Skip to main content
SpringerLink
Log in

A Historical Perspective on Arc Routing

  • Chapter
Arc Routing

  • 467 Accesses

Abstract

Arc routing problems consist of determining a least cost traversal of some arcs or edges of a graph, subject to side constraints. Such problems are encountered in a variety of practical situations such as road or street maintenance, garbage collection, mail delivery, school bus routing, meter reading, etc. Details on these applications are provided in Eiselt, Gendreau and Laporte (1995b), in Assad and Golden (1995), and in some chapters of this book. Billions of dollars each year are spent on arc routing operations, mainly by public administrations, and there exists a sizeable potential for savings. In recent years, new advances in optimization techniques and in computer technology have contributed to the dissemination and adoption of sophisticated arc routing software.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 389.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 499.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 499.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Alfa, A.S., and D.Q. Liu. 1988. Postman Routing Problem in a Hierarchical Network. Engineering Optimization 14, 127–138.

    Article  Google Scholar 

  2. Assad, A.A., and B.L. Golden. 1995. Arc Routing Methods and Applications. In Network Routing, M.O. Ball, T.L. Magnanti, C.L. Monma, and G.L. Nemhauser (eds.), Handbooks in Operations Research and Management Science. North-Holland, Amsterdam, 375–483.

    Google Scholar 

  3. Assad, A.A., W.L. Pearn and B.L. Golden. 1987. The Capacitated Chinese Postman Problem: Lower Bounds and Solvable Cases. American Journal of Mathematics and Management Science 7, 63–88.

    MathSciNet  MATH  Google Scholar 

  4. Benavent, E., V. Campos, A. Corberàn and E. Mota. 1992. The Capacitated Arc Routing Problem. Lower Bounds. Networks 22, 669–690.

    Article  MathSciNet  MATH  Google Scholar 

  5. Belenguer, J.M. and E. Benavent. 1998. A Cutting Plane Algorithm for the Capacitated Arc Routing Problem. Submitted for publication.

    Google Scholar 

  6. Beltrami, E.L., and L.D. Bodin. 1974. Networks and Vehicle Routing for Municipal Waste Collection. Networks 4, 65–94.

    Article  MATH  Google Scholar 

  7. Bodin, L.D., and S.J. Kursh. 1978. A Computer-Assisted System for the Routing and Scheduling of Street Sweepers. Operations Research 26, 525–537.

    Article  Google Scholar 

  8. Brucker, P. (1981) The Chinese postman problem for mixed graphs. Proc. Int. Workshop, Lecture Notes in Computer Science 100, 354–366.

    Article  MathSciNet  Google Scholar 

  9. Christofides, N. 1973. The Optimum Traversal of a Graph. Omega 1, 719–732.

    Article  Google Scholar 

  10. Christofides, N. 1976. Worst-Case Analysis of a New Heuristic for the Traveling Salesman Problem. Report No 388, Graduate School of Industrial Administration, Carnegie Mellon University, Pittsburgh.

    Google Scholar 

  11. Christofides, N., E. Benavent, V. Campos, A. Corberán and E. Mota. 1984. An Optimal Method for the Mixed Postman Problem. In System Modelling and Optimization, Lecture Notes in Control and Information Sciences 59, P. Thoft-Christensen (ed.). Springer, Berlin.

    Google Scholar 

  12. Christofides, N., V. Campos, A. Corberàn and E. Mota. 1981. An Algorithm for the Rural Postman Problem. Imperial College Report. I.C.O.R.81.5, London.

    Google Scholar 

  13. Christofides, N., V. Campos, A. Corberàn and E. Mota. 1986. An Algorithm for the Rural Postman Problem on a Directed Graph. Mathematical Programming Study 26, 155–166.

    Article  MATH  Google Scholar 

  14. Corberán, A., R. Marti, and A. Romero. 2000. A Tabu Search Algorithm for the Mixed Rural Postman Problem. Computers & Operations Research 27, 183–203.

    Article  MathSciNet  MATH  Google Scholar 

  15. Corberán, A., and J.M. Sanchis. 1994. A Polyhedral Approach to the Rural Postman Problem. European Journal of Operational Research 79, 95–114.

