Re: [Help-glpk] help

[glpk xypron]

Hello Daniele,

the following model contains a constraint of the type you refer to.
Please, read glpk-4.47/doc/gmpl.pdf carefully. It is included in the
source distribution of GLPK available at
ftp://ftp.gnu.org/gnu/glpk/glpk-4.47.tar.gz

param R;
param T;
param t;
set Q := { 1..T };
set W;
param r{W};
param d{W};
var x{W,Q}, >= 0, <=10;
maximize objective:
  sum{i in W, q in Q} x[i,q];
s.t. constraint:
  sum{i in W} sum{q in Q : q >= t-d[i] && q <= t-1} r[i] * x[i,q] <= R;
data;
set W := a b;
param R := 10;
param T := 5;
param t := 6;
param d :=
  [a] 2
  [b] 3;
param r :=
  [a] .5
  [b] .7;
end;

Best regards

Xypron
-------- Original-Nachricht --------
> Datum: Wed, 27 Jun 2012 11:02:27 +0200
> Betreff: Re: [Help-glpk] help

> Re: [Help-glpk] help
> 
> I have attached the image so it is clearer
> W is a set of tasks
> T is the set of the time allowed
> r (i) is the parameter of the requested resource the activity i-th
> d (i) is the duration of the i-th activity
> R is the parameter that represents the total resource available in the
> system
> X (i, q) is the variable
> 
> Thanks
> 
> 
> 2012/6/27 glpk xypron <address@hidden>
> 
> > Hello Daniele,
> >
> > from your description it is unclear what you mean by t.
> >
> > Is t the run parameter of the summation or is it a parameter controlling
> > the boundaries of the summation? It cannot be both.
> >
> > Please, write down your equation completely including the definition of
> > the sets and parameters. Either send it in tex or append an image file.
> >
> > Best regards
> >
> > Xypron
> >
> > -------- Original-Nachricht --------
> > > Datum: Tue, 26 Jun 2012 23:46:10 +0200
> > > Betreff: Re: [Help-glpk] help
> >
> > > Re: [Help-glpk] help
> > >
> > > r (i) is a parameter and represents the resource request from the i-th
> > > activities by the system.
> > > The variable is x (i, t) where i is the index of the activities of the
> > > whole W and t is the index of the time interval.
> > > R is the total available resource is not exceeded while d (i) is the
> > > duration of the i.th activity
> > >
> > > >
> > > >
> > > >
> > > >> On Tue, 26 Jun 2012, Daniele Micarelli wrote:
> > > >>
> > > >>  I have to solve a linear programming problem with the language and
> > I'm
> > > >>> planning mathprog
> > > >>> I have difficulty writing the following constraint: ΣΣ r (i) * x
> (i,
> > > t)
> > > >>> <= R
> > > >>> where the first summation is true for all belonging to the W and
> the
> > > >>> second
> > > >>> summation has as its lower end t-d(i) and upper bound as t-1
> > > >>>
> > > >>
> > > >> You've not made it clear what is a variable and what is not.
> > > >> If r and x are both variables, you are done.
> > > >> *Linear* programming does not involve products of variables.
> > > >>
> > > >> --
> >
> > --
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> >

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