) = - sum(cr, a(cr,p)*pd(cr));
display ms, mp, midyear, ts, sigma, delta, inv, rc;
Set ds 'demand scenarios (base year demand and growth rates)'
/ bg-700-06, bg-700-11, bg-900-06, bg-900-11 /;
Parameter
dt(ds,t) 'total demand for cement (1000 tpy)'
d(j,t,cf) 'regional demand for cement (1000 tpy)'
dd(j) 'demand distribution'
/ sanaa 28, hodeideh 27, taizz 20, ibb 12.5, dhamar 12.5 /;
dt("bg-700-06",t) = 700*1.06**(midyear(t) - 1980);
dt("bg-700-11",t) = 700*1.11**(midyear(t) - 1980);
dt("bg-900-06",t) = 900*1.06**(midyear(t) - 1980);
dt("bg-900-11",t) = 900*1.11**(midyear(t) - 1980);
d(j,t,"cement") = na;
display dd, dt;
Table rd(*,*) 'road distances from plants to markets (km)'
sanaa taizz hodeideh dhamar ibb port
amran 48 304 279 146 209 279
baijil 171 294 60 270 332 60
mafrak 319 63 213 220 157 213
port 231 276 5 329 371 ;
Table f(*,*) 'cost increase factors for motor transport'
sanaa hodeideh taizz dhamar ibb port
amran 1.15 1.14 1.16 1.14 1.16 1.14
baijil 1.14 1.11 1.13 1.13 1.14 1.11
mafrak 1.16 1.11 1.17 1.17 1.16 1.11
port 1.14 1.0 1.14 1.16 1.15 1.0 ;
Parameter
muf(i,j) 'cement transport cost (yr per ton)'
muv(j) 'import transport cost (yr per ton)'
mui(ci,i) 'import intermediate transport cost (yr per ton)'
mue(i) 'export transport cost (yr per ton)';
muf(i,j) = 30 + .47*f(i,j)*rd(i,j);
muv(j) = 30 + .47*f("port",j)*rd("port",j);
mue(i) = 30 + .47*f(i,"port")*rd(i,"port");
mui(ci,i) = 30 + .35*f(i,"port")*rd(i,"port");
mui("fuel ",i) = 1.5*mui("clinker",i);
display muf, muv, mue, mui;
$sTitle Breakeven Analysis
Parameter
tpn(i,*) 'transport protection (yr per ton)'
vc 'variable cost of cement production (yr per ton)'
fxc(i,s) 'fixed cost of cement production (yr per ton)'
ac(i,s) 'average cost of cement production (yr per ton)'
mbe(i,*) 'marginal breakeven price (yr per ton)'
abe(i,*) 'average breakeven price (yr per ton)';
tpn(i,"v-inputs") = -a("fuel","dry")*mui("fuel",i);
tpn(i,"plant-gate") = mue(i) - tpn(i,"v-inputs");
tpn(i,j) = muv(j) - (tpn(i,"v-inputs") + muf(i,j));
vc = 1.025*(-a("fuel","dry")*pv("fuel") + rc("dry") + rc("grind"));
fxc(i,s) = 1000*sigma*site(i)*(inv("dry-kiln",s)/size(s)
+ inv("mills","prop")) + 1.025*(fc("dry-kiln") + fc("mills"));
ac(i,s) = vc + fxc(i,s);
mbe(i,j) = vc - tpn(i,j);
mbe(i,"plant-gate") = vc - tpn(i,"plant-gate");
abe(i,j) = ac(i,"small") - tpn(i,j);
abe(i,"plant-gate") = ac(i,"small") - tpn(i,"plant-gate");
display tpn, vc, fxc, ac, mbe, abe;
$sTitle Model Specification
Variable
z(p,i,t) 'process level (1000 units per year)'
x(c,i,j,t) 'shipment of cement (1000 tpy)'
v(cf,j,t) 'imports of cement (1000 tpy)'
vi(c,i,t) 'imports of intermediates (1000 units per year)'
e(c,i,t) 'export of cement (1000 tpy)'
h(m,i,te) 'capacity expansion (1000 tpy)'
y(m,i,s,te) 'binary variable'
phi 'total discounted cost'
phikap(t) 'capital investment charge (mill yr per year)'
phipsi(t) 'recurrent cost (mill yr per year)'
