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[Help-glpk] Combine linear program

From: Alexandre . Depire
Subject: [Help-glpk] Combine linear program
Date: Thu, 22 Jan 2009 15:45:22 +0100


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


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
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