fertd.gms : Egypt - Dynamic Fertilizer Model

Description

An investment planning model of the Egyptian fertilizer sector.


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 : MIP


Category : GAMS Model library


Main file : fertd.gms

$title EGYPT - Dynamic Fertilizer Model    (FERTD,SEQ=14)

$onText
An investment planning model of the Egyptian fertilizer sector.


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.

The GAMS program has been changed slightly from the published version to
incorporate partial reduction of the model in order to reduce execution time.

Keywords: mixed integer linear programming, investment planning
$offText

$sTitle Set Definition
Set
   j    'demand regions'   / alexandria, behera , gharbia   , kafr-el-sh, dakahlia, damietta , sharkia
                             ismailia  , suez   , menoufia  , kalubia   , giza    , beni-suef, fayoum
                             minia     , assiout, new-valley, sohag     , quena   , aswan              /
   i    'plant locations'  / abu-kir, kafr-el-zt, talkha, abu-zaabal, helwan, suez, assiout, 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'
                             amm-n-gas  'ammonia: natural gas'
                             amm-r-gas  'ammonia: refinery gas'
                             phos-acid  'phosphoric acid'
                             c-nitr     'calcium nitrate'
                             c-amm-nitr 'calcium ammonium nitrate'
                             amm-sulf   'ammonium sulfate'
                             urea
                             amm-phos   'ammonium phosphate'
                             ssp        'single superphosphate'
                             tsp        'triple superphosphate'
                             nitro-phos 'nitrophosphates'            /
   me(m) 'productive units: expansion possibilities'
                           / sulf-a-s, amm-n-gas, phos-acid,
                             amm-sulf, urea     , amm-phos ,
                             ssp     , tsp      , nitro-phos /
   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'
                             amm-n-gas 'ammonia: natural gas'
                             amm-r-gas 'ammonia: refinery gas'
                             phos-acid 'phosphoric acid'
                             c-nitr    'calcium nitrate'
                             can-310   'calcium ammonium nitrate: 31.0 pct'
                             can-335   'calcium ammonium nitrate: 33.5 pct'
                             amm-sulf  'ammonium sulfate'
                             urea
                             map       'monammonium phosphate'
                             dap       'diammonium phosphate'
                             ssp-155   'single superphosphate: 15.5 pct'
                             tsp-pow   'triple superphosphate: powdered'
                             tsp       'triple superphosphate: granular'
                             nitrophos 'nitrophosphate: c-ntr and np-20-20' /
   g    'upgrading (conversion) activities'
                           / amm-c-n 'ammonia:  coke-oven to natural gas' /
   cq   'nutrients'        / n 'nitrogen', p2o5  'phosphorus' /
   c    'commodities'      / c-nitr      'calcium nitrate'
                             can-260     'calcium ammonium nitrate: 26.0 pct'
                             can-310     'calcium ammonium nitrate: 31.0 pct'
                             can-335     'calcium ammonium nitrate: 33.5 pct'
                             amm-sulf    'ammonium sulfate'
                             urea
                             map         'monammonium phosphate'
                             dap         'diammonium phosphate'
                             ssp-155     'single superphosphate: 15.5 pct'
                             tsp-pow     'triple superphosphate: powdered'
                             tsp         'triple superphosphate: granular'
                             np-20-20    'nitrophosphate 20-20-0'
                             c-250-55    'compound 25-5.5-0'
                             c-300-100   'compound 30-10-0'
                             ammonia
                             co2
                             nitr-acid   'nitric acid'
                             sulf-acid   'sulfuric acid'
                             phos-acid   'phosphoric acid'
                             el-aswan    'electricity from aswan dam'
                             coke-gas    'coke-oven gas'
                             nat-gas     'natural gas'
                             ref-gas     'refinery gas'
                             phos-rock   'phosphate rock'
                             limestone
                             el-sulfur   'elemental sulfur'
                             pyrites
                             electric    'electricity'
                             bf-gas      'blast-furnace gas'
                             water       'cooling water'
                             steam
                             bags
                             labor                                         /
   cf(c)  'final products' / urea, c-nitr, can-310, can-335, amm-sulf,
                             map, dap, ssp-155, tsp-pow, tsp, np-20-20 /
   ci(c)  'intermediate products'
                           / ammonia, co2, nitr-acid, sulf-acid, phos-acid /
   cs(c)  'intermediates for shipment'
                           / ammonia, sulf-acid, phos-acid /
   cr(c)  'raw materials'  / el-aswan, coke-gas, nat-gas, ref-gas, phos-rock,
                             limestone, el-sulfur, pyrites , sulf-acid        /
   cd(c)  'domestic materials'
                           / electric, bf-gas, water, steam, bags /
   c75(c) 'fertilizer used in 1975'
                           / urea, can-260,  can-310, can-335, amm-sulf,
                             dap, ssp-155, c-250-55, c-300-100          /
   tg     'time periods'   / 1979-81, 1982-84, 1985-87  /
   q      'cost categories'
                           / transport  'cost                       (mill le per year)'
                             d-r-c      'domestic recurrent cost    (mill le per year)'
                             operating  'cost                       (mill le per year)'
                             work-cap   'working capital cost       (mill le per year)'
                             capital-ch 'capital charges            (mill le per year)'
                             import-raw 'import cost: raw materials (mill le per year)'
                             import-fp  'import cost: final products(mill le per year)'
                             export     'export revenues            (mill le per year)' /;