philam(t) 'transport cost (mill yr per year)'
phipi (t) 'import cost (mill yr per year)'
phieps(t) 'export revenue (mill yr per year)'
phiw (t) 'working capital charge (mill yr per year)';
Positive Variable z, x, v, vi, e, h;
Binary Variable y;
Equation
mb(c,i,t) 'material balances (1000 units per year)'
cc(m,i,t) 'capacity constraints (1000 tpy)'
id(m,i,te) 'investment definition'
ich(m,i,te) 'investment choice'
limit(i) 'capacity limit(i) (1000 tpy)'
mr(cf,j,t) 'market requirement (1000 tpy)'
eb(t) 'export limit (1000 tpy)'
vb(t) 'import limit: cement (1000 tpy)'
vib(t) 'import limit: clinker (1000 tpy)'
obj 'total discounted costs'
apsi(t) 'recurrent cost acct (mill yr per year)'
akap(t) 'investment cost acct (mill yr per year)'
alam(t) 'transport cost acct (mill yr per year)'
api (t) 'import cost acct (mill yr per year)'
aeps(t) 'export revenue acct (mill yr per year)'
aw (t) 'working capital acct (mill yr per year)';
mb(c,i,t).. sum(p, a(c,p)*z(p,i,t)) + vi(c,i,t)$ci(c) =g= (sum(j, x(c,i,j,t)) + e(c,i,t))$cf(c);
cc(m,i,t).. sum(p, b(m,p)*z(p,i,t)) =l= k(m,i) + sum(tp$ts(t,tp), h(m,i,tp));
id(ms,i,te).. h(ms,i,te) =e= sum(s, size(s)*y(ms,i,s,te));
ich(ms,i,te).. sum(s, y(ms,i,s,te)) =l= 1.0;
limit(i).. sum(ms, k(ms,i) + sum(te, h(ms,i,te))) =l= klim(i);
mr(cf,j,t).. sum(i, x(cf,i,j,t)) + v(cf,j,t) =g= d(j,t,cf);
eb(t).. sum((cf,i), e(cf,i,t)) =l= ebu(t);
vb(t).. sum((cf,j), v(cf,j,t)) =l= vbu(t);
vib(t).. sum(i, vi("clinker",i,t)) =l= vibu(t);
obj.. phi =e= sum(t, delta(t)*(phikap(t) + phipsi(t) + philam(t)
+ phipi(t) + phiw(t) - phieps(t)));
apsi(t).. phipsi(t) =e= .001*(sum((p,i), rc(p)*z(p,i,t))
+ sum((i,m), fc(m)*(k(m,i) + sum(tp$ts(t,tp), h(m,i,tp)))));
akap(t).. phikap(t) =e= sigma*sum(tp$ts(t,tp), sum((ms,i,s), site(i)*inv(ms,s)*y(ms,i,s,tp))
+ sum((mp,i), site(i)*inv(mp,"prop")*h(mp,i,tp)));
alam(t).. philam(t) =e= .001*(sum(cf, sum((i,j), muf(i,j)*x(cf,i,j,t))
+ sum(j, muv(j)*v(cf,j,t))
+ sum(i, mue(i)*e(cf,i,t)))
+ sum((ci,i), mui(ci,i)*vi(ci,i,t)));
aeps(t).. phieps(t) =e= .001*sum((cf,i), e(cf,i,t));
api(t).. phipi(t) =e= .001*(sum((cf,j), pv(cf)*v(cf,j,t)) + sum((ci,i), pv(ci)*vi(ci,i,t)));
aw(t).. phiw(t) =e= .25*.1*(phipsi(t) + phipi(t));
Model yemen 'Yemen cement model' / all /;
* Definition of scenario number 16:
d(j,t,"cement") = dt("bg-900-11",t)*dd(j)/100;
vibu(t) = 0;
y.fx("dry-kiln","mafrak","small","1986-88") = 1;
solve yemen minimizing phi using mip;
display z.l, h.l;
Parameter
xx(i,*,t) 'cement shipments (1000 tpy)'
kh(*,t) 'total kiln capacity (1000 tpy)'
mcc(i,t,m) 'shadow price on capacity - undiscounted'
mmr(j,t) 'shadow price on requirements - undiscounted';
xx(i,j,t) = x.l("cement",i,j,t); xx(i,"**total**",t) = sum(j, xx(i,j,t));
kh(i,t) = sum(ms, k(ms,i) + sum(tp$ts(t,tp), h.l(ms,i,tp)));
kh("total",t) = sum(i, kh(i,t));
mcc(i,t,m) = cc.m(m,i,t)/delta(t)*1000;
mmr(j,t) = mr.m("cement",j,t)/delta(t)*1000;
display xx, kh, mcc, mmr;