$title APL1P Stochastic Programming Example for GAMS/DECIS (APL1P,SEQ=197)

$onText
Stochastic Electric Power Expansion Planning Problem.
This is a two-stage stochastic linear program.
Facing uncertain demand, decisions about generation
capacity need to be made.

This model is also used as an example in the
GAMS/DECIS user's guide.

Infanger, G, Planning Under Uncertainty - Solving Large-Scale
Stochastic Linear Programs, 1988.

Keywords: linear programming, stochastic programming, electric power generation
$offText

$if not set decisalg $set decisalg decism

Set
   g  'generators'    / g1, g2    /
   dl 'demand levels' / h , m , l /;

Parameter
   alpha(g) 'availability' / g1  0.68, g2  0.64 /
   ccmin(g) 'min capacity' / g1  1000, g2  1000 /
   ccmax(g) 'max capacity' / g1 10000, g2 10000 /
   c(g)     'investment'   / g1   4.0, g2   2.5 /;

Table f(g,dl) 'operating cost'
          h    m    l
   g1   4.3  2.0  0.5
   g2   8.7  4.0  1.0;

Parameter
   d(dl)  'demand'                  / h 1040, m 1040, l 1040 /
   us(dl) 'cost of unserved demand' / h   10, m   10, l   10 /;

* -----------------------------------------------
* define the core model
* -----------------------------------------------
Free Variable tcost 'total cost';

Positive Variable
   x(g)    'capacity of generators'
   y(g,dl) 'operation level'
   s(dl)   'unserved demand';

Equation
   cost       'total cost'
   cmin(g)    'minimum capacity'
   cmax(g)    'maximum capacity'
   omax(g)    'maximum operating level'
   demand(dl) 'satisfy demand';

cost..       tcost =e= sum(g, c(g)*x(g))
                    +  sum(g, sum(dl, f(g,dl)*y(g,dl)))
                    +  sum(dl,us(dl)*s(dl));

cmin(g)..    x(g)  =g= ccmin(g);

cmax(g)..    x(g)  =l= ccmax(g);

omax(g)..    sum(dl, y(g,dl)) =l= alpha(g)*x(g);

demand(dl).. sum(g, y(g,dl)) + s(dl) =g= d(dl);

Model apl1p / all /;

* -----------------------------------------------
* setting decision stages
* -----------------------------------------------
x.stage(g)       = 1;
y.stage(g,dl)    = 2;
s.stage(dl)      = 2;
cmin.stage(g)    = 1;
cmax.stage(g)    = 1;
omax.stage(g)    = 2;
demand.stage(dl) = 2;

* -----------------------------------------------
* defining independent stochastic parameters
* -----------------------------------------------
Set
   stoch  / out, pro                /
   omega1 / o11, o12, o13, o14      /
   omega2 / o21, o22, o23, o24, o25 /;

Table v1(stoch, omega1)
         o11   o12   o13   o14
   out  -1.0  -0.9  -0.5  -0.1
   pro   0.2   0.3   0.4   0.1;

Table v2(stoch, omega2)
         o21   o22   o23   o24   o25
   out  -1.0  -0.9  -0.7  -0.1  -0.0
   pro   0.1   0.2   0.5   0.1   0.1;

Table v3(stoch, omega1)
         o11   o12   o13   o14
   out   900  1000  1100  1200
   pro  0.15  0.45  0.25  0.15;

Table v4(stoch,omega1)
         o11   o12   o13   o14
   out   900  1000  1100  1200
   pro  0.15  0.45  0.25  0.15;

Table v5(stoch,omega1)
         o11   o12   o13   o14
   out   900  1000  1100  1200
   pro  0.15  0.45  0.25  0.15;

* -----------------------------------------------
* outputting stochastic file
* -----------------------------------------------
File stg / MODEL.STG /;
put stg;

put "INDEP DISCRETE" /;
loop(omega1, put "x g1  omax g1   ", v1("out", omega1), " period2 ", v1("pro", omega1) /;);
put "*" /;
loop(omega2, put "x g2  omax g2   ", v2("out", omega2), " period2 ", v2("pro", omega2) /;);
put "*" /;
loop(omega1, put "RHS demand h   ", v3("out", omega1),  " period2 ", v3("pro", omega1) /;);
put "*" /;
loop(omega1, put "RHS demand m   ", v4("out", omega1),  " period2 ", v4("pro", omega1) /;);
put "*" /;
loop(omega1, put "RHS  ", " demand  l   ", v5("out", omega1), " period2 ", v5("pro", omega1) /;);
putClose;

* -----------------------------------------------
* output a MINOS option file
* -----------------------------------------------
File mopt / MINOS.SPC /;
put  mopt;
put "begin"/;
put "rows 250"/;
put "columns 250"/;
put "elements 10000"/;
put "end"/;
putClose;

* -----------------------------------------------
* solve the model
* -----------------------------------------------
option lp = %decisalg%;

solve apl1p using lp minimizing tcost;

Scalar
   ccost 'capital cost'
   ocost 'operating cost';

ccost = sum(g, c(g)*x.l(g));
ocost = tcost.l - ccost;

display x.l, tcost.l, ccost, ocost, y.l, s.l;