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On the Maximum Benefit Chinese Postman Problem

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  • Pearn, W. L.
  • Wang, K. H.

Abstract

The Maximum Benefit Chinese Postman Problem (MBCPP) is a practical generalization of the classical Chinese Postman Problem (CPP), which has many real-world applications. In this paper, we consider the MBCPP on undirected networks, and show that the MBCPP is more complex than the Rural Postman Problem (RPP). We present a sufficient condition for the MBCPP solution to cover the whole network, and provide an upper bound. Based on the upper bound, we propose an efficient solution procedure to solve the MBCPP approximately. The proposed algorithm applies the minimal spanning tree and the minimal-cost matching algorithms, which performs well on problems satisfying the sufficient condition.

Suggested Citation

  • Pearn, W. L. & Wang, K. H., 2003. "On the Maximum Benefit Chinese Postman Problem," Omega, Elsevier, vol. 31(4), pages 269-273, August.
    • Handle: RePEc:eee:jomega:v:31:y:2003:i:4:p:269-273
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    References listed on IDEAS

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    1. Malandraki, Chryssi & Daskin, Mark S., 1993. "The maximum benefit Chinese postman problem and the maximum benefit traveling salesman problem," European Journal of Operational Research, Elsevier, vol. 65(2), pages 218-234, March.
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    Cited by:

    1. Ávila, Thais & Corberán, Ángel & Plana, Isaac & Sanchis, José M., 2016. "A branch-and-cut algorithm for the profitable windy rural postman problem," European Journal of Operational Research, Elsevier, vol. 249(3), pages 1092-1101.
    2. Colombi, Marco & Corberán, Ángel & Mansini, Renata & Plana, Isaac & Sanchis, José M., 2017. "The directed profitable rural postman problem with incompatibility constraints," European Journal of Operational Research, Elsevier, vol. 261(2), pages 549-562.
    3. Claudia Archetti & M. Grazia Speranza & Ángel Corberán & José M. Sanchis & Isaac Plana, 2014. "The Team Orienteering Arc Routing Problem," Transportation Science, INFORMS, vol. 48(3), pages 442-457, August.
    4. Summerfield, Nichalin S. & Dror, Moshe & Cohen, Morris A., 2015. "City streets parking enforcement inspection decisions: The Chinese postman’s perspective," European Journal of Operational Research, Elsevier, vol. 242(1), pages 149-160.
    5. Enrique Benavent & Ángel Corberán & Luís Gouveia & Maria Mourão & Leonor Pinto, 2015. "Profitable mixed capacitated arc routing and related problems," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 23(1), pages 244-274, April.

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