Skip to main content
SpringerLink
Log in

An Exact Algorithm for the Heterogeneous Fleet Vehicle Routing Problem with Time Windows and Three-Dimensional Loading Constraints

  • Conference paper
  • First Online:
Data and Decision Sciences in Action

Part of the book series: Lecture Notes in Management and Industrial Engineering ((LNMIE))

Abstract

One of our industry partners distributes a multitude of orders of fibre boards all over each of the Australian capital cites, a problem that has been formalised as the Heterogeneous Fleet Vehicle Routing Problem with Time Windows and Three-Dimensional Loading Constraints (3L-HFVRPTW). The fleet consists of two types of trucks with flat loading surfaces and slots for spacers that allow a subdivision into stacks of different sizes. A customer’s delivery can be positioned on more than one partition, but the deliveries have to be loaded in a strict LIFO order. Optimising the truck loads beyond the 75% that can be achieved manually provides value to the company because the deliveries are generally last-minute orders and the customers depend on the deliveries for their contract work on refurbishments. This paper presents an exact integer linear programming model that serves two purposes: (1) providing exact solutions for problems of a modest size as a basis for comparing the quality of heuristic solution methodologies, and (2) for further exploration of various relaxations, stack generation, and decomposition strategies that are based on the ILP model. We solved a few real-life instances by obtaining the exact optimal solution using CPLEX 12.61, whereas previously, the problem was solved manually by staff members of the furniture company.

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 169.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 219.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 219.99
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

References

  1. Akartunali, K., Mak-Hau, V., Tran, T.: A unified mixed-integer programming model for simultaneous fluence weight and aperture optimization in vmat, tomotherapy, and cyberknife. Comput. Oper. Res. 56, 134–150 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  2. Baldacci, R., Hadjiconstantinou, E., Mingozzi, A.: An exact algorithm for the capacitated vehicle routing problem based on a two-commodity network flow formulation. Oper. Res. 52(5), 723–738 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  3. Barkaoui, M., Gendreau, M.: An adaptive evolutionary approach for real-time vehicle routing and dispatching. Comput. Oper. Res. 40(7), 1766–1776 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  4. Bortfeldt, A.: A hybrid algorithm for the capacitated vehicle routing problem with three-dimensional loading constraints. Comput. Oper. Res. 39(9), 2248–2257 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  5. Ceschia, S., Schaerf, A.: Local search for a multi-drop multi-container loading problem. J. Heuristics 19(2), 275–294 (2013)

    Article  Google Scholar 

  6. Finke, G., Claus, A., Gunn, E.: A two-commodity network flow approach to the traveling salesman problem. Congressus Numerantium 41(1), 167–178 (1984)

    MathSciNet  MATH  Google Scholar 

  7. Fleszar, K., Osman, I.H., Hindi, K.S.: A variable neighbourhood search algorithm for the open vehicle routing problem. Eur. J. Oper. Res. 195(3), 803–809 (2009)

    Article  MATH  Google Scholar 

  8. Fukasawa, R., Lysgaard, J., Poggi de Arago, M., Reis, M., Uchoa, E., Werneck, R.: Robust branch-and-cut-and-price for the capacitated vehicle routing problem. In: Bienstock, D., Nemhauser, G. (eds.) Integer Programming and Combinatorial Optimization. Lecture Notes in Computer Science, vol. 3064, pp. 1–15. Springer, Berlin (2004)

    Google Scholar 

  9. Hong, L.: An improved lns algorithm for real-time vehicle routing problem with time windows. Comput. Oper. Res. 39(2), 151–163 (2012)

    Article  MATH  Google Scholar 

  10. Junqueira, L., Morabito, R.: Heuristic algorithms for a three-dimensional loading capacitated vehicle routing problem in a carrier. Comput. Ind. Eng. 88, 110–130 (2015)

    Article  Google Scholar 

  11. Mak, V., Ernst, A.T.: New cutting-planes for the time-and/or precedence-constrained ATSP and directed VRP. Math. Methods Oper. Res. 66(1), 69–98 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  12. Miller, C., Tucker, A., Zemlin, R.A.: Integer programming formulations and travelling salesman problems. J. ACM 7, 326–329 (1960)

    Article  MATH  Google Scholar 

  13. MirHassani, S., Abolghasemi, N.: A particle swarm optimization algorithm for open vehicle routing problem. Expert Syst. Appl. 38(9), 11547–11551 (2011)

