Skip to main content
SpringerLink
Log in

The VNS Approach for a Consistent Capacitated Vehicle Routing Problem Under the Shift Length Constraints

  • Conference paper
  • First Online:
Mathematical Optimization Theory and Operations Research (MOTOR 2019)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 1090))

Abstract

We consider a new real-world application of vehicle routing planning in a finite time horizon. A company has a set of capacitated vehicles in some depots and must serve a set of clients. There is a frequency for each client stating how often this client must be visited. Time intervals between two consecutive visits must be the same but the visiting schedule is flexible. To get some competitive advantage, the company tries to increase its service quality. To this end, each client should be visited by one driver only. The goal is to minimize the total length of vehicles’ paths over the planning horizon under the frequency constraints and driver shift length constraints. We present an integer linear programming model for this new consistent capacitated vehicle routing problem. To find near-optimal solutions, we design the Variable Neighborhood Search metaheuristic with eleven neighborhood structures. The driver shift length and capacity constraints are penalized and included into the objective function. Empirical results for real test instances from Orenburg region in Russia with up to 900 clients and four weeks in the planning horizon are discussed.

The reported study was funded by RFBR and Novosibirsk region according to the research project N 19-47-540005.

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 39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight 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

References

  1. Aarts, E., Lenstra, J.: Local Search in Combinatorial Optimization. Wiley, New York (1997)

    MATH  Google Scholar 

  2. Ahuja, R.K., Ergun, Ö., Orlin, J.B., Punnen, A.P.: A survey of very large-scale neighborhood search techniques. Discrete Appl. Math. 123(1–3), 75–102 (2002)

    Article  MathSciNet  Google Scholar 

  3. Alekseeva, E., Kochetov, Y., Plyasunov, A.: Complexity of local search for the p-median problem. Eur. J. Oper. Res. 191(3), 736–752 (2008)

    Article  MathSciNet  Google Scholar 

  4. Coene, S., Arnout, A., Spieksma, F.: On a periodic vehicle routing problem. J. Oper. Res. Soc. 61(12), 1719–1728 (2010)

    Article  Google Scholar 

  5. Cordeau, J.F., Gendreau, M., Laporte, G.: A tabu search heuristic for periodic and multi-depot vehicle routing problems. Networks 30(2), 105–119 (1997)

    Article  Google Scholar 

  6. Dantzig, G.B., Ramser, J.H.: The truck dispatching problem. Manage. Sci. 6(1), 80–91 (1959)

    Article  MathSciNet  Google Scholar 

  7. Davydov, I., Kochetov, Y., Carrizosa, E.: VNS heuristic for the \((r|p)\)-centroid problem on the plane. Electron. Notes Discrete Math. 39, 5–12 (2012)

    Article  MathSciNet  Google Scholar 

  8. Davydov, I., Kochetov, Y., Carrizosa, E.: A local search heuristic for the \((r|p)\)-centroid problem in the plane. Comput. OR 52, 334–340 (2014)

    Article  MathSciNet  Google Scholar 

  9. Diakova, Z., Kochetov, Y.: A double VNS heuristic for the facility location and pricing problem. Electron. Notes Discrete Math. 39, 29–34 (2012)

    Article  MathSciNet  Google Scholar 

  10. Gendreau, M., Hertz, A., Laporte, G.: A tabu search heuristic for the vehicle routing problem. Manage. Sci. 40(10), 1276–1290 (1994)

    Article  Google Scholar 

  11. Golden, B.L., Raghavan, S., Wasil, E.A.: The Vehicle Routing Problem: Latest Advances and New Challenges. Springer, US (2008). https://doi.org/10.1007/978-0-387-77778-8

    Book  MATH  Google Scholar 

  12. Groër, C., Golden, B., Wasil, E.: The consistent vehicle routing problem. Manuf. Serv. Oper. Manag. 11(4), 630–643 (2009)

    Article  Google Scholar 

  13. Grover, L.K.: Local search and the local structure of NP-complete problems. Oper. Res. Lett. 12(4), 235–243 (1992)

    Article  MathSciNet  Google Scholar 

  14. Gutin, G.Z., Yeo, A.: Small diameter neighbourhood graphs for the traveling salesman problem: at most four moves from tour to tour. Comput. Oper. Res. 26(4), 321–327 (1999)

    Article  MathSciNet  Google Scholar 

  15. Hemmelmayr, V.C., Doerner, K.F., Hartl, R.F.: A variable neighborhood search heuristic for periodic routing problems. Eur. J. Oper. Res. 195(3), 791–802 (2009)

