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The Chinese Postman Problem for Mixed Networks

Author

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  • Edward Minieka

    (University of Illinois at Chicago Circle)

Abstract

The Chinese postman problem is to find a least cost way to traverse each arc of a network at least once and to return to the vertex from which you started. Diverse problems such as the routing of road crews, police patrol scheduling, garbage collection and the programming of computer map printers can be modelled as Chinese postman problems. This paper surveys available solution techniques for the Chinese postman problem for totally undirected networks (when all streets are two-way streets) and for totally directed networks (when all streets are one-way streets). A known solution technique for networks with both directed and undirected arcs (both one-way and two-way streets) in which the degree of each vertex is an even number is also reviewed. A solution technique for these mixed networks in which some vertices have odd degree is presented. This technique is based on the before mentioned technique and requires the solution of a minimum cost flow problem on a network that is an extension of the original network. Some of the additional arcs in this network have gain factors (i.e., the flow leaving these arcs equals the flow entering times the gain factor) and the flows are required to be integer valued.

Suggested Citation

  • Edward Minieka, 1979. "The Chinese Postman Problem for Mixed Networks," Management Science, INFORMS, vol. 25(7), pages 643-648, July.
    • Handle: RePEc:inm:ormnsc:v:25:y:1979:i:7:p:643-648
    DOI: 10.1287/mnsc.25.7.643
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    Cited by:

    1. Abdullah Rasul & Jaho Seo & Shuoyan Xu & Tae J. Kwon & Justin MacLean & Cody Brown, 2022. "Optimization of Snowplow Routes for Real-World Conditions," Sustainability, MDPI, vol. 14(20), pages 1-17, October.
    2. Benavent, Enrique & Carrotta, Alessandro & Corberan, Angel & Sanchis, Jose M. & Vigo, Daniele, 2007. "Lower bounds and heuristics for the Windy Rural Postman Problem," European Journal of Operational Research, Elsevier, vol. 176(2), pages 855-869, January.
    3. Frank Plastria, 2009. "Asymmetric distances, semidirected networks and majority in Fermat–Weber problems," Annals of Operations Research, Springer, vol. 167(1), pages 121-155, March.
    4. Kampars Janis & Shmite Elina, 2014. "STORN: Solution to Traversal of Road Networks/ RCTI: izbraucama ceļu tīkla risinājums/ РПДС: Решение дорожных сетей для проезда," Information Technology and Management Science, Sciendo, vol. 17(1), pages 74-80, December.
    5. R Baldacci & E Bartolini & G Laporte, 2010. "Some applications of the generalized vehicle routing problem," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 61(7), pages 1072-1077, July.
    6. Enrique Benavent & Ángel Corberán & José Sanchis, 2010. "A metaheuristic for the min–max windy rural postman problem with K vehicles," Computational Management Science, Springer, vol. 7(3), pages 269-287, July.
    7. Irnich, Stefan, 2008. "Solution of real-world postman problems," European Journal of Operational Research, Elsevier, vol. 190(1), pages 52-67, October.

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