An APX for the Maximum-Profit Routing Problem with Variable Supply
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In this paper, we study the Maximum-Profit Routing Problem with Variable Supply (MPRP-VS). This is a more general version of the Maximum-Profit Public Transportation Route Planning Problem, or simply Maximum-Profit Routing Problem (MPRP), introduced in <cit.>. In this new version, the quantity q_i(t) supplied at site i is linearly increasing in time t, as opposed to <cit.>, where the quantity is constant in time. Our main result is a 5.5 logT (1 + ϵ) (1 + 1/1 + √(m))^2 approximation algorithm, where T is the latest time window and m is the number of vehicles used. In addition, we improve upon the MPRP algorithm in <cit.> under certain conditions.
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