$title Basic GUSS Test (SCENSOL1,SEQ=407)

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Contributor: Michael Bussieck
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Sets
     i   canning plants   / seattle, san-diego /
     j   markets          / new-york, chicago, topeka / ;

Parameters

     a(i)  capacity of plant i in cases
       /    seattle     350
            san-diego   600  /

     b(j)  demand at market j in cases
       /    new-york    325
            chicago     300
            topeka      275  / ;

Table d(i,j)  distance in thousands of miles
                  new-york       chicago      topeka
    seattle          2.5           1.7          1.8
    san-diego        2.5                        1.4  ;

Scalar f  freight in dollars per case per thousand miles  /90/ ;

Parameter c(i,j)  transport cost in thousands of dollars per case ;

         c(i,j) = f * d(i,j) / 1000 ;

Variables
     x(i,j)  shipment quantities in cases
     z       total transportation costs in thousands of dollars ;

Positive Variable x ;

Equations
     cost        define objective function
     supply(i)   observe supply limit at plant i
     demand(j)   satisfy demand at market j ;

cost ..        z  =e=  sum((i,j),  f * d(i,j) / 1000 *x(i,j)) ;

supply(i) ..   sum(j, x(i,j))  =l=  a(i) ;

demand(j) ..   sum(i, x(i,j))  =g=  b(j) ;

Equation e dummy n row;  e.. sum((i,j), x(i,j)) =n= 3;

Model transport /all/ ;

* The DICT set has three dimensions
* 1 Model symbol
* 2 Action type
* 3 Update parameter
* DICT needs to be specified by a data statement

set dict   / s.scenario   . ''
             o.   opt     .srep
             d.   param   .ds
             a.   param   .as
             x.   upper   .xup
             f.   param   .fs
             cost.marginal.xcost
             x.   level   .xx /

* Problems:
*   1 QCP will not work, nor MCP, MPECS.

set sX /s1*s10/;
$if not set dim $set dim 1
$ifE (%dim%>3)or(%dim%<1) $abort dim must be 1 to 3

$if %dim%==1 $set s "sX"       set sx #SX
$if %dim%==2 $set s "sX,sX"    set sx #SX:#SX
$if %dim%==3 $set s "sX,sX,sX" set sx #SX:#SX:#SX

Set s(%s%) /%sx%/;

Parameter
    ds(%s%,i,j)  updater for d
    as(%s%,i)    updater for a
    xup(%s%,i,j) updater for x.up
    fs(%s%)      updater for f
    xcost(%s%)   collector for marginal of cost
    xx(%s%,i,j)  collector for level of x

$eolCom //
Set ma GUSS Model Attributes / system.GUSSModelAttributes /;
Parameter
    o(*)         GUSS options
       / OptfileInit  0   // Read solver options for initial solve
         Optfile      0   // Read solver options for successive solves
         LogOption    0   // 0 - Moderate log (default)
                          // 1 - Minimal log
                          // 2 - Detailed log
         NoHotStart   0   // Disable hot start capability in solver that
                          // supports hot starts
         NoMatchLimit 0   // Limit of unmatched scenario records (default 0)
         RestartType  0   // Determines restart point for the scenarios
                          // 0 - Restart from last solution (default)
                          // 1 - Restart from solution of base case
                          // 2 - Restart from input point
         SkipBaseCase 0   // Switch for solving the base case
         SolveEmpty   0   // Limit of solved empty scenarios,
                          // afterwards scenarios will be skipped (default 0)
         UpdateType   0   // Scenario update mechanism:
                          // 0 - set everything to 0 and apply changes (default)
                          // 1 - reestablish base case and apply changes
                          // 2 - build on top of last scenario and apply changes
       /
    srep(%s%,ma)  Solution attributes / #s.(ModelStat na, SolveStat na, ObjVal na) /;

ds(s,i,j)  = max(0,uniform(-5,2)) + eps;
as(s,i)    = a(i)*(1+normal(0.05,0.1));
xup(s,i,j) = uniform(120,300);
fs(s)      = uniform(80,100);

$if set goto $goTo %goto%

* Run GUSS
$label scensl1
Solve transport using lp minimizing z scenario dict;

* If we get a license error (global solver) just terminate
if (transport.modelstat=%modelStat.licensingProblem%,
    abort.noerror 'too big for global solvers');

display xx, xcost;
$if set goto $exit

parameter repsl1(%s%,ma); repsl1(s,ma)$srep(s,ma) = srep(s,ma);
repsl1(s,'objval')$(repsl1(s,'modelstat')<>1) = 0;

* Check if calculated obj coincides with objval.
Parameter xdiff(%s%);
xdiff(s)$repsl1(s,'objval') = round(repsl1(s,'objval') - sum((i,j),  fs(s) * ds(s,i,j) / 1000 *xx(s,i,j)),4);
abort$card(xdiff) xdiff, repsl1, fs, ds, xx;

* Now run GUSS with solvelink %solveLink.loadLibrary%
$label scensl5
option solvelink=%solveLink.loadLibrary%;
Solve transport using lp minimizing z scenario dict;
$if set goto $exit
parameter repsl5(%s%,ma); repsl5(s,ma)$srep(s,ma) = srep(s,ma);
repsl5(s,'objval')$(repsl5(s,'modelstat')<>1) = 0;

* Check if calculated obj coincides with objval.
xdiff(s)$repsl5(s,'objval') = round(repsl5(s,'objval') - sum((i,j),  fs(s) * ds(s,i,j) / 1000 *xx(s,i,j)),4);
abort$card(xdiff) xdiff, repsl5, fs, ds, xx;

* Run this in the traditional way:
$label gams
option limrow=0, limcol=0, solprint=silent;
parameter repiter;
loop(s,
   d(i,j)    = ds(s,i,j);
   a(i)      = as(s,i);
   x.up(i,j) = xup(s,i,j);
   f         = fs(s);
   Solve transport using lp minimizing z;
   repiter(s,'modelstat') = transport.modelstat;
   repiter(s,'solvestat') = transport.solvestat;
   if (transport.modelstat = %modelStat.optimal%,
      repiter(s,'objval') = transport.objval));

$if set goto $exit

parameter repdiff; alias(*,u);

set ma1(ma) / modelstat, solvestat, objval /;
repdiff(s,ma1) = round(repiter(s,ma1) - repsl1(s,ma1),5);
abort$card(repdiff) 'iter and sl1 differ', repdiff, repiter, repsl1;

repdiff(s,ma1) = round(repiter(s,ma1) - repsl5(s,ma1),5);
abort$card(repdiff) 'iter and sl5 differ', repdiff, repiter, repsl5;