Skip to main content
SpringerLink
Log in

Shortest path problems with left-side time windows

  • Original Paper
  • Published:
Optimization Letters Aims and scope Submit manuscript

Abstract

“Time is life” is popular now, considering of some optimization models with time windows is necessary. In this paper, we propose a new type of time windows which is left-side time windows, and then consider the shortest path problems with left-side time windows as well as the shortest path problems with multi-left-side time windows. The objectives of these problems are not simply the sum of their weights on such paths, but their travelling cycles which make one day as their travelling time unit. The optimal algorithms are presented for both the shortest path problem with single left-side time windows and the shortest path problem with multi-left-side time windows.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Ali A.: The selection and scheduling of telecommunication calls with time windows. Eur. J. Oper. Res. 167, 243–256 (2005)

    Article  MATH  Google Scholar 

  2. Aminu U.F., Eglese R.W.: A constrained programming approach to the Chinese postman problem with time windows. Comput. Oper. Res. 33, 3423–3431 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  3. Ana O., Lidija Z.S.: A vehicle routing algorithm for the distribution of fresh vegetables and similar perishable food. J. Food Eng. 85, 285–295 (2008)

    Article  Google Scholar 

  4. Azi N., Gendreau M., Potvin J.Y.: An exact algorithm for a single-vehicle routing problem with time windows and multiple routes. Eur. J. Oper. Res. 178, 755–766 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  5. Chaovalitwongse W.A., Kim D.K., Pardalos P.M.: GRASP with a new local search scheme for vehicle routing problems with time windows. J. Comb. Optim. 7, 179–207 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  6. Chen Y.L., Yang H.H.: Finding the first K shortest paths in a time-window network. Comput. Oper. Res. 31, 499–513 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  7. Gentili M.: Visiting a network of services with time constraints. Comput. Oper. Res. 30, 1187–1217 (2003)

    Article  MATH  Google Scholar 

  8. Jean-Yves P., Xu Y., Ilham B.: Vehicle routing and scheduling with dynamic travel times. Comput. Oper. Res. 33, 1129–1137 (2006)

    Article  MATH  Google Scholar 

  9. Marinakis Y., Migdalas A., Pardalos P.M.: Expanding neighborhood search-GRASP for the probabilistic traveling salesman problem. Optim. Lett. 2, 351–361 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  10. Mitrović-Minić S., Krishnamurti R.: The multiple TSP with time windows:vehicle bounds based on precedence graphs. Oper. Res. Lett. 34, 111–120 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  11. Pang K.W.: An adaptive parallel route construction heuristic for the vehicle routing problem with time windows constraints. Expert Syst. Appl. 38, 11939–11946 (2011)

    Article  Google Scholar 

  12. Sancho N.G.F.: Shortest Path Problems with Time Windows on Nodes and Arcs. J. Math. Anal. Appl. 186(3), 643–648 (1994)

    Article  MathSciNet  MATH  Google Scholar 

  13. Sedeño-Noda A., Alcaide D., González-Martin C.: Network flow approaches to pre-emptive open-shop scheduling problems with time windows. Eur. J. Oper. Res. Discrete Optim. 174, 1501–1518 (2006)

    MATH  Google Scholar 

  14. Wang H., Wen Y.: Time-constrained Chinese postman problems. Comput. Math. Appl. 44, 375–387 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  15. Xu J., Yan F., Li S.: Vehicle routing optimization with soft time windows in a fuzzy random environment. Transp. Res. Part E Logist. Transp. Rev. 47, 1075–1091 (2011)

    Article  Google Scholar 

  16. Yang H.H., Chen Y.L.: Finding K shortest looping paths with waiting time in a time-window network. Appl. Math. Model. 30, 458–465 (2006)

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Mathematics and Computer Science, Yunnan Nationalities University, Kunming, 650031, People’s Republic of China

    Tongquan Zhang

  2. Department of Mathematics, Faculty of Science, Kunming University of Science and Technology, Kunming, 650093, People’s Republic of China

    Ying Yin

  3. Department of Mathematics, School of Mathematics and Statistics, Yunnan University, Kunming, 650091, People’s Republic of China

    Jianping Li

Authors
  1. Tongquan Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ying Yin
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Jianping Li
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Tongquan Zhang.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Zhang, T., Yin, Y. & Li, J. Shortest path problems with left-side time windows. Optim Lett 6, 1935–1943 (2012). https://doi.org/10.1007/s11590-011-0390-3

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11590-011-0390-3

Keywords

Search

Navigation