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Finding the Optimal a Priori Tour and Location of a Traveling Salesman with Nonhomogeneous Customers

Author

Listed:
  • Oded Berman

    (University of Massachusetts---Harbor Campus, Boston, Massachusetts)

  • David Simchi-Levi

    (Columbia University, New York, New York)

Abstract

This paper deals with the following routing problem: on any given day a subset of k out of n nodes of a network require a service visit (0 (le) k (le) n ). Each node of the network can generate a request with a given probability. The problem is to find an a priori tour with a minimum expected length through the n nodes such that any k given nodes will be visited in the same order they appear in the a priori tour. In contrast to other work, the probabilities of placing a demand at the different nodes are allowed to differ one from the other. Also discussed is the problem of finding the optimal home location (origin) for the service unit.

Suggested Citation

  • Oded Berman & David Simchi-Levi, 1988. "Finding the Optimal a Priori Tour and Location of a Traveling Salesman with Nonhomogeneous Customers," Transportation Science, INFORMS, vol. 22(2), pages 148-154, May.
    • Handle: RePEc:inm:ortrsc:v:22:y:1988:i:2:p:148-154
    DOI: 10.1287/trsc.22.2.148
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    Cited by:

    1. Albareda-Sambola, Maria & Fernández, Elena & Saldanha-da-Gama, Francisco, 2011. "The facility location problem with Bernoulli demands," Omega, Elsevier, vol. 39(3), pages 335-345, June.
    2. Igor Averbakh & Oded Berman & David Simchi‐Levi, 1994. "Probabilistic a priori routing‐location problems," Naval Research Logistics (NRL), John Wiley & Sons, vol. 41(7), pages 973-989, December.
    3. Wen-Huei Yang & Kamlesh Mathur & Ronald H. Ballou, 2000. "Stochastic Vehicle Routing Problem with Restocking," Transportation Science, INFORMS, vol. 34(1), pages 99-112, February.
    4. Albareda-Sambola, Maria & Vlerk, Maarten H. van der & Fernandez, Elena, 2002. "Exact solutions to a class of stochastic generalized assignment problems," Research Report 02A11, University of Groningen, Research Institute SOM (Systems, Organisations and Management).
    5. Albareda-Sambola, Maria & van der Vlerk, Maarten H. & Fernandez, Elena, 2006. "Exact solutions to a class of stochastic generalized assignment problems," European Journal of Operational Research, Elsevier, vol. 173(2), pages 465-487, September.
    6. repec:dgr:rugsom:02a11 is not listed on IDEAS
    7. Hunkar Toyoglu & Oya Ekin Karasan & Bahar Yetis Kara, 2011. "Distribution network design on the battlefield," Naval Research Logistics (NRL), John Wiley & Sons, vol. 58(3), pages 188-209, April.
    8. Bianchi, Leonora & Campbell, Ann Melissa, 2007. "Extension of the 2-p-opt and 1-shift algorithms to the heterogeneous probabilistic traveling salesman problem," European Journal of Operational Research, Elsevier, vol. 176(1), pages 131-144, January.
    9. Jian Yang & Patrick Jaillet & Hani Mahmassani, 2004. "Real-Time Multivehicle Truckload Pickup and Delivery Problems," Transportation Science, INFORMS, vol. 38(2), pages 135-148, May.

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