Skip to main content
SpringerLink
Log in
Book cover

Conference on Algorithms and Discrete Applied Mathematics

CALDAM 2016: Algorithms and Discrete Applied Mathematics pp 176–189Cite as

Approximation Algorithms for Cumulative VRP with Stochastic Demands

  • Conference paper

Part of the Lecture Notes in Computer Science book series (LNTCS,volume 9602)

Abstract

In this paper we give randomized approximation algorithms for stochastic cumulative VRPs for split and unsplit deliveries. The approximation ratios are \(2(1+\alpha )\) and 7 respectively, where \(\alpha \) is the approximation ratio for the metric TSP. The approximation factor is further reduced for trees and paths. These results extend the results in [Technical note - approximation algorithms for VRP with stochastic demands. Operations Research, 2012] and [Routing vehicles to minimize fuel consumption. Operations Research Letters, 2013].

Keywords

  • Approximation algorithms
  • Cumulative VRPs
  • Stochastic demand

This is a preview of subscription content, access via your 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

Learn about institutional subscriptions

References

  1. Altinkemer, K., Gavish, B.: Heuristics for unequal weight delivery problems with a fixed error guarantee. Oper. Res. Lett. 6(4), 149–158 (1987)

    CrossRef  MathSciNet  MATH  Google Scholar 

  2. Archetti, C., Feillet, D., Gendreau, M., Speranza, M.G.: Complexity of the VRP and SDVRP. Transp. Res. Part C. 19(5), 741–750 (2011)

    CrossRef  Google Scholar 

  3. Arora, S.: Polynomial time approximation schemes for euclidean traveling salesman and other geometric problems. J. ACM (JACM) 45(5), 753–782 (1998)

    CrossRef  MathSciNet  MATH  Google Scholar 

  4. Bertsimas, D.: Probabilistic combinatorial optimization problems. Ph.D. thesis, Massachusetts Institute of Technology (1988)

    Google Scholar 

  5. Bertsimas, D.J.: A vehicle routing problem with stochastic demand. Oper. Res. 40(3), 574–585 (1992)

    CrossRef  MathSciNet  MATH  Google Scholar 

  6. Bertsimas, D.J., Simchi-Levi, D.: A new generation of vehicle routing research: robust algorithms, addressing uncertainty. Oper. Res. 44(2), 286–304 (1996)

    CrossRef  MATH  Google Scholar 

  7. Christofides, N.: Worst-case analysis of a new heuristic for the travelling salesman problem. Technical report, DTIC Document (1976)

    Google Scholar 

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

    CrossRef  MathSciNet  MATH  Google Scholar 

  9. Demir, E., Bektaş, T., Laporte, G.: A review of recent research on green road freight transportation. Eur. J. Oper. Res. 237(3), 775–793 (2014)

    CrossRef  MATH  Google Scholar 

  10. Gaur, D.R., Mudgal, A., Singh, R.R.: Routing vehicles to minimize fuel consumption. Oper. Res. Lett. 41(6), 576–580 (2013)

    CrossRef  MathSciNet  MATH  Google Scholar 

  11. Gaur, D.R., Singh, R.R.: Cumulative vehicle routing problem: a column generation approach. In: Ganguly, S., Krishnamurti, R. (eds.) CALDAM 2015. LNCS, vol. 8959, pp. 262–274. Springer, Heidelberg (2015)

    Google Scholar 

  12. Gendreau, M., Laporte, G., Séguin, R.: Stochastic vehicle routing. Eur. J. Oper. Res. 88(1), 3–12 (1996)

    CrossRef  MATH  Google Scholar 

  13. Golden, B.L., Wong, R.T.: Capacitated ARC routing problems. Networks 11(3), 305–315 (1981)

    CrossRef  MathSciNet  MATH  Google Scholar 

  14. Gupta, A., Nagarajan, V., Ravi, R.: Technical note - approximation algorithms for VRP with stochastic demands. Oper. Res. 60(1), 123–127 (2012)

