consider the following model:

min${\displaystyle \underset{j=1}{\overset{2}{}}}{c}_j{x}_j+E\{{\displaystyle \underset{j=1}{\overset{2}{}}}{\displaystyle \underset{i=1}{\overset{3}{}}}{f}_{ij}{y}_{ij}\},$

$\frac{s}{t},x_j,b_j$

$,j=1,2$

$,{\displaystyle \underset{i=1}{\overset{3}{}}}{y}_{ij},0$

$,{\displaystyle \underset{j=1}{\overset{2}{}}}{y}_{ij},j=1,2$

$,y_{ij},d_i$

$x_j,i=1,2,3$

$,$

$,$

$,$

$,$

$,$

where

$d_i,$ demand $in$ load segment $i$

${}_j,$ availability $of$ generator $j$

$c_j,$ investment cost $to$ build generator $j$

$f_{ij},$ operating cost

$x_j,$ generator capacities

$y_{ij},$ operating level for generator $jin$ load level $i$

$b_j,$min capacity for generator $j$

with the following data $on$ the supply side:

TECH $ID$ TECHNOLOGY INV. COST$(\frac{\text{\$}}{K}WH)$ ANNUAL FIXED $O$&$M$ COST$(\frac{\text{\$}}{K}WH)$ AVAILIBITY FACTOR

$4$ Oil Fired Power Plant$-$NON RENEWABLE $103228\mathrm{.}80\mathrm{.}75$

$12$ Large Onshore Wind Turbine$-$RENEWABLE $114021\mathrm{.}60\mathrm{.}9$

$9$ Nuclear $LWR$ Power Plant$-$NON RENEWABLE $292864\mathrm{.}20\mathrm{.}75$

and the following information $on$ the demand side are provided $in$ the graph.

according $to$ all these informations,

and the following information on the demand side:

Lc

a$)$ Formulate the model using GAMS and solve it $($with MINOS$)$ as a cost minimizing deterministic power expansion model $($using the three technologies associated to your name in the following table$).$ Arbitrarily set minimum capacity levels for the technologies and perform a sensitivity analysis on this parameter.

b$)$ Reformulate and solve the model $($with DECIS$)$ as a stochastic power expansion problem where demand is specified as a random parameter that takes values of $\frac{+}{-}15\%$ with $25\%$ probability each. Compare the results to those of part $($a$)$ and discuss the differences.