Alias(i,ip);

$sTitle Consumption and Demand Data
Table cf75(j,c75) '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 dem80(*,cq) 'demand projections in nutrients (1000 tpy)'
             n  p2o5
   medium  496   112
   high    542   112;


Parameter eta(tg) 'urea consumption restriction' / 1979-81 .60
                                                   1982-84 .75
                                                   1985-87 .85 /;

Table alpha(c,cq) 'nutrient content'
                n    p2o5
   urea       .46
   c-nitr     .155
   can-260    .26
   can-310    .31
   can-335    .335
   amm-sulf   .206
   map        .11   .54
   dap        .18   .46
   ssp-155          .155
   tsp-pow          .46
   tsp              .46
   np-20-20   .20   .20
   c-250-55   .25   .055
   c-300-100  .30   .10 ;

Parameter
   cn75(j,cq)  'consumption of nutrients 1974-75      (1000 tpy)'
   cn75t(cq)   'total nutrient consumption 1974-75    (1000 tpy)'
   rdc(j,cq)   'regional distribution of consumption'
   cinc(cq)    'consumption increment'
   db(cq,j,tg) 'demand in nutrients                   (1000 tpy)'
   midyear(tg) / 1979-81 1980, 1982-84 1983, 1985-87 1986 /;

cn75(j,cq)  = sum(c75, alpha(c75,cq)*cf75(j,c75));
cn75t(cq)   = sum(j, cn75(j,cq));
rdc(j,cq)   = cn75(j,cq)/cn75t(cq);
cinc(cq)    = (dem80("medium",cq) - cn75t(cq))/5;
db(cq,j,tg) = rdc(j,cq)*(cn75t(cq) + cinc(cq)*(midyear(tg)-1975));

Parameter
   eh(tg) 'total export restriction  (1000 tpy)'
   eb(tg) 'maximum export by product (1000 tpy)';

eh(tg) = 100;
eb(tg) = 25;

display cn75, cn75t, rdc, cinc, db, midyear, eh, eb;

Parameter dsum 'demand summary';

dsum(cq,j,tg)                    = db(cq,j,tg);
dsum("n","**total**",tg)         = sum(j, dsum("n",j,tg));
dsum("p2o5","**total**",tg)      = sum(j, dsum("p2o5",j,tg));
dsum("**total**","**total**",tg) = sum((cq,j), dsum(cq,j,tg));

display dsum;

$sTitle Transportation Data
Table road(j,i) 'road distances (km)'
              abu-kir  kafr-el-zt  talkha  abu-zaabal  helwan  suez  assiout  aswan
   alexandria      16         119     187         210     244   362      607   1135
   behera          76          42     120          50     184   288      547   1065
   gharbia        150          20      55          65     122   226      485   1003
   kafr-el-sh     145          20      35         105     162   266      525   1043
   dakahlia       208          58       3         138     152   219      515   1033
   damietta       267         131      66         216     233   286      596   1114
   sharkia        240          78      58          60     110   214      473    991
   ismailia       365         241     146         142     173    89      536   1054
   suez           370         246     298         224     178            541   1059
   menoufia       157          33      90         154     109   213      472    990
   kalubia        190          66      81          97      76   180      439    957
   giza           287         133     146          48       9   169      372    890
   beni-suef      359         248     261         163     105   270      257    775
   fayoum         341         230     243         145      88   252      308    826
   minia          384         372     386         288     230   394      132    650
   assiout        616         504     518         420     362   527             518
   new-valley     815         703     717         619     561   726      199    519
   sohag          715         603     617         519     461   626       99    419
   quena          858         746     760         662     604   769      242    276
   aswan         1134        1022    1036         938     880  1045      518       ;