    Article  MATH  Google Scholar 

  16. Dror, M., H. Stern and P. Trudeau. 1987. Postman Tour on a Graph With Precedence Relation on Arcs. Networks 17, 283–294.

    Article  MathSciNet  MATH  Google Scholar 

  17. Edmonds, J., and E.L. Johnson. 1973. Matching, Euler Tours and the Chinese Postman Problem. Mathematical Programming 5, 88–124.

    Article  MathSciNet  MATH  Google Scholar 

  18. Eiselt, H.A., M. Gendreau, and G. Laporte. 1995. Arc Routing Problems, Part I: The Chinese Postman Problem. Operations Research 43, 231–242.

    Article  MathSciNet  MATH  Google Scholar 

  19. Eiselt, H.A., M. Gendreau, and G. Laporte. 1995. Arc Routing Problems, Part II: The Rural Postman Problem. Operations Research 43, 399–414.

    Article  MathSciNet  MATH  Google Scholar 

  20. Euler, L. 1736. Solutio Problematis ad Geometrica Situs Pertinentis. Commentarii academiae scientarum Petropolitanae 8, 128–140.

    Google Scholar 

  21. Euler, L. (J.R. Newman, Ed.). 1953. Leonhard Euler and the Koenigsberg Bridges. Scientific American 189, 66–70.

    Google Scholar 

  22. Even, S. 1979. Graph Algorithms. Computer Science Press, Rockville.

    Google Scholar 

  23. Fleischner, H. 1990. Eulerian Graphs and Related Topics (Part 1, Volume 1), Annals of Discrete Mathematics 45. North-Holland, Amsterdam.

    Google Scholar 

  24. Fleischner, H. 1991. Eulerian Graphs and Related Topics (Part 1, Volume 2), Annals of Discrete Mathematics 45. North-Holland, Amsterdam.

    Google Scholar 

  25. Fleury, M. 1885. Deux Problèmes de Géométrie de Situation. Journal de Mathématiques Élémentaires, 157.

    Google Scholar 

  26. Ford, L.R. and D.R. Fulkerson. 1962. Flows in Networks. Princeton University Press, Princeton, N.J.

    MATH  Google Scholar 

  27. Frederickson, G.N. 1979. Approximation Algorithms for Some Postman Problem. Journal of the ACM 26, 538–554.

    Article  MathSciNet  MATH  Google Scholar 

  28. Ghiani, G., and G. Improta. 2000. An Algorithm for the Hierarchical Chinese Postman Problem. Operations Research Letters. Forthcoming.

    Google Scholar 

  29. Ghiani, G., and G. Laporte. 2000. A Branch-and-Cut Algorithm for the Undirected Rural Postman Problem. Mathematical Programming. Forthoming.

    Google Scholar 

  30. Golden, B.L., and R.T. Wong. 1981. Capacitated Arc Routing Problems. Networks 11, 305–315.

    Article  MathSciNet  MATH  Google Scholar 

  31. Guan, M. 1962. Graphic Programming Using Odd and Even Points. Chinese Mathematics 1, 273–277.

    Google Scholar 

  32. Haslam, E., and J.R. Wright. 1991. Application of Routing Technologies to Rural Snow and Ice Control. Transportation Research Record 1304, 202–211.

    Google Scholar 

  33. Hertz, A., Laporte, G., and P. Nanchen-Hugo. 1999. Improvement Procedures for the Undirected Rural Postman Problem. INFORMS Journal on Computing 11, 53–62.

    Article  MathSciNet  MATH  Google Scholar 

  34. Hertz, A., Laporte, G., and M. Mittaz. 2000. A Tabu Search Heuristic for the Capacitated Arc Routing Problem. Operations Research. Forthcoming.

    Google Scholar 

  35. Hierholzer, C. 1873. Über die Möglichkeit, einen Linienzug ohne Wiederholung und ohne Unterbrechung zu umfahren. Mathematische Annalen VI, 30–32.

