$title 'Basic GUSS Test' (SCENSOL4,SEQ=642)

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Contributor: Michael Bussieck, February 2014
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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 s /s1*s10/;

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
         SkipBaseCase 1   // Switch for solving the base case
         UpdateType   0   // Scenario update mechanism:
                          // 0 - set everything to 0 and apply changes
                          // 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) /;

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);

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

display srep;