Table rail(i,ip) 'interplant rail distances  (km)'
               abu-kir  kafr-el-zt  talkha  abu-zaabal  helwan  suez  assiout  aswan
   kafr-el-zt      128
   talkha          196         58
   abu-zaabal      219         85      138
   helwan          253        142      155          57
   suez            371        246      298         224     178
   assiout         616        504      518         420     362   527
   aswan          1134       1022     1036         938     880  1045     518        ;


Table ied(i,*) 'import export distances (kms)'
                 barge      road     rail-e
   abu-kir          16                   16
   kafr-el-zt      104         6        104
   talkha          199                  199
   abu-zaabal      210        .1        210
   helwan          183                  166
   suez            346        50         10
   assiout         583                  583
   aswan          1087        10       1087;

Parameter
   muf(i,j)  'transport cost (le per ton): final products'
   mufv(j)   'transport cost (le per ton): imported final products'
   mue(i)    'transport cost (le per ton): exports'
   mui(i,ip) '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);
muf(i,j)    = ( .5 + .0144*road(j,i)            )$road(j,i);
mufv(j)     = ( .5 + .0144*min(road(j,"abu-kir"),road(j,"suez")) )$min(road(j,"abu-kir"),road(j,"suez"));
mue(i)      = ( .5 + .0300*ied(i,"rail-e") )$ied(i,"rail-e");
mui(i,ip)   = (3.5 + .0300*rail(i,ip)          )$rail(i,ip);
mur(i)      = (1.0 + .0030*ied(i,"barge")      )$ied(i,"barge")
            + ( .5 + .0144*ied(i,"road" )      )$ied(i,"road ");

display road, muf, mufv, mue, mui, mur;

$sTitle Technology Data
Parameter a(c,p) 'input-output coefficients';

Table a0(c,p) 'input-output coefficients'
               sulf-a-s  sulf-a-p  nitr-acid  amm-elec  amm-c-gas  amm-n-gas  amm-r-gas  phos-acid  c-nitr  amm-sulf   urea
   nitr-acid                           1.00                                                          -.66
   phos-acid                                                                                 1.00
   c-nitr                                                                                            1.00
   amm-sulf                                                                                                    1.00
   urea                                                                                                               1.00
   ammonia                           -.292       1.00       1.00      1.00        1.00                         -.26   -.58
   co2                                                                1.00                                            -.58
   sulf-acid     1.00       1.00                                                            -1.80              -.76
   el-aswan                                    -12.00
   coke-gas                                                -2.00
   nat-gas                                                          -33.00
   ref-gas                                                                        -.98
   phos-rock                                                                                -2.35
   limestone                                                                                         -.35
   el-sulfur     -.334
   pyrites                 -.826
   electric    -50.00     -75.00    -231.00             -1960.00    -33.00      -50.00    -144.00            -19.00 -75.00
   bf-gas                                                -609.00
   water       -20.00     -60.00       -.60              -700.00    -10.00      -14.00      -4.00            -17.00
   steam                                                   -4.00                                                     -1.50
   bags                                                                                            -22.00    -22.00 -22.00

       +        tsp   can-310  can-335    map    dap  ssp-155  tsp-pow  nitrophos
   nitr-acid             -.71     -.76                                       -.51
   phos-acid   -.74                      -.99   -.87              -.74
   c-nitr                                                                     .57
   tsp         1.00
   can-310               1.00
   can-335                        1.00
   map                                   1.00
   dap                                          1.00
   ssp-155                                               1.00
   tsp-pow                                                        1.00
   np-20-20                                                                   .43
   ammonia               -.20     -.21   -.15   -.23                         -.06
   sulf-acid                                             -.41
   phos-rock   -.35                                      -.62     -.35       -.27
   limestone             -.12     -.04
   electric  -28.00                    -22.00 -22.00   -14.00   -23.00     -52.00
   water               -49.00   -49.00                  -6.00    -2.00     -19.00
   steam       -.10      -.40     -.40   -.10   -.15              -.20       -.30
   bags      -22.00    -23.00   -23.00 -22.00 -22.00   -22.00   -23.00     -23.00                                         ;