    Article  MathSciNet  Google Scholar 

  36. König, D. 1936. Theorie der endlichen und unendlichen Graphen. Akademische Verlagsgesellschaft, Leipzig.

    Google Scholar 

  37. Lemieux, P.F., and L. Campagna. 1984. The Snow Ploughing Problem Solved by a Graph Theory Algorithm. Civil Engineering Systems 1, 337–341.

    Article  Google Scholar 

  38. Lenstra, J.K., and A.H.G. Rinnooy Kan. 1976. On General Routing Problems. Networks 6, 273–280.

    Article  MathSciNet  MATH  Google Scholar 

  39. Letchford, A.N., and R.W. Eglese. 1998. The Rural Postman Problem with Deadline Classes. European Journal of Operational Research 105, 390–400.

    Article  MATH  Google Scholar 

  40. Letchford, A.N. 1996. Polyhedral Results for Some Constrained Arc-Routing Problems. Ph.D. Thesis, Department of Management Science, Lancaster University.

    Google Scholar 

  41. Lucas, M.É. 1894. Récréations Mathématiques IV. Gauthiers-Villars et fils, Paris.

    Google Scholar 

  42. Manber, U., and S. Israni. 1984. Pierce Point Minimization and Optimal Torch Path Determination in Flame Cutting. Journal of Manufacturing Systems 3, 81–89.

    Article  Google Scholar 

  43. Minieka, E. 1979. The Chinese Postman Problem for Mixed Networks. Management Science 25, 643–648.

    Article  MathSciNet  MATH  Google Scholar 

  44. Nobert, Y., and J.-C. Picard. 1996. An Optimal Algorithm for the Mixed Chinese Postman Problem. Networks 27, 95–108.

    Article  MathSciNet  MATH  Google Scholar 

  45. Orloff, C.S. 1974. A Fundamental Problem in Vehicle Routing. Networks 4, 35–64.

    Article  MathSciNet  MATH  Google Scholar 

  46. Papadimitriou, C.H. 1976. On the Complexity of Edge Traversing. Journal of the ACM 23, 544–554.

    Article  MathSciNet  MATH  Google Scholar 

  47. Pearn, W.-L. 1989. Approximate Solutions for the Capacitated Arc Routing Problem. Computers & Operations Research 16, 589–600.

    Article  MathSciNet  MATH  Google Scholar 

  48. Pearn, W.-L. 1991. Augment-Insert Algorithms for the Capacitated Arc Routing Problem. Computers & Operations Research 18, 189–198.

    Article  MATH  Google Scholar 

  49. Sanchis, J.M. 1990. El Poliedro del Problema del Cartero Rural. Ph.D. Thesis, Universidad de Valencia, Spain.

    Google Scholar 

  50. Stricker, R. 1970. Public Sector Vehicle Routing: The Chinese Postman Problem. M.Sc. Dissertation, Department of Electrical Engineering, Massachusetts Institute of Technology, Cambridge, Mass.

    Google Scholar 

  51. van Aardenne-Ehrenfest, T., and N.G. de Bruijn. 1951. Circuits and Trees in Oriented Linear Graphs. Simon Stevin 28, 203–217.

    MathSciNet  MATH  Google Scholar 

  52. Win, Z. 1987. Contributions to Routing Problems. Doctoral Dissertation, Universität Augsburg, Germany.

    Google Scholar 

  53. Win, Z. 1989. On the Windy Postman Problem in Eulerian Graphs. Mathematical Programming 44, 97–112.

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. University of New Brunswick, Canada

    H. A. Eiselt

  2. Universite de Montréal, Canada

    Gilbert Laporte

Authors
  1. H. A. Eiselt
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Gilbert Laporte
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Department of Management Information Systems, University of Arizona, Tucson, Arizona, 85721, USA

    Moshe Dror

Rights and permissions

Reprints and permissions

Copyright information

© 2000 Springer Science+Business Media New York

About this chapter

Cite this chapter

Eiselt, H.A., Laporte, G. (2000). A Historical Perspective on Arc Routing. In: Dror, M. (eds) Arc Routing. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-4495-1_1

Download citation

  • DOI: https://doi.org/10.1007/978-1-4615-4495-1_1

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4613-7026-0

  • Online ISBN: 978-1-4615-4495-1

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation