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

Anthony, Barbara M.; Chung, Christine; Das, Ananya; Yuen, David

doi:10.4230/OASIcs.ATMOS.2024.8

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Document Identifiers

DOI: 10.4230/OASIcs.ATMOS.2024.8
URN: urn:nbn:de:0030-drops-211964

Author Details

Barbara M. Anthony

Southwestern University, Georgetown, TX, USA

Christine Chung

Connecticut College, New London, CT, USA

Ananya Das

Middlebury College, VT, USA

David Yuen

Independent Researcher, Kapolei, HI, USA

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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)
https://doi.org/10.4230/OASIcs.ATMOS.2024.8

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.

Subject Classification

ACM Subject Classification

Theory of computation → Routing and network design problems
Applied computing → Transportation

Keywords

Dial-a-Ride problems
Lower bounds
Vehicle routing

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References

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