Table b(m,p) 'capacity utilization matrix'
              sulf-a-s  sulf-a-p  nitr-acid  amm-elec  amm-c-gas  amm-n-gas  amm-r-gas  phos-acid  c-nitr  amm-sulf  urea
   sulf-a-s        1.0
   sulf-a-p                  1.0
   nitr-acid                            1.0
   amm-elec                                       1.0
   amm-c-gas                                                 1.0
   amm-n-gas                                                            1.0
   amm-r-gas                                                                       1.0
   phos-acid                                                                                  1.0
   c-nitr                                                                                             1.0
   amm-sulf                                                                                                     1.0
   urea                                                                                                               1.0

        +      tsp  can-310  can-335  map  dap  ssp-155  tsp-pow  nitrophos
   c-nitr                                                                .6
   c-amm-nitr           1.0      1.0
   amm-phos                           1.0  1.0
   ssp                                              1.0      1.0
   tsp         1.0
   nitro-phos                                                           1.0                                              ;

$sTitle Prices
Parameter pv(c) 'import price (cif us$ per ton 1975)' / pyrites       17.5
                                                        el-sulfur     55
                                                        urea         150
                                                        can-260      100
                                                        can-310      110
                                                        can-335      120
                                                        amm-sulf      75
                                                        map          220
                                                        dap          210
                                                        ssp-155       80
                                                        tsp          150
                                                        np-20-20     150   /;

Table pd(i,c) 'domestic raw material prices'
              limestone  nat-gas  coke-gas  ref-gas  el-aswan  phos-rock  sulf-acid
*                le/ton  le/mscf   le/mncm  le/mncm    le/mwh     le/ton     le/ton
   abu-kir                   .56
   kafr-el-zt                                                        5.0
   talkha           1.2      .56
   abu-zaabal                                                        4.0
   helwan           1.2      .60        16                                      3.0
   suez             1.2      .65                  8                  6.0
   assiout                                                           3.5
   aswan            1.2                                     1                      ;

$eolCom //
Parameter pmisc(c) 'miscellanous material cost'/ electric    .007      // le/kwh
                                                 bf-gas      .0075     // le/m3
                                                 water       .031      // le/m3
                                                 steam      1.25       // le/ton
                                                 bags        .28   /;  // le/unit

Scalar plab 'price of labor (le per man year)' / 360 /;

Parameter
   pe(c)   'export price (us$ per ton 1975)'
   oc(c,p) 'process operating cost for miscellenous inputs (le per unit level)';

pe(cf)             = .7*pv(cf);
a(c,p)$(not cd(c)) = a0(c,p);
oc(cd,p)           = - pmisc(cd)*a0(cd,p);

display pv, pe, a, oc;

$sTitle Capacity Data
Table dcap(i,m) 'design capacities of plants (tons per day)'
              sulf-a-s sulf-a-p nitr-acid amm-elec amm-c-gas amm-n-gas amm-r-gas c-nitr c-amm-nitr amm-sulf urea ssp
   abu-kir                                                        1000                                      1500
   kafr-el-zt      200       50                                                                                  600
   talkha                            1050                         1600                        1000          1650
   abu-zaabal      542      227                                                                                  600
   helwan                             282                172                                   364       35
   suez                               572                                    230    758                 200
   assiout         250                                                                                           600
   aswan                              800      450                                            1100                  ;

* talkha.ammonia =  400 talkha i + 1200 talkha ii    ???

Parameter
   caput(i) 'capacity utilization factor' / abu-kir .9, kafr-el-zt .85
                                            talkha  .9, abu-zaabal .85
                                            helwan  .7, suez       .7
                                            assiout .9, aswan      1.0  /
   k(m,i)   'initial capacity (1000 tpy)';

k(m,i)   = .33*caput(i)*dcap(i,m);

display k;

$sTitle Investment Costs
* fix  fixed cost in mill. us$
* prop variable cost in 1000 us$/ton/year

