  We consider the Maximum-Profit Routing Problem (MPRP), a variant of pick-up
routing problem introduced in \cite{Armaselu-arXiv-2016, Armaselu-PETRA}, in
which the goal is to maximize total profit. The original MPRP restricts
vehicles to visit a site at most once. In this paper, we consider extensions of
MPRP, in which a site may be visited by a vehicle multiple times. Specifically,
we consider two versions: one in which the quantity to be picked up at each
site is constant in time (MPRP-M), and one with time-varying supplied
quantities, which increase linearly in time (MPRP-VS). For each of these
versions, we come up with a constant-factor polynomial-time approximaltion
scheme.
