$TourCos{t}_k$	the final tour cost of $r_k$ within a given partition of the targets
$Tou{r}_k$	the final tour of $r_k$ within a given partition of the targets
$F_k$	a set of edges in the forest corresponding to $r_k$
${\mathcal{C}}_k$	a set of connected components in $F_k$
$Y_k\left(C\right)$	the dual variable of a set C in ${\mathcal{C}}_k$, which keeps track of ${\sum }_{S\subseteq C}{Y}_k\left(S\right)$