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Online traveling salesman problem with deadlines and service flexibility

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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.

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Notes

  1. By acceptance, we consider the situation that the online server starts moving towards the accepted request when the request is released, but with possibility to detour during its movement.

  2. Offline half line is the half line where offline server locates.

  3. Online half line is the half line where online server locates.

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Acknowledgments

The authors would like to acknowledge the financial support from Grants of National Science Foundation of China (Nos. 71071123 and 60921003), and Grants of Changjiang Scholars and Innovative Research Team in University (No. IRT1173).

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Authors and Affiliations

  1. School of Management, Xi’an Jiaotong University, Xi’an , 710049, China

    Xingang Wen, Yinfeng Xu & Huili Zhang

  2. Tilburg CentER, Tilburg University, P.O. Box 90153, 5000 LE , Tilburg, The Netherlands

    Xingang Wen

  3. State Key Lab for Manufacturing Systems Engineering, Xi’an , 710049, China

    Yinfeng Xu & Huili Zhang

Authors
  1. Xingang Wen
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  2. Yinfeng Xu
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  3. Huili Zhang
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Correspondence to Xingang Wen.

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Wen, X., Xu, Y. & Zhang, H. Online traveling salesman problem with deadlines and service flexibility. J Comb Optim 30, 545–562 (2015). https://doi.org/10.1007/s10878-013-9654-4

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  • DOI: https://doi.org/10.1007/s10878-013-9654-4

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