INSTANCE:
Rooted tree
,
a forward travel time
,
a backward travel time
,
a release time
,
and an handling time
.
SOLUTION:
A vehicle routing schedule that starts from ,
visits all nodes of
T, returns to ,
and, for any node ,
starts processing
not before the release time ,
i.e., a permutation
of
and a waiting function w such that, for any i,
where d(u,v) denotes the length of the unique path from u to v.
,
a forward travel time
,
a backward travel time
,
a release time
,
and an handling time
.
,
visits all nodes of
T, returns to 
,
starts processing
,
i.e., a permutation 
of
and a waiting function w such that, for any i,
![\begin{displaymath}
d(v_0,v_{\pi(1)})+\sum_{j=1}^{i-1}[w(v_{\pi(j)})+h(v_{\pi(j)})+
d(v_{\pi(j)},v_{\pi(j+1)})] \geq r(v_{\pi(i)})
\end{displaymath}](img865.gif)
![\begin{eqnarray*}
& & d(v_0,v_{\pi(1)})+\sum_{j=1}^{n-1}[w(v_{\pi(j)})+h(v_{\pi...
...\pi(j+1)})] + w(v_{\pi(n)}) + h(v_{\pi(n)}) + d(v_{\pi(n)},v_0).
\end{eqnarray*}](img866.gif)