Table inv(m,*) 'investment cost'
                fix   prop
   amm-sulf     3.2   32.1
   urea        16.7   52.2
   amm-phos     4.5   32.4
   ssp          7.5   25.5
   tsp          7.0   34.2
   nitro-phos   8.0   70.0
   sulf-a-s     8.5   33.0
   amm-n-gas   47.9  103.8
   phos-acid   10.0   57.0;

Parameter
   omega(m)  'fixed-charge portion of investment   (million le per year)'
   omegag(g) 'fixed-charge for capacity conversion (million le per year)'
   omegal    'fixed-charge portion for labor                     (units)'
   nu(m)     'variable portion of investment   (million le per 1000 tpy)'
   nul       'variable charge portion for labor     (units per 1000 tpy)'
   hb(m)     'maximum capacity expansion                      (1000 tpy)'
   f(m,g,i)  'capacity  conversion                            (1000 tpy)'
   sf        'site factor'
   sigma     'capital recovery factor'
   delta     'discount factor'
   life      'life of productive unit                            (years)'
   oer       'official exchange rate                        (le per us$)'
   rho       'opportunity cost of capital';

sf                = 1.3;
omega(m)          = 1000*sf*inv(m,"fix");
omegag("amm-c-n") = 20 * 1000 * sf;
nu(m)             = sf*inv(m,"prop");
omegal            = .5;
nul               = .00125;

hb(m)  = 600;

f("amm-n-gas","amm-c-n","helwan") =  k("amm-c-gas","helwan");
f("amm-c-gas","amm-c-n","helwan") = -k("amm-c-gas","helwan");

life = 15;
rho  = .1;
oer  = .4;

sigma     = rho*(1+rho)**life/((1+rho)**life-1);
delta(tg) =   (1+rho)**(1976-midyear(tg))
            + (1+rho)**(1975-midyear(tg))
            + (1+rho)**(1974-midyear(tg));

display omega, nu, f, sigma, delta;

Set
   mpos(m,i)     'productive unit possibilities'
   ppos(p,i)     'process possibilities'
   cposp(c,i)    'commodity production possibilities'
   cposn(c,i)    'commodity consumption possibilities'
   cposi(c,ip,i) 'commodity production and consumption possibilities - interplant'
   cposr(c,i)    'imported input commodity consumption possibilities'
   cpose(c,i)    'export commodity possibilities'
   cposd(c,i)    'domestic commodity purchase possibilities'
   fpos(g,i)     'upgrading possibilities'
   hpos(m,i)     'expansion unit possibilities'
   t(tg)         'time periods' / 1979-81, 1982-84, 1985-87 /;

mpos(m,i)  = no; ppos(p,i)  = no; cposp(c,i) = no; cposn(c,i) = no; cposi(c,i,ip) = no;
cposr(c,i) = no; cpose(c,i) = no; cposd(c,i) = no; fpos(g,i)  = no; hpos(m,i)     = no;

Alias(t,tp);

Parameter ts(t,tp) 'time summation matrix';

ts(t,tp) = 1$(ord(t) ge ord(tp));

display ts;

$sTitle Equations

Variable
   z(p,i,t)     'process level                                (1000 tpy)'
   xf(c,i,j,t)  'domestic shipment activity: final products   (1000 tpy)'
   xi(c,i,ip,t) 'domestic shipment activity: intermediates    (1000 tpy)'
   vf(c,j,t)    'imports: final products                      (1000 tpy)'
   vr(c,i,t)    'imports: raw materials                       (1000 tpy)'
   e(c,i,t)     'exports                                      (1000 tpy)'
   et(t)        'total exports in year                        (1000 tpy)'
   u(c,i,t)     'domestic raw material purchases                 (units)'
   h(m,i,t)     'capacity expansion                           (1000 tpy)'
   up(g,i,t)    'binary variable: upgrading'
   y(m,i,t)     'binary variable: expansion'
   psi          'total cost (discounted)                    (million le)'
   psic(q,t)    'total cost components (undiscounted) (mill le per year)';

Positive Variable z, xf, xi, vf, vr, e, u, h;
Binary   Variable up, y;

