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Technical Note---Approximation Algorithms for VRP with Stochastic Demands

Author

Listed:
  • Anupam Gupta

    (Computer Science Department, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213)

  • Viswanath Nagarajan

    (IBM T. J. Watson Research Center, Yorktown Heights, New York 10598)

  • R. Ravi

    (Tepper School of Business, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213)

Abstract

We consider the vehicle routing problem with stochastic demands (VRPSD). We give randomized approximation algorithms achieving approximation guarantees of 1 + (alpha) for split-delivery VRPSD, and 2 + (alpha) for unsplit-delivery VRPSD; here (alpha) is the best approximation guarantee for the traveling salesman problem. These bounds match the best known for even the respective deterministic problems [Altinkemer, K., B. Gavish. 1987. Heuristics for unequal weight delivery problems with a fixed error guarantee. Oper. Res. Lett. 6 (4) 149--158; Altinkemer, K., B. Gavish. 1990. Heuristics for delivery problems with constant error guarantees. Transportation Res. 24 (4) 294--297]. We also show that the “cyclic heuristic” for split-delivery VRPSD achieves a constant approximation ratio, as conjectured in Bertsimas [Bertsimas, D. J. 1992. A vehicle routing problem with stochastic demand. Oper. Res. 40 (3) 574--585].

Suggested Citation

  • 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.
    • Handle: RePEc:inm:oropre:v:60:y:2012:i:1:p:123-127
    DOI: 10.1287/opre.1110.0967
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    References listed on IDEAS

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    1. Gendreau, Michel & Laporte, Gilbert & Seguin, Rene, 1996. "Stochastic vehicle routing," European Journal of Operational Research, Elsevier, vol. 88(1), pages 3-12, January.
    2. 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.
    3. Dimitris J. Bertsimas, 1992. "A Vehicle Routing Problem with Stochastic Demand," Operations Research, INFORMS, vol. 40(3), pages 574-585, June.
    4. M. Haimovich & A. H. G. Rinnooy Kan, 1985. "Bounds and Heuristics for Capacitated Routing Problems," Mathematics of Operations Research, INFORMS, vol. 10(4), pages 527-542, November.
    5. Moshe Dror, 2002. "Vehicle Routing with Stochastic Demands: Models & Computational Methods," International Series in Operations Research & Management Science, in: Moshe Dror & Pierre L’Ecuyer & Ferenc Szidarovszky (ed.), Modeling Uncertainty, chapter 0, pages 625-649, Springer.
    6. Dimitris J. Bertsimas & David Simchi-Levi, 1996. "A New Generation of Vehicle Routing Research: Robust Algorithms, Addressing Uncertainty," Operations Research, INFORMS, vol. 44(2), pages 286-304, April.
    7. Stewart, William R. & Golden, Bruce L., 1983. "Stochastic vehicle routing: A comprehensive approach," European Journal of Operational Research, Elsevier, vol. 14(4), pages 371-385, December.
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    Cited by:

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    3. Maciej Rysz & Foad Mahdavi Pajouh & Pavlo Krokhmal & Eduardo L. Pasiliao, 2018. "Identifying risk-averse low-diameter clusters in graphs with stochastic vertex weights," Annals of Operations Research, Springer, vol. 262(1), pages 89-108, March.
    4. Maciej Rysz & Mohammad Mirghorbani & Pavlo Krokhmal & Eduardo L. Pasiliao, 2014. "On risk-averse maximum weighted subgraph problems," Journal of Combinatorial Optimization, Springer, vol. 28(1), pages 167-185, July.
    5. 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.

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