mexss.gms : Mexico Steel - Small Static

Description

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, The Planning of Investment Programs in the Steel Industry. The Johns Hopkins University Press, Baltimore and London, 1984.

Small Model of Type : LP


Category : GAMS Model library


Main file : mexss.gms

$Title Mexico Steel - Small Static   (MEXSS,SEQ=15)
$Stitle Set Definitions

$Ontext

A simplified representation of the Mexican steel sector is used
to introduce a process industry production and distribution
scheduling problem.


Kendrick, D, Meeraus, A, and Alatorre, J, The Planning of Investment
Programs in the Steel Industry. The Johns Hopkins University Press,
Baltimore and London, 1984.

A scanned version of this out-of-print book is accessible at
http://www.gams.com/docs/pdf/steel_investment.pdf

$Offtext

 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 ;