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. $offtext sets 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 /; Variables x(i) capacity installed y(i,j) operating level cost total cost Positive Variables x,y; Equations 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 / Parameter 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 Equations 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;