apl1p.gms : Stochastic Programming Example for DECIS
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.
Reference:
- Infanger, G, Planning Under Uncertainty - Solving Large-Scale Stochastic Linear Programs.
Small Model of Type: DECIS
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$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.
$offtext
$if not set decisalg $set decisalg decism
set g generators / g1, g2/;
set dl demand levels /h, m, l/;
parameter alpha(g) availability / g1 0.68, g2 0.64 /;
parameter ccmin(g) min capacity / g1 1000, g2 1000 /;
parameter ccmax(g) max capacity / g1 10000, g2 10000 /;
parameter 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 /;
parameter 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;
positive variable y(g, dl) operation level;
positive variable s(dl) unserved demand;
equations
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 /;
set omega1 / o11, o12, o13, o14 /;
set 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;
scalar 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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