Skip to main content
SpringerLink
Log in

Competitive Analysis for the On-line Truck Transportation Problem

  • Published:
Journal of Global Optimization Aims and scope Submit manuscript

Abstract

In this paper, the on-line k-truck transportation problem (k-OLTTP) whose objects are to be transported between the vertices of a given graph on which there are k mobile trucks to be scheduled is proposed. It is motivated by the research concerning on-line k-truck problem and on-line transportation problem. The goal is to minimize the makespan which is consumed to complete some on-line request sequence. Some preliminary knowledge is introduced and the model of k-OLTTP is established firstly. Two versions of a special case of k-OLTTP, namely 1-OLTTP, have been studied and some results are obtained. For the first version, Open-1-OLTTP, a lower bound of competitive ratio 2 is presented and two optimal on-line algorithms, Reschedule Strategy (RS) and Lay Over Strategy (LOS) respectively, are analyzed. For the second version, Close-1-OLTTP, a lower bound of competitive ratio \({1 \over 2} + {1 \over 2} \cdot \sqrt{1 + {4\over\theta}}\), where θ is the ratio between the time consumed by the loaded truck and the empty truck to travel the same distance, is also developed and on-line algorithms RS and LOS are proved to have competitive ratio 2. Finally, some interesting remarks concerning OLTTP and its future research are discussed.

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. W.M. Ma Y.F. Xu K.L. Wang (2001) ArticleTitleOn-line k-truck problem and its competitive algorithm Journal of Global Optimization 21 IssueID1 15–25 Occurrence Handle10.1023/A:1017982528216

    Article  Google Scholar 

  2. Ascheuer N., Krumke S.O., Rambau J. (1999), The on-line transportation problem: competitive scheduling of elevators. Preprint No. 98/24, Konrad-Zuse für Informationstechnik, Berlin(ZIB).

  3. Ascheuer N., Grotschel M., Krumke S.O., Rambau J. (1998), Combinatorial online optimization. In: Proc. of the International Conference of Operations Research (OR’98), Zurich Springer.

  4. W.M. Ma Y.F. Xu J. You J. Liu K.L. Wang (2004) ArticleTitleOn the k-Truck scheduling problem International Journal of Foundations of Computer Science 15 IssueID1 127–141 Occurrence Handle10.1142/S0129054104002340

    Article  Google Scholar 

  5. Beck, J.C., Prosser P. and Selensky E. (2002), Graph transformations for the vehicle routing and job shop scheduling problems. ICGT 2002, LNCS 2505, 60–74.

  6. Blaewicz, J., Domschke, W. and Pesch E. (1996), The job shop scheduling problem: conventional and new solution techniques, European Journal of Operational Research, 93, 1–33.

    Google Scholar 

  7. B. Chen A.P.A. Vestjens (1997) ArticleTitleScheduling on identical machines: how good is LPT in an on-line setting? Operations Research Letter 21 165–169 Occurrence Handle10.1016/S0167-6377(97)00040-0

    Article  Google Scholar 

  8. D.D. Sleator R.E. Tarjan (1985) ArticleTitleAmortized efficiency of list update and paging rules Communication of the ACM 28 202–208 Occurrence Handle10.1145/2786.2793

    Article  Google Scholar 

  9. M.M. Karlin L. Rudlph D.D. Sleator (1988) ArticleTitleCompetitive snoopy caching Algorithmica 3 79–119 Occurrence Handle10.1007/BF01762111

    Article  Google Scholar 

  10. Manasse M.S., McGeoch L.A., Sleator D.D. (1988), Competitive algorithms for on-line problems. In: Proc. 20th Annual ACM Symp. on Theory of Computing, 322–333.

  11. A. Borodin N. Linial M. Sake (1992) ArticleTitleAn optimal on-line algorithm for metrical task systems Journal of ACM 39 745–763 Occurrence Handle10.1145/146585.146588

    Article  Google Scholar 

  12. Ben-David S., Borodin A., Karp R.M., Tardos G., Wigderson A. (1990), On the power of randomization in on-line algorithms. In: Proc. of the 22nd Annual ACM Symp. on Theory of Computing, 379–386.

  13. W.M. Ma J. You Y.F. Xu J. Liu K.L. Wang (2002) ArticleTitleOn the on-line number of snacks problem Journal of Global Optimization 24 IssueID4 449–462 Occurrence Handle10.1023/A:1021253103047

    Article  Google Scholar 

  14. Albers, S. and Bals, H. (2003), Dynamic TCP acknowledgement: Penalizing long delays. In: Proc. 14th ACM-SIAM Symposium on Discrete Algorithms, 47–55.

  15. Bartal, Y and Mendel, M. (2004), Randomized Algorithms for the k-Server Problem in Growth Rate Bounded Metric Spaces. In: Proc. of the 15th ACM-SIAM Symp. on Discrete Algorithms, January 2004.

  16. Borodin A. El-Yaniv R. (1998), Online Computation and Competitive Analysis, Cambridge University Press.

Download references

Author information

Authors and Affiliations

  1. School of Economics and Management, Tsinghua University, Beijing, 100084, P. R. China

    Weimin Ma & Guoqing Chen

  2. Department of Computing, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong

    Weimin Ma, James N. K. Liu & Jane You

Authors
  1. Weimin Ma
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. James N. K. Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Guoqing Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Jane You
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to James N. K. Liu.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Ma, W., Liu, J.N.K., Chen, G. et al. Competitive Analysis for the On-line Truck Transportation Problem. J Glob Optim 34, 489–502 (2006). https://doi.org/10.1007/s10898-005-2849-1

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10898-005-2849-1

Keywords

Search

Navigation