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A Preference Order Dynamic Program for a Stochastic Traveling Salesman Problem

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  • Edward P. C. Kao

    (University of Houston, Houston, Texas)

Abstract

Consider a traveling salesman problem with stochastic travel times. Our objective is to find a tour with maximum probability of completion by a specified time. This paper presents a preference order dynamic program for solving the problem. To facilitate computation, we introduce a branch-and-bound strategy in the solution procedure. Finally, we propose an implicit enumeration algorithm as an alternative approach.

Suggested Citation

  • Edward P. C. Kao, 1978. "A Preference Order Dynamic Program for a Stochastic Traveling Salesman Problem," Operations Research, INFORMS, vol. 26(6), pages 1033-1045, December.
    • Handle: RePEc:inm:oropre:v:26:y:1978:i:6:p:1033-1045
    DOI: 10.1287/opre.26.6.1033
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    Cited by:

    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. Zhouchun Huang & Qipeng Phil Zheng & Eduardo Pasiliao & Vladimir Boginski & Tao Zhang, 2019. "A cutting plane method for risk-constrained traveling salesman problem with random arc costs," Journal of Global Optimization, Springer, vol. 74(4), pages 839-859, August.
    3. Yu Zhang & Zhenzhen Zhang & Andrew Lim & Melvyn Sim, 2021. "Robust Data-Driven Vehicle Routing with Time Windows," Operations Research, INFORMS, vol. 69(2), pages 469-485, March.
    4. Hongtao Lei & Gilbert Laporte & Bo Guo, 2012. "A generalized variable neighborhood search heuristic for the capacitated vehicle routing problem with stochastic service times," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 20(1), pages 99-118, April.
    5. Chen, Lichun & Miller-Hooks, Elise, 2012. "Optimal team deployment in urban search and rescue," Transportation Research Part B: Methodological, Elsevier, vol. 46(8), pages 984-999.
    6. Elgesem, Aurora Smith & Skogen, Eline Sophie & Wang, Xin & Fagerholt, Kjetil, 2018. "A traveling salesman problem with pickups and deliveries and stochastic travel times: An application from chemical shipping," European Journal of Operational Research, Elsevier, vol. 269(3), pages 844-859.
    7. Astrid S. Kenyon & David P. Morton, 2003. "Stochastic Vehicle Routing with Random Travel Times," Transportation Science, INFORMS, vol. 37(1), pages 69-82, February.
    8. Letchford, Adam N. & Nasiri, Saeideh D., 2015. "The Steiner travelling salesman problem with correlated costs," European Journal of Operational Research, Elsevier, vol. 245(1), pages 62-69.
    9. Kang, Seungmo & Ouyang, Yanfeng, 2011. "The traveling purchaser problem with stochastic prices: Exact and approximate algorithms," European Journal of Operational Research, Elsevier, vol. 209(3), pages 265-272, March.
    10. Häme, Lauri & Hakula, Harri, 2013. "Dynamic journeying under uncertainty," European Journal of Operational Research, Elsevier, vol. 225(3), pages 455-471.
    11. Maciej Nowak & Tadeusz Trzaskalik, 2013. "Interactive procedure for a multiobjective stochastic discrete dynamic problem," Journal of Global Optimization, Springer, vol. 57(2), pages 315-330, October.
    12. Hossein Hashemi Doulabi & Gilles Pesant & Louis-Martin Rousseau, 2020. "Vehicle Routing Problems with Synchronized Visits and Stochastic Travel and Service Times: Applications in Healthcare," Transportation Science, INFORMS, vol. 54(4), pages 1053-1072, July.
    13. Chen, Lu & Gendreau, Michel & Hà, Minh Hoàng & Langevin, André, 2016. "A robust optimization approach for the road network daily maintenance routing problem with uncertain service time," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 85(C), pages 40-51.

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