apl1pca.gms : Stochastic Programming Example for DECIS

Description

```Stochastic Electric Power Expansion Planning Problem.
This is a two-stage stochastic linear program.
Facing uncertain demand, decisions about generation

Compared to APL1P this model introduces dependent
stochastic parameters.

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

Small Model of Type : DECIS

Category : GAMS Model library

Main file : apl1pca.gms

``````\$title APL1PCA Stochastic Programming Example for GAMS/DECIS (APL1PCA,SEQ=198)

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

Compared to APL1P this model introduces dependent
stochastic parameters.

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 /;

Table v1(stoch, omega1)
o11  o12
out   2.1  1.0
pro   0.5  0.5;

Set omega2 / o21, o22 /;

Table v2(stoch, omega2)
o21  o22
out   2.0  1.0
pro   0.2  0.8;

Parameter
hm1(dl) / h 300, m 400, l 200 /
hm2(dl) / h 100, m 150, l 300 /;

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

put "BLOCKS DISCRETE" /;

Scalar h1;

loop(omega1,
put "BL v1 period2 ", v1("pro", omega1)/;
loop(dl,
h1 = hm1(dl) * v1("out", omega1);
put "RHS demand ",dl.tl:1, " ", h1/;
);
);

loop(omega2,
put "BL v2 period2 ", v2("pro", omega2)/;
loop(dl,
h1 = hm2(dl) * v2("out", omega2);
put "RHS demand ",dl.tl:1, " ", h1/;
);
);

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;
``````
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