Wednesday, June 25, 2008

Modeling question

>Hi all, does anybody knows how to attack a problem like the following ?
>
>Z: min (sum t(sum k(Ct,k Xt,k)))
>s.t.
>1) (sum t(sum k(Ct,k Xt,k)) GE costant
>2) (sum k(Qi,k Xt,k)) + Si,t LE Bi,t + Si,t-1 (i:1..I;t:1..T)
>3) (sum t(Xt,k)) LE 1 (t:1..T)
>4) Xt,k = (0;1)
>
>All ideas will be appreciated !!!!

A problem like this is very easily coded in a modeling system like AMPL or GAMS. If I understand the notation correctly this would look like:

binary variable x(t,k);
equations
obj
e1(i,t)
e2(k)
;
obj.. z =e=sum((t,k),C(t,k)*X(t,k));
z.lo = constant;
e1(i,t).. sum(k, Q(i,k)*X(t,k))+S(i,t) =L= B(i,t)+S(i,t-1);
e2(k).. sum(t, X(t,k)) =L= 1;