    Article  Google Scholar 

  14. Moura, A., Oliveira, J.F.: An integrated approach to the vehicle routing and container loading problems. OR Spectrum 31(4), 775–800 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  15. Rivera, J.C., Afsar, H.M., Prins, C.: Mathematical formulations and exact algorithm for the multitrip cumulative capacitated single-vehicle routing problem. Eur. J. Oper. Res. 249(1), 93–104 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  16. Pace, S., Turky, A., Moser, I., Aleti, A.: Distributing fibre boards: a practical application of the heterogeneous fleet vehicle routing problem with time windows and three-dimensional loading constraints. In: International Conference On Computational Science, pp. 2257–2266. ACM, NY, USA (2015). doi:10.1016/j.procs.2015.05.382

  17. Subramanian, A., Uchoa, E., Ochi, L.S.: A hybrid algorithm for a class of vehicle routing problems. Comput. Oper. Res. 40(10), 2519–2531 (2013)

    Article  MATH  Google Scholar 

  18. Szeto, W., Wu, Y., Ho, S.C.: An artificial bee colony algorithm for the capacitated vehicle routing problem. Eur. J. Oper. Res. 215(1), 126–135 (2011)

    Article  Google Scholar 

  19. Tao, Y., Wang, F.: An effective tabu search approach with improved loading algorithms for the 3l-cvrp. Comput. Oper. Res. 55(C), 127–140 (2015)

    Google Scholar 

  20. Tarantilis, C., Zachariadis, E., Kiranoudis, C.: A hybrid metaheuristic algorithm for the integrated vehicle routing and three-dimensional container-loading problem. IEEE Trans. Intell. Transp. Syst. 10(2), 255–271 (2009)

    Article  Google Scholar 

  21. Toth, P., Vigo, D.: Models, relaxations and exact approaches for the capacitated vehicle routing problem. Discrete Appl. Math. 123(1), 487–512 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  22. Wei, L., Zhang, Z., Lim, A.: An adaptive variable neighborhood search for a heterogeneous fleet vehicle routing problem with three-dimensional loading constraints. IEEE Comput. Intell. Mag. 9(4), 18–30 (2014)

    Article  Google Scholar 

  23. Zachariadis, E.E., Tarantilis, C.D., Kiranoudis, C.T.: The pallet-packing vehicle routing problem. Transp. Sci. 46(3), 341–358 (2012)

    Article  Google Scholar 

  24. Zachariadis, E.E., Tarantilis, C.D., Kiranoudis, C.T.: Designing vehicle routes for a mix of different request types, under time windows and loading constraints. Eur. J. Oper. Res. 229(2), 303–317 (2013)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Information Technology, Deakin University, Waurn Ponds, Geelong, Australia

    Vicky Mak-Hau

  2. Department of Computer Science and Software Engineering, Swinburne University of Technology, Melbourne, Australia

    I. Moser

  3. Faculty of Information Technology, Monash University, Caulfield, Australia

    Aldeida Aleti

Authors
  1. Vicky Mak-Hau
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. I. Moser
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Aldeida Aleti
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Vicky Mak-Hau .

Editor information

Editors and Affiliations

  1. School of Engineering and Information Technology, University of New South Wales, Canberra, Aust Capital Terr, Australia

    Ruhul Sarker

  2. School of Engineering and Information Technology, University of New South Wales, Canberra, Aust Capital Terr, Australia

    Hussein A. Abbass

  3. Data 61, Commonwealth Scientific and Industrial Research Organisation (CSIRO), Melbourne, Victoria, Australia

    Simon Dunstall

  4. Data 61, Commonwealth Scientific and Industrial Research Organisation (CSIRO), Melbourne, Victoria, Australia

    Philip Kilby

  5. Strategic Capability Analysis Department, Defence Science and Technology Group, Canberra, Aust Capital Terr, Australia

    Richard Davis

  6. Department of Defence, War Research Centre, Canberra, Aust Capital Terr, Australia

    Leon Young

Rights and permissions

Reprints and permissions

Copyright information

© 2018 Springer International Publishing AG

About this paper

Cite this paper

Mak-Hau, V., Moser, I., Aleti, A. (2018). An Exact Algorithm for the Heterogeneous Fleet Vehicle Routing Problem with Time Windows and Three-Dimensional Loading Constraints. In: Sarker, R., Abbass, H., Dunstall, S., Kilby, P., Davis, R., Young, L. (eds) Data and Decision Sciences in Action. Lecture Notes in Management and Industrial Engineering. Springer, Cham. https://doi.org/10.1007/978-3-319-55914-8_7

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-55914-8_7

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-55913-1

  • Online ISBN: 978-3-319-55914-8

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation