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Approximation algorithms for some extensions of the maximum profit routing problem

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  • Bogdan Armaselu

Abstract

In this paper, we consider extensions of the Maximum-Profit Public Transportation Route Planning Problem, or simply Maximum-Profit Routing Problem (MPRP), introduced in Armaselu and Daescu (Approximation algorithms for the maximum profit pick-up problem with time windows and capacity constraint, 2016. arXiv:1612.01038 , Interactive assisting framework for maximum profit routing in public transportation in smart cities, PETRA, 13–16, 2017). Specifically, we consider MPRP with Time-Variable Supply (MPRP-VS), in which the quantity $$q_i(t)$$ q i ( t ) supplied at site i is linearly increasing in time t, as opposed to the original MPRP problem, where the quantity is constant in time. For MPRP-VS, our main result is a $$5.5 \log {T} (1 + \epsilon ) \left( 1 + \frac{1}{1 + \sqrt{m}}\right) ^2$$ 5.5 log T ( 1 + ϵ ) 1 + 1 1 + m 2 approximation algorithm, where T is the latest time window and m is the number of vehicles used. We also study the MPRP with Multiple Vehicles per Site, in which a site may be visited by a vehicle multiple times, which can have 2 flavors: with quantities fixed in time (MPRP-M), and with time-variable quantities (MPRP-MVS). Our algorithmic solution to MPRP-VS can also improve upon the MPRP algorithm in Armaselu and Daescu (2017) under certain conditions. In addition, we simulate the MPRP-VS algorithm on a few benchmark, real-world, and synthetic instances.

Suggested Citation

  • Bogdan Armaselu, 2023. "Approximation algorithms for some extensions of the maximum profit routing problem," Journal of Combinatorial Optimization, Springer, vol. 45(1), pages 1-22, January.
    • Handle: RePEc:spr:jcomop:v:45:y:2023:i:1:d:10.1007_s10878-022-00944-0
    DOI: 10.1007/s10878-022-00944-0
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    1. Christos H. Papadimitriou & Mihalis Yannakakis, 1993. "The Traveling Salesman Problem with Distances One and Two," Mathematics of Operations Research, INFORMS, vol. 18(1), pages 1-11, February.
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    3. Michael Drexl, 2012. "Synchronization in Vehicle Routing---A Survey of VRPs with Multiple Synchronization Constraints," Transportation Science, INFORMS, vol. 46(3), pages 297-316, August.
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