[BCP] BCP MCF example question

[Matthew Galati]

Hi - I am trying to create a version of the MCF example in DIP.

I am trying to follow the example data provided and the write-up. Is the following an equivalent formulation to what is presented in the write-up? Some of the notation in the write-up is ill-posed, so it's a bit hard to follow.

Thanks,
Matt


   //---
   //--- (Integer) Multi-Commodity Flow Problem (MCF).
   //---
   //--- We are given:
   //---    (1) a directed graph G=(N,A),
   //---    (2) a set of commodities K, where each commodity is
   //---         a source-sink pair.
   //---
   //--- min  sum{k in K} sum{(i,j) in A} w[i,j] x[i,j,k]
   //--- s.t. sum{(j,i) in A} x[i,j,k] -
   //---      sum{(i,j) in A} x[i,j,k] = d[i,k], for all i in N
   //---      sum{k in K} x[i,j,k] >= l[i,j],       for all (i,j) in A
   //---      sum{k in K} x[i,j,k] <= u[i,j],       for all (i,j) in A
   //---      x[i,j,k] integer >= l[i,j] <= u[i,j], for all (i,j) in A
   //--- For k=(s,t) in K,
   //---    d[i,k] = -d[k] if i=s
   //---           =  d[k] if i=t
   //---           =  0, otherwise
   //---