Originally posted by: SRDesai

I needed to model the LP given in the attached image. Here is my progress on the same.  I am unable to model the constraints. Any help in this regard would be appreciated.

int     n       = ...;
range   Nodes  = 1..n;


tuple       edge        {int i; int j;}
setof(edge) Edges       = {<i,j> | i,j in Nodes};
int         Weight[Edges] = ...;

dvar float+ z[Edges];


maximize
  
    sum(e in Edges) z[e]*Weight[e];
 
 subject to
 {
 forall (v in Nodes)
   sum(e in Edges:e == <u,v>) e - sum(<w,v> in Edges) <w,v> == 0;

Regards,

SRDesai

You are close. You just have to do the filtering of edges differently. The conservation constraint would read:

forall (v in Nodes)
   sum(e_out in Edges: e_out.i == v) z[e_out] - sum(e_in in Edges : e_in.j == v) z[e_in] == 0;