[Help-glpk] Combine linear program

[Alexandre . Depire]

hello,

I would like to know if the following
problem could be done with GLPK or any software (free) ?

Let x(i,j) in {0,1} for i in I, and
j in J, unknown variable
Let y(i,j) in R, for i in I, j in J,
unknown variable
Let a(i,j), l(i,j) and u(i,j) known
data
Let K an subset of IxJ, K={(ik,jk)}
 known

Problem:

Min sum( x( i , j ) )
        subject
to
        $
x( ik , jk )=1                
              /* some x(i,j)=1, the
others could be found */
        $
max    y( ik , jk ) >= a( ik , jk ) + U*x(ik,jk)
         
       subject to
         
      linear constraint on y(i,j)
         
      a(i,j)-l(i,j)*x(i,j) <= y(i,j) <= a(i,j)+u(i,j)*x(i,j)

thanks for your help

Alexandre DEPIRE