    CrossRef  MathSciNet  MATH  Google Scholar 

  15. Haimovich, M., Rinnooy Kan, A.H.G.: Bounds and heuristics for capacitated routing problems. Math. Oper. Res. 10(4), 527–542 (1985)

    CrossRef  MathSciNet  MATH  Google Scholar 

  16. Kara, I., Kara, B.Y., Yetis, M.K.: Energy minimizing vehicle routing problem. In: Dress, A.W.M., Xu, Y., Zhu, B. (eds.) COCOA 2007. LNCS, vol. 4616, pp. 62–71. Springer, Heidelberg (2007)

    CrossRef  Google Scholar 

  17. Kara, I., Kara, B.Y., Yetis, M.K.: Cumulative vehicle routing problems. In: Vehicle Routing Problem, pp. 85–98 (2008)

    Google Scholar 

  18. Labbé, M., Laporte, G., Mercure, H.: Capacitated vehicle routing on trees. Oper. Res. 39(4), 616–622 (1991)

    CrossRef  MATH  Google Scholar 

  19. Mitchell, J.S.B.: Guillotine subdivisions approximate polygonal subdivisions: a simple polynomial-time approximation scheme for geometric TSP, k-MST, and related problems. SIAM J. Comput. 28(4), 1298–1309 (1999)

    CrossRef  MathSciNet  MATH  Google Scholar 

  20. Stewart, W.R., Golden, B.L.: Stochastic vehicle routing: a comprehensive approach. Eur. J. Oper. Res. 14(4), 371–385 (1983)

    CrossRef  MATH  Google Scholar 

  21. Xiao, Y., Zhao, Q., Kaku, I., Yuchun, X.: Development of a fuel consumption optimization model for the capacitated vehicle routing problem. Comput. Oper. Res. 39(7), 1419–1431 (2012)

    CrossRef  MathSciNet  MATH  Google Scholar 

Download references

Acknowledgements

This work was supported in part by an NSERC Discovery Grant. AM was supported in part by ISIRD grant from IIT Ropar. Part of the work was done while DRG was visiting IIT (BHU) Varanasi and RRS was at IIT Ropar. Authors would like to thank K. K. Shukla for his inputs on the split version of the problem on trees that is noted as a corollary in the paper.

Author information

Authors and Affiliations

  1. Department of Mathematics and Computer Science, University of Lethbridge, 4401 University Drive, Lethbridge, AB, Canada

    Daya Ram Gaur

  2. Department of Computer Science and Engineering, Indian Institute of Technology Ropar, Nangal Road, Rupnagar, 140001, Punjab, India

    Apurva Mudgal

  3. Department of Information Technology, Indian Institute of Information Technology Allahabad, Jhalwa, Allahabad, 211012, Uttar Pradesh, India

    Rishi Ranjan Singh

Authors
  1. Daya Ram Gaur
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Apurva Mudgal
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Rishi Ranjan Singh
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Rishi Ranjan Singh .

Editor information

Editors and Affiliations

  1. Indian Institute of Science, Bangalore, India

    Sathish Govindarajan

  2. Carleton University, Ottawa, ON, Canada

    Anil Maheshwari

Rights and permissions

Reprints and Permissions

Copyright information

© 2016 Springer International Publishing Switzerland

About this paper

Cite this paper

Gaur, D.R., Mudgal, A., Singh, R.R. (2016). Approximation Algorithms for Cumulative VRP with Stochastic Demands. In: Govindarajan, S., Maheshwari, A. (eds) Algorithms and Discrete Applied Mathematics. CALDAM 2016. Lecture Notes in Computer Science(), vol 9602. Springer, Cham. https://doi.org/10.1007/978-3-319-29221-2_15

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-29221-2_15

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-29220-5

  • Online ISBN: 978-3-319-29221-2

  • eBook Packages: Computer ScienceComputer Science (R0)

search

Navigation