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An integer programming approach for the Chinese postman problem with time-dependent travel time

Author

Listed:
  • Jinghao Sun

    (Northeastern University)

  • Yakun Meng

    (Northeastern University)

  • Guozhen Tan

    (Dalian University of Technology)

Abstract

The Chinese postman problem with time-dependent travel time (CPPTDT) is a generalization of the classical Chinese postman problem (CPP), where the travel time on an arc depends on the time of beginning of travel along it. While CPP and its almost static variants can be solved by integer program successfully, there are very challenging time varying CPP variants, such as CPPTDT, which are difficult to be formulated directly. The first and the only integer programming formulation modeling the time varying CPP directly was presented in the pioneering work of Wang and Wen (Comput Math Appl 44:375–387, 2002), which was unfortunately based on a strong assumption that each basic cycle in the graph must visit the depot. In this work, we propose a new integer programming formulation for the CPPTDT without any unrealistic assumptions, namely, the arc-cycle formulation, which can be viewed as an extended version of the formulation given by Wang and Wen. The constraint set of this formulation can be divided into two parts. The first part has a strong combinatorial structure, which is linear and used to define the polytope of cycle-path alternation sequence (CPAS). We determine the dimension of the CPAS polytope and identify the facet defining inequalities which may be helpful to tighten the integer programming formulation. The second part is closely related to time-dependent travel time and is nonlinear. The linearization is provided to the case when all the travel times are piecewise functions of beginning time, and several strong, valid inequalities are also proposed. The computation results with a cutting plane algorithm using the new cuts are reported on several randomly generated instances.

Suggested Citation

  • Jinghao Sun & Yakun Meng & Guozhen Tan, 2015. "An integer programming approach for the Chinese postman problem with time-dependent travel time," Journal of Combinatorial Optimization, Springer, vol. 29(3), pages 565-588, April.
  • Handle: RePEc:spr:jcomop:v:29:y:2015:i:3:d:10.1007_s10878-014-9755-8
    DOI: 10.1007/s10878-014-9755-8
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    References listed on IDEAS

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    1. Angel Corberán & Gustavo Mejía & José M. Sanchis, 2005. "New Results on the Mixed General Routing Problem," Operations Research, INFORMS, vol. 53(2), pages 363-376, April.
    2. Tagmouti, Mariam & Gendreau, Michel & Potvin, Jean-Yves, 2007. "Arc routing problems with time-dependent service costs," European Journal of Operational Research, Elsevier, vol. 181(1), pages 30-39, August.
    3. Chryssi Malandraki & Mark S. Daskin, 1992. "Time Dependent Vehicle Routing Problems: Formulations, Properties and Heuristic Algorithms," Transportation Science, INFORMS, vol. 26(3), pages 185-200, August.
    4. H. A. Eiselt & Michel Gendreau & Gilbert Laporte, 1995. "Arc Routing Problems, Part I: The Chinese Postman Problem," Operations Research, INFORMS, vol. 43(2), pages 231-242, April.
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    Cited by:

    1. Thibaut Vidal & Rafael Martinelli & Tuan Anh Pham & Minh Hoàng Hà, 2021. "Arc Routing with Time-Dependent Travel Times and Paths," Transportation Science, INFORMS, vol. 55(3), pages 706-724, May.
    2. Merve Kayacı Çodur & Mustafa Yılmaz, 2020. "A time-dependent hierarchical Chinese postman problem," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 28(1), pages 337-366, March.
    3. Jianbin Xin & Benyang Yu & Andrea D’Ariano & Heshan Wang & Meng Wang, 2022. "Time-dependent rural postman problem: time-space network formulation and genetic algorithm," Operational Research, Springer, vol. 22(3), pages 2943-2972, July.

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