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Worst Case Analysis for Pickup and Delivery Problems with Consecutive Pickups and Deliveries

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Algorithms and Computation (ISAAC 2009)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5878))

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Abstract

The pickup and delivery problem (PDP) asks to find a set of routes with the minimum travel cost to serve a given set of requests. PDP is called the multi-trip PDP with consecutive pickups and deliveries (PDPCMT) if it has an additional requirement such that any vehicle which has begun a delivery action is not allowed to take pickup actions until all of the loads on the vehicle are delivered. In this paper, we are interested in how the least travel cost can be increased by the additional requirement, and examine the maximum ratio of the optimal value of PDPCMT to that of PDP over all instances with p requests. We show that the maximum ratio is bounded from above by O(logp) and from below by Ω(logp/loglogp).

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Author information

Authors and Affiliations

  1. Department of Applied Mathematics and Physics Graduate School of Informatics, Kyoto University, Yoshida Honmachi, Sakyo, Kyoto, 606-8501, Japan

    Yoshitaka Nakao & Hiroshi Nagamochi

Authors
  1. Yoshitaka Nakao
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  2. Hiroshi Nagamochi
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Editor information

Editors and Affiliations

  1. Dept. of Electrical and Computer Engineering, University of Hawaii, Holmes Hall 483, 2540 Dole Street, 96822, Honolulu, HI, USA

    Yingfei Dong

  2. Department of Computer Science, University of Texas at Dallas, 75083, Dallas, TX, USA

    Ding-Zhu Du

  3. Department of Computer Science, University of California, 93106, Santa Barbara, CA, USA

    Oscar Ibarra

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© 2009 Springer-Verlag Berlin Heidelberg

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Nakao, Y., Nagamochi, H. (2009). Worst Case Analysis for Pickup and Delivery Problems with Consecutive Pickups and Deliveries. In: Dong, Y., Du, DZ., Ibarra, O. (eds) Algorithms and Computation. ISAAC 2009. Lecture Notes in Computer Science, vol 5878. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-10631-6_57

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  • DOI: https://doi.org/10.1007/978-3-642-10631-6_57

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-10630-9

  • Online ISBN: 978-3-642-10631-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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