Equation
   obj         'objective function                    (million le discounted)'
   ak          'accounting: capital cost charges           (mill le per year)'
   ap          'accounting: domestic recurrent cost        (mill le per year)'
   ao          'accounting: operating cost                 (mill le per year)'
   al          'accounting: transport cost                 (mill le per year)'
   am          'accounting: working capital                (mill le per year)'
   air         'accounting: import cost for raw materials  (mill le per year)'
   aif         'accounting: import cost for final products (mill le per year)'
   ae          'accounting: export revenue                 (mill le per year)'
   mbd(cq,j,t) 'material balance: demand                           (1000 tpy)'
   mbu(j,t)    'material balance: urea consumption                 (1000 tpy)'
   mb(c,i,t)   'material balance: plants                           (1000 tpy)'
   cc(i,m,t)   'capaciy constraint                                 (1000 tpy)'
   mm(i,m,t)   'maximum capacity expansion                         (1000 tpy)'
   ex(g,i)     'mutual exclusivity constraint                         (unity)'
   eca(t)      'aggregate export constraint                        (1000 tpy)'
   ecmax(t)    'export constraint by market share: maximum         (1000 tpy)'
   ecmin(t)    'export constraint by market share: minimum         (1000 tpy)';

obj..     psi =e= sum(t, delta(t)*sum(q, psic(q,t)));

mbd(cq,j,t).. sum(cf, alpha(cf,cq)*( vf(cf,j,t)$pv(cf) + sum(i$cposp(cf,i), xf(cf,i,j,t)) )) =g= db(cq,j,t);

mbu(j,t)..    alpha("urea","n")*( vf("urea",j,t) + sum(i$cposp("urea",i), xf("urea",i,j,t)) ) =l= eta(t)*db("n",j,t);

mb(c,i,t)..    sum(p$ppos(p,i), a(c,p)*z(p,i,t))
            +  sum(ip,  xi(c,ip,i,t)$cposi(c,ip,i) - xi(c,i,ip,t)$cposi(c,i,ip))
            +  u(c,i,t)$cposd(c,i) + vr(c,i,t)$cposr(c,i)
           =g= sum(j, xf(c,i,j,t))$cposp(c,i) + e(c,i,t)$cpose(c,i);

cc(i,m,t)$mpos(m,i).. sum(p$ppos(p,i), b(m,p)*z(p,i,t)) =l= k(m,i) + sum(tp$ts(t,tp), .9*h(m,i,tp)$hpos(m,i)
                                                                   + sum(g, f(m,g,i)*up(g,i,tp)) );

mm(i,me,t)$hpos(me,i).. h(me,i,t) =l= hb(me)*y(me,i,t);

ex(g,i)$fpos(g,i)..     sum(t, up(g,i,t)) =l= 1;

eca(t)..      et(t) =e= sum((cf,i)$cpose(cf,i), e(cf,i,t));

**** something fishy
ecmax(t+1)..     et(t+1) =l= 1.3*et(t);

ecmin(t+1)..     et(t+1) =g= et(t);

ak(t)..  psic("capital-ch",t) =e= oer*sum(tp$ts(t,tp), sigma*(
                                              sum((i,me)$hpos(me,i), omega(me)*y(me,i,tp) + nu(me)*h(me,i,tp))
                                            + sum((i,g)$fpos(g,i), omegag(g)*up(g,i,tp)) ) ) / 1000;

ap(t)..  psic("d-r-c",t) =e= sum((c,i)$cposd(c,i), pd(i,c)*u(c,i,t)) / 1000;

ao(t)..  psic("operating",t) =e= (sum((cd,p,i)$ppos(p,i), oc(cd,p)*z(p,i,t))
                                  + plab*sum(tp$ts(t,tp), sum((me,i)$hpos(me,i), omegal*y(me,i,tp) + nul*h(me,i,tp)) )
                                    ) / 1000;

al(t)..  psic("transport",t) =e=  (sum(cf,   sum((i,j)$cposp(cf,i), muf(i,j)*xf(cf,i,j,t))
                                           + sum(j, mufv(j)*vf(cf,j,t))
                                           + sum(i$cpose(cf,i), mue(i)*e(cf,i,t)) )
                                 + sum((cs,i,ip)$cposi(cs,i,ip), mui(i,ip)*xi(cs,i,ip,t))
                                 + sum((cr,i)$cposr(cr,i), mur(i)*vr(cr,i,t))             ) / 1000;

am(t)..  psic("work-cap",t)   =e= .025*(psic("d-r-c",t) + psic("operating",t) + psic("import-raw",t));

air(t).. psic("import-raw",t) =e= oer*sum((cr,i)$cposn(cr,i), pv(cr)*vr(cr,i,t)) / 1000;

aif(t).. psic("import-fp",t)  =e= oer*sum((cf,j), pv(cf)*vf(cf,j,t)) / 1000;

ae(t)..  psic("export",t)     =e= - oer*sum((cf,i)$cpose(cf,i), pe(cf)*e(cf,i,t)) / 1000;

