4OR

, Volume 12, Issue 4, pp 359–372 | Cite as

Approximating the length of Chinese postman tours

  • Nathalie Bostel
  • Philippe Castagliola
  • Pierre Dejax
  • André Langevin
Research paper

Abstract

This article develops simple and easy-to-use approximation formulae for the length of a Chinese Postman Problem (CPP) optimal tour on directed and undirected strongly connected planar graphs as a function of the number of nodes and the number of arcs for graphs whose nodes are randomly distributed on a unit square area. These approximations, obtained from a multi-linear regression analysis, allow to easily forecast the length of a CPP optimal tour for various practical combinations of number of arcs and nodes ranging, from 10 to 300 nodes and 15 to 900 arcs.

Keywords

Vehicle routing Logistics Statistics Transport 

Mathematics Subject Classification

90B06 Logistics and transportation 62J02 General nonlinear regression 

References

  1. Beardwood J, Halton J, Hammersley J (1959) The shortest path through many points. Math Proc Cambr Philos Soc 55(4):299–327CrossRefGoogle Scholar
  2. Box G, Cox D (1964) An analysis of transformations. J R Stat Soc Ser B 26(2):211–252Google Scholar
  3. Butsch A, Kalcsics J, Laporte G (2013) Districting for arc routing. Tech. rep, Karlsruhe Institute of TechnologyGoogle Scholar
  4. Christofides N, Eilon S (1969) Expected distances in distribution problems. Oper Res Q 20(4):437–443CrossRefGoogle Scholar
  5. Daganzo C (1984a) The distance travelled to visit \(n\) points with a maximum of \(c\) stops per vehicle: an analytic model and an application. Transp Sci 18(4):331–350CrossRefGoogle Scholar
  6. Daganzo C (1984b) The length of tours in zones of different shapes. Transp Res B Methodol 18(2):135–145CrossRefGoogle Scholar
  7. Daganzo C (2005) Logistics systems analysis. Lecture notes in economics and mathematical systems, vol 36, 4th edn. Springer, BerlinGoogle Scholar
  8. Edmonds J (1965) Paths, trees, and flowers. Can J Math 17:449–467CrossRefGoogle Scholar
  9. Eilon S, Watson-Gandy C, Christofides N (1971) Distribution management: mathematical modelling and practical analysis, vol 36. Hafner, New YorkGoogle Scholar
  10. Geoffrion A (1976) The purpose of mathematical programming is insight not numbers. Interfaces 7(1):81–92CrossRefGoogle Scholar
  11. Guan M (1962) Graphic programming using odd and even points. Chin Math 1:273–277Google Scholar
  12. Hall R (1986) Discrete models/continuous models. Omega Int J Manag Sci 14(3):213–220CrossRefGoogle Scholar
  13. Langevin A, Mbaraga P, Campbell J (1996) Continuous approximation models in freight distribution: an overview. Transp Res Part B Methodol 30(3):163–188CrossRefGoogle Scholar
  14. Muyldermans L (2013) District and sector design for arc routing applications. In: Worshop on arc mouting problems 1 (WARP 1), CopenhagenGoogle Scholar
  15. Nelder J, Mead R (1965) A simplex method for function minimization. Comput J 7(4):308–313CrossRefGoogle Scholar
  16. Newell G (1973) Scheduling, location, transportation and continuum mechanics: some simple approximations to optimization problems. SIAM J Appl Math 25(3):346–360CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Nathalie Bostel
    • 1
  • Philippe Castagliola
    • 1
  • Pierre Dejax
    • 2
  • André Langevin
    • 3
  1. 1.LUNAM UniversitéUniversité de Nantes, IRCCyN UMR CNRS 6597NantesFrance
  2. 2.LUNAM UniversitéÉcole des Mines de Nantes, IRCCyN UMR CNRS 6597NantesFrance
  3. 3.Department of Mathematics and Industrial Engineering, CIRRELTÉcole Polytechnique de MontréalMontrealCanada

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