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DOI: 10.4230/OASIcs.ATMOS.2024.8

New Bounds on the Performance of SBP for the Dial-a-Ride Problem with Revenues (Short Paper)

Authors: Barbara M. Anthony, Christine Chung, Ananya Das, and David Yuen

Published in: OASIcs, Volume 123, 24th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2024)

Abstract

We revisit the Segmented Best Path (sbp) algorithm for online DARP in an offline setting with revenues and a time limit. The goal is to find a subset of the inputted ride requests that can be served within the time limit while maximizing the total revenue earned. sbp divides the time into segments and greedily chooses the highest-revenue path of requests to serve within each time segment. We show that sbp’s performance has an upper bound of 5. Further, while sbp is a tight 4-approximation in the uniform-revenue case, we find that with non-uniform revenues, the approximation ratio of sbp has a lower bound strictly greater than 4; in particular, we provide a lower bound of (√e + 1)/(√e - 1) ≈ 4.08299, which we show can be generalized to instances with ratio greater than 4.278.

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Barbara M. Anthony, Christine Chung, Ananya Das, and David Yuen. New Bounds on the Performance of SBP for the Dial-a-Ride Problem with Revenues (Short Paper). In 24th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2024). Open Access Series in Informatics (OASIcs), Volume 123, pp. 8:1-8:6, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{anthony_et_al:OASIcs.ATMOS.2024.8,
  author =	{Anthony, Barbara M. and Chung, Christine and Das, Ananya and Yuen, David},
  title =	{{New Bounds on the Performance of SBP for the Dial-a-Ride Problem with Revenues}},
  booktitle =	{24th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2024)},
  pages =	{8:1--8:6},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-95977-350-8},
  ISSN =	{2190-6807},
  year =	{2024},
  volume =	{123},
  editor =	{Bouman, Paul C. and Kontogiannis, Spyros C.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.ATMOS.2024.8},
  URN =		{urn:nbn:de:0030-drops-211964},
  doi =		{10.4230/OASIcs.ATMOS.2024.8},
  annote =	{Keywords: Dial-a-Ride problems, Lower bounds, Vehicle routing}
}

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New Bounds on the Performance of SBP for the Dial-a-Ride Problem with Revenues (Short Paper)

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