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Probabilistic Traveling Salesman Problem with Deadlines

Author

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  • Ann M. Campbell

    (Department of Management Sciences, University of Iowa, Iowa City, Iowa 52242)

  • Barrett W. Thomas

    (Department of Management Sciences, University of Iowa, Iowa City, Iowa 52242)

Abstract

Time-constrained deliveries are one of the fastest growing segments of the delivery business, and yet there is surprisingly little literature that addresses time constraints in the context of stochastic customer presence. We begin to fill that void by introducing the probabilistic traveling salesman problem with deadlines (PTSPD). The PTSPD is an extension of the well-known probabilistic traveling salesman problem (PTSP) in which, in addition to stochastic presence, customers must also be visited before a known deadline. We present two recourse models and a chance constrained model for the PTSPD. Special cases are discussed for each model, and computational experiments are used to illustrate under what conditions stochastic and deterministic models lead to different solutions.

Suggested Citation

  • Ann M. Campbell & Barrett W. Thomas, 2008. "Probabilistic Traveling Salesman Problem with Deadlines," Transportation Science, INFORMS, vol. 42(1), pages 1-21, February.
    • Handle: RePEc:inm:ortrsc:v:42:y:2008:i:1:p:1-21
    DOI: 10.1287/trsc.1070.0203
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    3. 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.
    4. Alexander M. Stroh & Alan L. Erera & Alejandro Toriello, 2022. "Tactical Design of Same-Day Delivery Systems," Management Science, INFORMS, vol. 68(5), pages 3444-3463, May.
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    6. 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.
    7. Ann Campbell & Michel Gendreau & Barrett Thomas, 2011. "The orienteering problem with stochastic travel and service times," Annals of Operations Research, Springer, vol. 186(1), pages 61-81, June.
    8. Tengyu Wu & Lin He & Haiyan Yu, 0. "Online traveling salesman problem with time cost and non-zealous server," Journal of Combinatorial Optimization, Springer, vol. 0, pages 1-24.
    9. Ji, Chenlu & Mandania, Rupal & Liu, Jiyin & Liret, Anne, 2022. "Scheduling on-site service deliveries to minimise the risk of missing appointment times," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 158(C).
    10. 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.
    11. Tengyu Wu & Lin He & Haiyan Yu, 2022. "Online traveling salesman problem with time cost and non-zealous server," Journal of Combinatorial Optimization, Springer, vol. 44(3), pages 2143-2166, October.
    12. Chuck Holland & Jack Levis & Ranganath Nuggehalli & Bob Santilli & Jeff Winters, 2017. "UPS Optimizes Delivery Routes," Interfaces, INFORMS, vol. 47(1), pages 8-23, February.
    13. Yossiri Adulyasak & Patrick Jaillet, 2016. "Models and Algorithms for Stochastic and Robust Vehicle Routing with Deadlines," Transportation Science, INFORMS, vol. 50(2), pages 608-626, May.
    14. Li, Xiang & Zhou, Jiandong & Zhao, Xiande, 2016. "Travel itinerary problem," Transportation Research Part B: Methodological, Elsevier, vol. 91(C), pages 332-343.
    15. Klapp, Mathias A. & Erera, Alan L. & Toriello, Alejandro, 2020. "Request acceptance in same-day delivery," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 143(C).
    16. Errico, F. & Desaulniers, G. & Gendreau, M. & Rei, W. & Rousseau, L.-M., 2016. "A priori optimization with recourse for the vehicle routing problem with hard time windows and stochastic service times," European Journal of Operational Research, Elsevier, vol. 249(1), pages 55-66.
    17. Klapp, Mathias A. & Erera, Alan L. & Toriello, Alejandro, 2018. "The Dynamic Dispatch Waves Problem for same-day delivery," European Journal of Operational Research, Elsevier, vol. 271(2), pages 519-534.
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    21. Li Ping Gan & Will Recker, 2013. "Stochastic Preplanned Household Activity Pattern Problem with Uncertain Activity Participation (SHAPP)," Transportation Science, INFORMS, vol. 47(3), pages 439-454, August.

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