Maximum-Profit Routing Problem with Multiple Vehicles per Site

TL;DR

This paper extends the Maximum-Profit Routing Problem to allow multiple visits per site and introduces approximation algorithms for these new variants, enhancing routing efficiency in profit maximization scenarios.

Contribution

It proposes new variants of MPRP with multiple site visits and provides polynomial-time approximation schemes for these versions, advancing routing optimization methods.

Findings

Developed MPRP-M with constant quantities and approximation schemes.

Introduced MPRP-VS with linearly increasing quantities and approximation schemes.

Achieved constant-factor polynomial-time approximations for both variants.

Abstract

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.