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Technical Note—Heuristics for Delivery Problems with Constant Error Guarantees

Author

Listed:
  • Kemal Altinkemer

    (Purdue University, West Lafayette, Indiana 47907)

  • Bezalel Gavish

    (Vanderbilt University, Nashville, Tennessee 37203)

Abstract

In this paper Q Iterated Optimal Tour Partitioning, and Best Optimal Tour Partitioning algorithms are studied and analyzed for their worst case error. Both algorithms are based on partitioning an optimal traveling salesman tour in order to generate a feasible solution to the unit weight delivery problem. They have a worst case error bound of 2 − 1/ Q where Q is the maximal number of customers a vehicle could visit and N is the total number of customers. Similar worst case error bounds are shown when the algorithms are applied to an α-optimal traveling salesman tour.

Suggested Citation

  • Kemal Altinkemer & Bezalel Gavish, 1990. "Technical Note—Heuristics for Delivery Problems with Constant Error Guarantees," Transportation Science, INFORMS, vol. 24(4), pages 294-297, November.
    • Handle: RePEc:inm:ortrsc:v:24:y:1990:i:4:p:294-297
    DOI: 10.1287/trsc.24.4.294
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    Cited by:

    1. Patrick Jaillet & Michael R. Wagner, 2008. "Generalized Online Routing: New Competitive Ratios, Resource Augmentation, and Asymptotic Analyses," Operations Research, INFORMS, vol. 56(3), pages 745-757, June.
    2. Tetsuo Asano & Naoki Katoh & Kazuhiro Kawashima, 2001. "A New Approximation Algorithm for the Capacitated Vehicle Routing Problem on a Tree," Journal of Combinatorial Optimization, Springer, vol. 5(2), pages 213-231, June.
    3. Anupam Gupta & Viswanath Nagarajan & R. Ravi, 2012. "Technical Note---Approximation Algorithms for VRP with Stochastic Demands," Operations Research, INFORMS, vol. 60(1), pages 123-127, February.
    4. Zhang, Meng & Wang, Nengmin & He, Zhengwen & Jiang, Bin, 2021. "Vehicle routing optimization for hazmat shipments considering catastrophe avoidance and failed edges," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 150(C).
    5. Yuanxiao Wu & Xiwen Lu, 0. "Capacitated vehicle routing problem on line with unsplittable demands," Journal of Combinatorial Optimization, Springer, vol. 0, pages 1-11.
    6. Yuanxiao Wu & Xiwen Lu, 2022. "Capacitated vehicle routing problem on line with unsplittable demands," Journal of Combinatorial Optimization, Springer, vol. 44(3), pages 1953-1963, October.
    7. Shoshana Anily & Julien Bramel, 1999. "Approximation algorithms for the capacitated traveling salesman problem with pickups and deliveries," Naval Research Logistics (NRL), John Wiley & Sons, vol. 46(6), pages 654-670, September.
    8. Inge Li Gørtz & Marco Molinaro & Viswanath Nagarajan & R. Ravi, 2016. "Capacitated Vehicle Routing with Nonuniform Speeds," Mathematics of Operations Research, INFORMS, vol. 41(1), pages 318-331, February.
    9. Zhou Xu & Liang Xu & Chung‐Lun Li, 2010. "Approximation results for min‐max path cover problems in vehicle routing," Naval Research Logistics (NRL), John Wiley & Sons, vol. 57(8), pages 728-748, December.

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