tforss.gms : Antalya Forestry Model - Steady State

Description

This model finds the best management plan for new forests in a steady state
condition.

Reference

  • Bergendorff, H, Glenshaw, P, and Meeraus, A, The Planning of Investment Programs in the Paper Industry. Tech. rep., The World Bank, 1980.

Small Model of Type : LP


Category : GAMS Model library


Main file : tforss.gms

$Title Antalya Forestry Model - Steady State  (TFORSS,SEQ=61)

$Ontext

   This model finds the best management plan for new forests in a steady state
   condition.


Bergendorff, H, Glenshaw, P, and Meeraus, A, The Planning of Investment
Programs in the Paper Industry. Tech. rep., The World Bank, 1980.

$Offtext

 Sets  c     commodities      / pulplogs,  sawlogs,  residuals,  pulp,  sawnwood /
       cf(c) final products   / pulp,  sawnwood  /
       cl(c) log types        / pulplogs,  sawlogs /
       s     species          / nigra,  brutia /
       k     site classes     / good, medium, poor /
       at    tree age         / a-10, a-20, a-30, a-40, a-50, a-60, a-70, a-80 /
       p     processes        / pulp-pl,  pulp-sl,  pulp-rs,  sawing    /
       m     productive units / pulp-mill,  saw-mill /

 Parameter  scd(k)    site class distribution / good .25, medium .50 , poor .25 /
            land(s)   land available (1000ha) / nigra 143.679, brutia 227.58 /


 Table      ymf(at,k,s,cl)  yield of managed forest (m3 per ha)

               nigra.pulplogs  nigra.sawlogs   brutia.pulplogs  brutia.sawlogs
  a-10.good                                          17.5
  a-10.medium
  a-10.poor

  a-20.good            120.0                         66.8
  a-20.medium           95.0                         51.1
  a-20.poor             80.0                         37.8

  a-30.good            132.6        37.4             91.3         25.7
  a-30.medium          120.2        14.8             81.4         10.0
  a-30.poor            115.0                         71.3

  a-40.good            121.0        99.0             91.3         74.7
  a-40.medium          115.5        59.5             86.5         44.5
  a-40.poor            119.0        21.0             90.1         15.9

  a-50.good            108.0       162.0             76.0        114.0
  a-50.medium          112.0       108.0             77.0         74.0
  a-50.poor            112.2        57.8             92.0         47.6

  a-60.good            104.0       221.0             76.0        116.0
  a-60.medium          106.0       159.0             76.0        113.0
  a-60.poor            110.0        90.0             95.2         77.8

  a-70.good            105.0       270.0             78.0        200.0
  a-70.medium           98.0       207.0             72.0        153.0
  a-70.poor             97.0       128.0             88.0        116.0

  a-80.good            102.0       323.0             76.0        240.0
  a-80.medium          105.0       235.0             80.0        177.0
  a-80.poor             92.0       163.0             84.0        148.0

$Eject

 Table  a(c,p) input output matrix

               pulp-pl  pulp-sl  pulp-rs    sawing

 pulplogs       -1.0
 sawlogs                 -1.0               -1.0
 residuals                        -1.0       0.4
 pulp             .207     .207     .207
 sawnwood                                    0.6


 Table  b(m,p)  capacity utilization

               pulp-pl  pulp-sl  pulp-rs  sawing

 pulp-mill        1        1        1
 saw-mill                                   1


 Parameter pc(p)   process cost (us$ per m3 input)    / (pulp-pl,pulp-sl,pulp-rs)  5.96, sawing  6.00 /
           pd(cf)  sales price  (us$ per unit)        / pulp      147.0 ,  sawnwood  70.0 /
           nu(m)   investment costs (us$ per m3 input) / pulp-mill  37.8 ,  saw-mill  61.5 /
           age(at) age of trees    ( years )

 Scalars mup  planting cost  (us$ per ha)  / 150.0 /
         muc  cutting cost   (us$ per m3)  /   7.0 /
         life plant life     (years)       /  30   /
         rho  discount rate                /    na / ;

 age(at) = 10*ord(at);

$Stitle model definition

  Equations  lbal(cl)      log balances
             bal(c)        material balances of wood processing
             cap(m)        wood processing capacities
             landc(s,k)    land availability constraint
             ainvc         investment cost
             aproc         process cost
             asales        sales revenue
             acutc         cutting cost
             aplnt         planting cost
             benefit

  Variables  v(s,k,at)  management of new forest    (1000ha per year)
             r(c)       supply of logs to industry  (1000m3 per year)
             z(p)       process level               (1000m3 input per year)
             h(m)       capacity                    (1000m3 input per year)
             x(c)       final shipments             (1000 units per year)
             phik       investment cost             (1000us$ per year)
             phir       process cost                (1000us$ per year)
             phix       sales revenue               (1000us$ per year)
             phil       cutting cost                (1000us$ per year)
             phip       planting cost               (1000us$ per year)
             phi        total benefits              (discounted cost);

 Positive Variables v, z, x ;

 lbal(cl)..      r(cl) =e= sum((s,k,at), ymf(at,k,s,cl)*v(s,k,at));

 bal(c)..       sum(p, a(c,p)*z(p)) + r(c)$cl(c) =g= x(c)$cf(c) ;

 cap(m)..       sum(p, b(m,p)*z(p)) =e= h(m) ;

 landc(s,k)..   sum(at, v(s,k,at)*age(at)) =l= land(s)*scd(k);


 ainvc..        phik =e= rho/(1-(1+rho)**(-life))*sum(m, nu(m)*h(m));

 aproc..        phir =e= sum(p, pc(p)*z(p)) ;

 asales..       phix =e= sum(cf, pd(cf)*x(cf)) ;

 acutc..        phil =e= muc*sum(cl, r(cl)) ;

 aplnt..        phip =e= mup*sum((s,k,at), v(s,k,at)*(1+rho)**age(at)) ;

 benefit..      phi  =e= phix - phik - phir - phil - phip ;

  Model forest / all /;

$Stitle case selection and report definitions

 Set       rhoset / rho-03, rho-05,rho-07,rho-10 /;
 Parameter landcl(s,k)        clean level of landc
           repr(cl,rhoset)    summary report on log supply           (1000m3 per year)
           reprp(s,k,rhoset)  summary report on rotation period      (years)
           repsp(s,k,rhoset)  summary report on shadow price of land (us$ per ha)
           rhoval(rhoset) / rho-03 .03, rho-05 .05, rho-07 .07, rho-10 .1 /;

loop(rhoset,
   rho = rhoval(rhoset);
   Solve forest maximizing phi using lp;
   landcl(s,k)       = round(landc.l(s,k),3);
   repr(cl  ,rhoset) = r.l(cl);
   reprp(s,k,rhoset) = (landcl(s,k)/sum(at, v.l(s,k,at)))$landcl(s,k);
   repsp(s,k,rhoset) = landc.m(s,k) );

 Display repr, reprp, repsp;