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Maximizing Revenues for On-Line Dial-a-Ride

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Combinatorial Optimization and Applications (COCOA 2014)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8881))

Abstract

We consider the On-Line Dial-a-Ride Problem, where a server fulfills requests that arrive over time. Each request has a source, destination, and release time. We study a variation of this problem where each request also has a revenue that the server earns for fulfilling the request. The goal is to serve requests within a time limit while maximizing the total revenue. We first prove that no deterministic online algorithm can be competitive unless the input graph is complete and edge weights are unit. We therefore focus on these graphs and present a 2-competitive algorithm for this problem. We also consider two variations of this problem: (1) the input graph is complete bipartite and (2) there is a single node that is the source for every request, and present a 1-competitive algorithm for the former and an optimal algorithm for the latter.

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Notes

  1. 1.

    Note that since \(v_{last}\) can be at most the maximum allowed revenue, this proof shows non-competitiveness for \(b\) equal to all possible revenue values.

  2. 2.

    We note that there are at least two enhancements that can improve the performance of grf without improving the competitive ratio: (1) In steps 2 and 7, instead of simply moving to the request that earns the greatest revenue, the algorithm can serve a request if there is one available while performing this move. (2) In steps 3 and 8, the algorithm can check if a request with higher revenue has been released since the previous step and if so, serve this request instead of \(r\).

  3. 3.

    If at any time \(t\), there is no request issued, we can generate a “dummy” request of the form \((s, d, t, 0)\), where \(s\) and \(d\) are nodes in the input graph, since neither grf nor any optimal algorithm would accept this request.

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Author information

Authors and Affiliations

  1. Middlebury College, Middlebury, VT, 05753, USA

    Ananya Christman

  2. Abbott Laboratories, Lake Forest, IL, 60045, USA

    William Forcier

Authors
  1. Ananya Christman
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  2. William Forcier
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Corresponding author

Correspondence to Ananya Christman .

Editor information

Editors and Affiliations

  1. Zhejiang Normal University, Jinhua, Zhejiang, China

    Zhao Zhang

  2. University of Texas, Tyler, Texas, USA

    Lidong Wu

  3. University of Texas, Dallas, Texas, USA

    Wen Xu

  4. University of Texas, Dallas, USA

    Ding-Zhu Du

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Christman, A., Forcier, W. (2014). Maximizing Revenues for On-Line Dial-a-Ride. In: Zhang, Z., Wu, L., Xu, W., Du, DZ. (eds) Combinatorial Optimization and Applications. COCOA 2014. Lecture Notes in Computer Science(), vol 8881. Springer, Cham. https://doi.org/10.1007/978-3-319-12691-3_38

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  • DOI: https://doi.org/10.1007/978-3-319-12691-3_38

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-12690-6

  • Online ISBN: 978-3-319-12691-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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