[Help-glpk] Newbie question

[Berglund Mattias]

Hello all!

 

I am trying to write a model how to minimize the production cost 

given the total demand and production cost per production plant. 

 

The thing is that I don't want have all production plants in use as it is now given my model below.
I would only like to start up a new plant when the demand of all the cheaper production isn't suffient.

 

I think my problem is a mix of different kind of problems and not a pure minimize problem.

Please, can someone help me out on this?

Best regards Mattias Berglund

 

 

set PLANTS;

param plant{i in PLANTS};
/* Production plants */

 

param maxlim{i in PLANTS};
/* maximum production, MWh*/

 

param minlim{i in PLANTS};
/* minimum production, MWh*/

 

param cost{i in PLANTS};
/* cost kr/MWh */

 

param demand;
/* total demand MWh */

 

var p{i in PLANTS} >=0;

/*production at plant i */

minimize z: sum{i in PLANTS} cost[i]*p[i];
/* minimize the total production cost */

 

s.t. limits{i in PLANTS} : minlim[i] <= p[i] <= maxlim[i];
/* for each plant within production limits */

 

s.t. totalproduction     : sum{i in PLANTS} p[i] >= demand;
/* The total production = demand*/

data;

 

param demand := 300;               /* MWh */

set PLANTS := vp vp3 p1 p2;     /* production units*/

 

param maxlim :=
  vp  80
  vp3 96
  p1  220
  p2  110; 

 
param minlim :=
  vp  16
  vp3 12
  p1  160
  p2  40;

 

 

param cost :=
  vp  20
  vp3 21
  p1  30
  p2  25;