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Online traveling salesman problem with deadlines and service flexibility

Author

Listed:
  • Xingang Wen

    (Xi’an Jiaotong University
    Tilburg University)

  • Yinfeng Xu

    (Xi’an Jiaotong University
    State Key Lab for Manufacturing Systems Engineering)

  • Huili Zhang

    (Xi’an Jiaotong University
    State Key Lab for Manufacturing Systems Engineering)

Abstract

Considering the customer psychology while waiting to be served, we introduce a more reasonable form of deadlines into online traveling salesman problem (OL-TSP) with service flexibility. The salesman can choose whether to serve or not when a new request arrives. By rejecting the request or missing its deadline, penalties will be generated. The goal is to minimize server’s costs (travel makespan plus the penalties of missed requests). We show that no deterministic or randomized online algorithms can achieve constant competitive ratio for OL-TSP with deadlines and service flexibility on general metric space. While on constrained metric space (such as truncated line segment), we present lower bound, give an algorithm, and analyze the competitive ratio.

Suggested Citation

  • Xingang Wen & Yinfeng Xu & Huili Zhang, 2015. "Online traveling salesman problem with deadlines and service flexibility," Journal of Combinatorial Optimization, Springer, vol. 30(3), pages 545-562, October.
    • Handle: RePEc:spr:jcomop:v:30:y:2015:i:3:d:10.1007_s10878-013-9654-4
    DOI: 10.1007/s10878-013-9654-4
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    References listed on IDEAS

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    1. Patrick Jaillet & Michael R. Wagner, 2006. "Online Routing Problems: Value of Advanced Information as Improved Competitive Ratios," Transportation Science, INFORMS, vol. 40(2), pages 200-210, May.
    2. 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.
    3. Michiel Blom & Sven O. Krumke & Willem E. de Paepe & Leen Stougie, 2001. "The Online TSP Against Fair Adversaries," INFORMS Journal on Computing, INFORMS, vol. 13(2), pages 138-148, May.
    4. V Portougal & D Trietsch, 2001. "Stochastic scheduling with optimal customer service," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 52(2), pages 226-233, February.
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    Cited by:

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    2. 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.
    3. Mengyuan Gou & Haiyan Yu, 2023. "Online Delivery Problem for Hybrid Truck–Drone System with Independent and Truck-Carried Drones," Sustainability, MDPI, vol. 15(2), pages 1-15, January.
    4. 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.
    5. Henan Liu & Huili Zhang & Yi Xu, 2021. "The m-Steiner Traveling Salesman Problem with online edge blockages," Journal of Combinatorial Optimization, Springer, vol. 41(4), pages 844-860, May.
    6. Shanxiu Jiang & Li Luo, 2019. "Online in-time service problem with minimal server assignment," Journal of Combinatorial Optimization, Springer, vol. 37(1), pages 114-122, January.

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