    Article  Google Scholar 

  16. Irnich S., Toth, P., Vigo, D.: The family of vehicle routing problems.In: Vehicle Routing: Problems, Methods, and Applications, pp. 1–33. Society for Industrial and Applied Mathematics, Philadelphia (2014)

    Google Scholar 

  17. Kernighan, B., Lin, S.: An efficient heuristic procedure for partitioning graphs. Bell Syst. Tech. J. 49(2), 291–307 (1970)

    Article  Google Scholar 

  18. Khmelev, A., Kochetov, Y.: A hybrid VND method for the split delivery vehicle routing problem. Electron. Notes Discrete Math. 47, 5–12 (2015)

    Article  MathSciNet  Google Scholar 

  19. Kochetov, Y., Kononova, P., Paschenko, M.: Formulation space search approach for the teacher/class timetabling problem. Yugoslav J. Oper. Res. 18(1), 1–11 (2008)

    Article  MathSciNet  Google Scholar 

  20. Kochetov, Y., Khmelev, A.: A hybrid algorithm of local search for the heterogeneous fixed fleet vehicle routing problem. J. Appl. Ind. Math. 9(4), 503–518 (2015)

    Article  MathSciNet  Google Scholar 

  21. Kochetov, Y.: Computational bounds for local search in combinatorial optimization. Comput. Math. Math. Phys. 48(5), 747–763 (2008)

    Article  MathSciNet  Google Scholar 

  22. Kononova, P., Kochetov, Y.: The variable neighborhood search for the two machine flow shop problem with a passive prefetch. J. Appl. Ind. Math. 7(1), 54–67 (2013)

    Article  MathSciNet  Google Scholar 

  23. Kovacs, A.A., Golden, B.L., Hartl, R.F., Parragh, S.N.: Vehicle routing problems in which consistency considerations are important: a survey. Networks 63(3), 192–213 (2014)

    Article  Google Scholar 

  24. Kovacs, A.A., Parragh, S.N., Hartl, R.F.: A template-based adaptive large neighborhood search for the consistent vehicle routing problem. Networks 63(1), 60–81 (2014)

    Article  MathSciNet  Google Scholar 

  25. Kulachenko, I., Kononova, P., Kochetov, Y., Kurochkin, A.: The variable neighborhood search for a consistent vehicle routing problem under the shift length constraints. In: Proceedings of the 9-th IFAC Conference Manufacturing Modelling, Management and Control MIM 2019 (2019, Accepted)

    Google Scholar 

  26. Mladenovic, N., Hansen, P.: Variable neighborhood search. Comput. Oper. Res. 24, 1097–1100 (1997)

    Article  MathSciNet  Google Scholar 

  27. Mladenovic, N., Hansen, P.: Developments of variable neighborhood search. In: Ribeiro, C., Hansen, P. (eds.) Essays and Surveys in Metaheuristics, vol. 2, 1st edn, pp. 415–439. Springer, Boston (2002). https://doi.org/10.1007/978-1-4615-1507-4_19

    Chapter  Google Scholar 

  28. Talbi, E.G.: Metaheuristics: From Design to Implementation. Wiley, USA (2009)

    Book  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Novosibirsk State University, Novosibirsk, Russia

    Igor Kulachenko & Polina Kononova

  2. Sobolev Institute of Mathematics SB RAS, Novosibirsk, Russia

    Polina Kononova

Authors
  1. Igor Kulachenko
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Polina Kononova
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Polina Kononova .

Editor information

Editors and Affiliations

  1. Sobolev Institute of Mathematics, Novosibirsk, Russia

    Igor Bykadorov

  2. University of Greenwich, London, UK

    Vitaly Strusevich

  3. University of Aveiro, Aveiro, Portugal

    Tatiana Tchemisova

Rights and permissions

Reprints and permissions

Copyright information

© 2019 Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Kulachenko, I., Kononova, P. (2019). The VNS Approach for a Consistent Capacitated Vehicle Routing Problem Under the Shift Length Constraints. In: Bykadorov, I., Strusevich, V., Tchemisova, T. (eds) Mathematical Optimization Theory and Operations Research. MOTOR 2019. Communications in Computer and Information Science, vol 1090. Springer, Cham. https://doi.org/10.1007/978-3-030-33394-2_5

Download citation

  • DOI: https://doi.org/10.1007/978-3-030-33394-2_5

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-33393-5

  • Online ISBN: 978-3-030-33394-2

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation