lands.gms : Optimal Investment

**Description**

The following two-stage problem consists of determining the optimal capacity investment in various types of power plants so as to meet next period demands for electricity. Four power plants are considered and they can operate in three different modes. The next period demand for each of the three modes are to be met. There is a budget constraint and also a constraint on the minimum total capacity.

**Reference**

- Louveaux, F V, and Smeers, Y, Optimal Investments for Electricity Generation: A Stochastic Model and a Test Problem. In Ermoliev, Y, and Wets, R J, Eds, Numerical Techniques for Stochastic Optimization Problems. Springer Verlag, 1988, pp. 445-452.

**Small Model of Type :** LP

**Category :** GAMS Model library

**Main file :** lands.gms

```
$title Optimal Investment (LANDS,SEQ=188)
$onText
The following two-stage problem consists of determining the optimal
capacity investment in various types of power plants so as to meet
next period demands for electricity. Four power plants are considered
and they can operate in three different modes. The next period demand
for each of the three modes are to be met. There is a budget
constraint and also a constraint on the minimum total capacity.
Louveaux, F V, and Smeers, Y, Optimal Investments for Electricity
Generation: A Stochastic Model and a Test Problem. In
Ermoliev, Y, and Wets, R J, Eds, Numerical Techniques for
Stochastic Optimization Problems. Springer Verlag, 1988,
pp. 445-452.
This problem will be solved in two steps, we solve each scenario
separately and then all three scenarios together.
Keywords: linear programming, investment optimization, stochastic programming
$offText
Set
i 'power plant type' / plant-1*plant-4 /
j 'operating mode' / mode-1*mode-3 /;
Parameter
c(i) 'investment cost' / plant-1 10, plant-2 7, plant-3 16, plant-4 6 /
d(j) 'energy demand' / mode-1 na, mode-2 3, mode-3 2 /;
Table f(i,j) 'operating cost'
mode-1 mode-2 mode-3
plant-1 40 24 4
plant-2 45 27 4.5
plant-3 32 19.2 3.2
plant-4 55 33 5.5;
Scalar
m 'min installed capacity' / 12 /
b 'budget limit' / 120 /;
Variable
x(i) 'capacity installed'
y(i,j) 'operating level'
cost 'total cost';
Positive Variable x, y;
Equation
defcost 'definition of total cost'
mincap 'minimum installed capacity'
bbal 'budget constraint'
powbal(i) 'power balance'
dembal(j) 'demand balance';
defcost.. cost =e= sum(i, c(i)*x(i)) + sum((i,j), f(i,j)*y(i,j));
mincap.. sum(i, x(i)) =g= m;
bbal.. sum(i, c(i)*x(I)) =l= b;
powbal(i).. sum(j, y(i,j)) =l= x(i);
dembal(j).. sum(i, y(i,j)) =g= d(j);
Model det / all /;
Set s 'nodes' / s-1*s-3 /;
Parameter
dvar(s) / s-1 3, s-2 5, s-3 7 /
prob(s) / s-1 .3, s-2 .4, s-3 .3 /
repdet 'scenario report';
loop(s,
d('mode-1') = dvar(s);
solve det minimizing cost using lp;
repdet('cost',s) = cost.l;
repdet(i,s) = x.l(i);
repdet('prob',s) = prob(s);
det.solPrint = %solPrint.Quiet%;
);
* make model stochastic
Parameter ds(j,s) 'stochastic demand';
Positive Variable ys(i,j,s) 'operating level';
Equation
defcosts 'definition of total cost'
powbals(i,s) 'power balance'
dembals(j,s) 'demand balance';
defcosts.. cost =e= sum(i, c(i)*x(i)) + sum((i,j,s), prob(s)*f(i,j)*ys(i,j,s));
powbals(i,s).. sum(j, ys(i,j,s)) =l= x(i);
dembals(j,s).. sum(i, ys(i,j,s)) =g= ds(j,s);
Model stoc / defcosts, mincap, bbal, powbals, dembals /;
ds(j,s) = d(j);
ds('mode-1',s) = dvar(s);
solve stoc minimizing cost using lp;
repdet('cost','hedge') = cost.l;
repdet(i,'hedge') = x.l(i);
display repdet;
```