Model
   model1 'base case model'                    / mbd, mb, mbu, cc, mm, ex, eca, obj, ak, ap, ao, al, am, air, aif, ae /
   model2 'basecase without urea requirements' / model1 - mbu /
   model3 'basecase with bounds on exports'    / model1 + ecmax + ecmin /;

$onText
Scenario Definitions:
basecase : model1 with: et.up(t) = 100; e.up(cf,i,t) = 25; y.fx("phos-acid","abu-zaabal","1979-81") = 1;
scenario1: basecase with: y.fx("nitro-phos","suez","1979-81") = 1;
scenario2: basecase with: z.lo("c-nitr","suez",t) = 150;
scenario3: model1 with: et.up(t) = +inf; e.up(cf,i,t) = +inf; y.fx(m,i,t) = 0;
scenario4: model3 with: et(.up("1979-81") = 500; e.up(cf,i,t) = +inf; y.fx("phos-acid","abu-zaabal","1979-81") = 1;
                                                                      y.fx("amm-n-gas","suez","1982-84")       = 1;
                                                                      y.fx("urea","suez","1982-84")            = 1;
                                                                      y.fx("urea","suez","1985-87")            = 1;
scenario5: model3 with: et.up("1979-81") = 250; y.fx("phos-acid","abu-zaabal","1979-81") = 1;
scenario6: model1 with: et.up(t) = 100; e.up(cf,i,t) = 25; vf.fx(cf,j,t) = 0;
                        y.fx("phos-acid","abu-zaabal","1979-81") = 1; y.fx("sulf-a-s","abu-zaabal","1982-84")  = 1;
scenario7: model2 with: et.up(t) = 100; e.up(cf,i,t) = 25; y.fx("phos-acid","abu-zaabal","1979-81") = 1;
$offText

$sTitle Model Reductions and Scenarios
* set-up for basecase;

Set hposx  expansion possibilities / phos-acid.abu-zaabal /;

hpos(me,i)     = hposx(me,i);

mpos(m,i)      = yes$(k(m,i) + sum(g, abs(f(m,g,i)))) + hpos(m,i);
ppos(p,i)      = yes$(sum(m$(not mpos(m,i)), b(m,p)) eq 0);

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) = yes$(cposp(cs,i)*cposn(cs,ip));
cposr(cr,i)    = yes$(cposn(cr,i)$pv(cr));
cposd(cr,i)    = yes$(cposn(cr,i)$pd(i,cr));
cpose(cf,i)    = yes$(cposp(cf,i)$pe(cf));

fpos(g,i) = yes$sum(m, f(m,g,i) ne 0);

display mpos, ppos, cposp, cposn, cposi, cposr, cposd, cpose, fpos;

y.fx(me,i,t) = 0;
y.fx("phos-acid","abu-zaabal","1979-81") = 1;

e.up(cf,i,t)$cpose(cf,i) = eb(t);
et.up(t) = eh(t);

solve model1 minimizing psi using mip;

* define summary reports:
Parameter
   imports
   sumxf
   sumxi
   production
   exports;

imports("final-prod",t)    = sum((cf,j), vf.l(cf,j,t));
imports("inter-prod",t)    = sum((cr,i), vr.l(cr,i,t));
sumxf(i,t,cf)              = sum(j, xf.l(cf,i,j,t));
sumxf(i,t,"total")         = sum(cf, sumxf(i,t,cf));
sumxi(i,t,cs)              = sum(ip, xi.l(cs,i,ip,t));
sumxi(i,t,"total")         = sum(cs, sumxi(i,t,cs));
production("final-prod",t) = sum((p,i)$(sum(cf, a(cf,p)) eq 1), z.l(p,i,t));
production("inter-prod",t) = sum((p,i), z.l(p,i,t)) - production("final-prod",t);
exports("final-prod",t)    = sum((cf,i), e.l(cf,i,t));
exports("inter-prod",t)    = sum((c,i), e.l(c,i,t)) - exports("final-prod",t);

display psic.l, production, imports, exports, sumxf, sumxi;