Description
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.
Small Model of Type : SP
Category : GAMS EMP library
Main file : apl1pcasp.gms
$title Stochastic Electric Power Expansion Planning Problem (APL1PCASP,SEQ=71)
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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.
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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 hm1(dl) / h 300, m 400, l 200 /;
parameter hm2(dl) / h 100, m 150, l 300 /;
parameter df1 random demand multiplier /1/
df2 random demand multiplier /1/;
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= df1*hm1(dl) + df2*hm2(dl);
model apl1p /all/;
file emp / '%emp.info%' /; put emp '* problem %gams.i%' /;
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randvar df1 discrete 0.5 2.1 0.5 1.0
randvar df2 discrete 0.2 2.0 0.8 0.2
stage 2 df1 df2
stage 2 omax demand
stage 2 y s
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putclose;
Set scen scenarios / s1*s4 /;
parameter s_df1(scen), s_df2(scen);
Set dict / scen .scenario. ''
df1 .randvar . s_df1
df2 .randvar . s_df2 /;
solve apl1p using emp min tcost scenario dict;