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We consider the Maximum-Profit Routing Problem (MPRP), a variant of pick-uprouting problem introduced in \cite{Armaselu-arXiv-2016, Armaselu-PETRA}, inwhich the goal is to maximize total profit. The original MPRP restrictsvehicles to visit a site at most once. In this paper, we consider extensions ofMPRP, 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 eachsite is constant in time (MPRP-M), and one with time-varying suppliedquantities, which increase linearly in time (MPRP-VS). For each of theseversions, we come up with a constant-factor polynomial-time approximaltionscheme.

Maximum-Profit Routing Problem with Multiple Vehicles per Site