$title Stochastic Electric Power Expansion Planning Problem (APL1PSP,SEQ=70)

$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.

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

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 us(dl) cost of unserved demand / h   10, m   10, l   10 /;

parameter alpha(g) availability / g1 0.68, g2 0.64          /
          d(dl)    demand       / h  1040, m  1040, l  1040 /;

* -----------------------------------------------
* 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/;

set omega / o1*o5 /;

table  stochasticalpha(omega,g)     availability distribution on generator g
     g1   g2
 o1  1.0  1.0
 o2  0.9  0.9
 o3  0.5  0.7
 o4  0.4  0.1
 o5       0.0
;

table  alphaprobability(omega,g)    availability probabilities
     g1   g2
 o1  0.2  0.1
 o2  0.3  0.2
 o3  0.4  0.5
 o4  0.1  0.1
 o5       0.1
;

parameter stochasticd(omega)  demand distribution
          / o1 900,  o2 1000, o3 1100, o4 1200/
          dprobability(omega) demand probabilities
          / o1 0.15, o2 0.45, o3 0.25, o4 0.15/ ;

file emp / '%emp.info%' /; put emp '* problem %gams.i%';
loop(g,
   put / 'randvar ' alpha.tn(g) ' discrete ';
   loop(omega$alphaprobability(omega,g), put alphaprobability(omega,g):5:2 stochasticalpha(omega,g):5:2));
loop(dl,
   put / 'randvar ' d.tn(dl) ' discrete ';
   loop(omega$dprobability(omega), put dprobability(omega):5:2 stochasticd(omega):5:0));
putclose / 'stage 2 alpha d'
         / 'stage 2 omax demand'
         / 'stage 2 y s';

Set scen scenarios / s1*s5 /;
parameter  s_alpha(scen,g), s_d(scen,dl);

Set dict / scen   .scenario.''
           alpha  .randvar. s_alpha
           d      .randvar. s_d /;

solve apl1p using emp min tcost scenario dict;