Skip to main content
SpringerLink
Log in

A branch-cut-and-price algorithm for the cumulative capacitated vehicle routing problem

  • Research Paper
  • Published:
4OR Aims and scope Submit manuscript

Abstract

The Cumulative Capacitated Vehicle Routing Problem is a variant of the classic routing problem in which the objective function is to minimize the sum of arrival times to customers. This article proposes a model for the problem that uses position indexes in order to calculate the contribution of the travel time of an edge to the arrival times of the remaining customers on a route. The model is implemented and solved by the branch-cut-and-price (BCP) algorithm in the VRPSolver package. Computational experiments indicate that the proposed BCP model is superior to the literature, being able to solve many open instances. Good results were also obtained for the Multi-Depot variant of the problem.

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

Fig. 1
Fig. 2
Fig. 3

Similar content being viewed by others

Notes

  1. https://www.cpubenchmark.net/compare/Intel-i7-3770-vs-Intel-Core2-Duo-P8700/896vs975.

References

  • Abeledo H, Fukasawa R, Pessoa A, Uchoa E (2013) The time dependent traveling salesman problem: polyhedra and algorithm. Math Program Comput 5(1):27–55

    Article  Google Scholar 

  • Augerat P, Belenguer JM, Benavent E, Corberán A, Naddef D, Rinaldi G (1995) Computational results with a branch and cut code for the capacitated vehicle routing problem. Tech. Rep. 949-M, Université Joseph Fourier, Grenoble, France

  • Baldacci R, Christofides N, Mingozzi A (2008) An exact algorithm for the vehicle routing problem based on the set partitioning formulation with additional cuts. Math Program 115:351–385

    Article  Google Scholar 

  • Baldacci R, Mingozzi A, Roberti R (2011) New route relaxation and pricing strategies for the vehicle routing problem. Oper Res 59(5):1269–1283

    Article  Google Scholar 

  • Blum A, Chalasani P, Coppersmith D, Pulleyblank B, Raghavan P, Sudan M (1994) The minimum latency problem. In: Proceedings of the twenty-sixth annual ACM symposium on theory of computing, pp 163–171

  • Bruni M, Nucamendi-Guillén S, Khodaparasti S, Beraldi P (2019) The cumulative capacitated vehicle routing problem with profits under uncertainty. Advances in optimization and decision science for society. Springer, Services and Enterprises, Berlin, pp 311–322

    Google Scholar 

  • Bulhoes T, Sadykov R, Uchoa E (2018) A branch-and-price algorithm for the minimum latency problem. Comput Oper Res 93:66–78

    Article  Google Scholar 

  • Campbell AM, Vandenbussche D, Hermann W (2008) Routing for relief efforts. Transp Sci 42(2):127–145

    Article  Google Scholar 

  • Christofides N, Eilon S (1969) An algorithm for the vehicle-dispatching problem. J Oper Res Soc 20(3):309–318

    Article  Google Scholar 

  • Christofides N, Mingozzi A, Toth P (1979) The vehicle routing problem. In: Mingozzi A, Toth P, Sandi C, Christofides N (eds) Combinatorial optimization. Wiley, Hoboken

    Google Scholar 

  • Cinar D, Ervural BC, Gakis K, Pardalos PM (2017) Constructive algorithms for the cumulative vehicle routing problem with limited duration. In: Sustainable logistics and transportation, Springer, pp 57–86

  • Contardo C, Martinelli R (2014) A new exact algorithm for the multi-depot vehicle routing problem under capacity and route length constraints. Discrete Optim 12:129–146

    Article  Google Scholar 

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

    Google Scholar 

  • Corona-Gutiérrez K, Cruz ML, Nucamendi-Guillén S, Olivares-Benitez E (2020) The cumulative capacitated vehicle routing problem including priority indexes. In: Green transportation and new advances in vehicle routing problems, Springer, pp 91–129

  • Dunning I, Huchette J, Lubin M (2017) JuMP: a modeling language for mathematical optimization. SIAM Rev 59(2):295–320

    Article  Google Scholar 

  • Irnich S, Desaulniers G (2005) Shortest path problems with resource constraints. In: Desaulniers G, Desrosiers J, Solomon MM (eds) Column Gener. Springer, Boston, pp 33–65

    Chapter  Google Scholar 

  • Jepsen M, Petersen B, Spoorendonk S, Pisinger D (2008) Subset-row inequalities applied to the vehicle-routing problem with time windows. Oper Res 56(2):497–511

    Article  Google Scholar 

  • Kara I, Kara BY, Yetiş MK (2008) Cumulative vehicle routing problems. In: Caric T, Gold H (eds) Vehicle routing problem, IntechOpen, Rijeka, chap 6, pp 85–98, https://doi.org/10.5772/5812

  • Ke L (2018) A brain storm optimization approach for the cumulative capacitated vehicle routing problem. Memet Comput 10(4):411–421

    Article  Google Scholar 

  • Kyriakakis NA, Marinaki M, Marinakis Y (2021) A hybrid ant colony optimization-variable neighborhood descent approach for the cumulative capacitated vehicle routing problem. Comput Oper Res p 105397

  • Lalla-Ruiz E, Voß S (2020) A popmusic approach for the multi-depot cumulative capacitated vehicle routing problem. Optim Lett 14(3):671–691

    Article  Google Scholar 

  • Laporte G, Nobert Y (1983) A branch and bound algorithm for the capacitated vehicle routing problem. Oper-Res-Spektrum 5(2):77–85

    Article  Google Scholar 

  • Liu R, Jiang Z (2019) A hybrid large-neighborhood search algorithm for the cumulative capacitated vehicle routing problem with time-window constraints. Appl Soft Comput 80:18–30

    Article  Google Scholar 

  • Lucena A (1990) Time-dependent traveling salesman problem-the deliveryman case. Networks 20(6):753–763

    Article  Google Scholar 

  • Lysgaard J, Wøhlk S (2014) A branch-and-cut-and-price algorithm for the cumulative capacitated vehicle routing problem. Eur J Oper Res 236(3):800–810

    Article  Google Scholar 

  • Montoya-Torres JR, Franco JL, Isaza SN, Jiménez HF, Herazo-Padilla N (2015) A literature review on the vehicle routing problem with multiple depots. Comput Ind Eng 79:115–129

    Article  Google Scholar 

  • Ngueveu SU, Prins C, Calvo RW (2010) An effective memetic algorithm for the cumulative capacitated vehicle routing problem. Comput Oper Res 37(11):1877–1885

    Article  Google Scholar 

  • Nucamendi-Guillén S, Angel-Bello F, Martínez-Salazar I, Cordero-Franco AE (2018) The cumulative capacitated vehicle routing problem: new formulations and iterated greedy algorithms. Expert Syst Appl 113:315–327

    Article  Google Scholar 

  • Nucamendi-Guillén S, Flores-Díaz D, Olivares-Benitez E, Mendoza A (2020) A memetic algorithm for the cumulative capacitated vehicle routing problem including priority indexes. Appl Sci 10(11):3943

    Article  Google Scholar 

  • Osorio-Mora A, Soto-Bustos M, Gatica G, Palominos P, Linfati R (2021) The multi-depot cumulative vehicle routing problem with mandatory visit times and minimum delayed latency. IEEE Access 9:27210–27225

    Article  Google Scholar 

  • Pecin D, Pessoa A, Poggi M, Uchoa E (2017) Improved branch-cut-and-price for capacitated vehicle routing. Math Program Comput 9(1):61–100

    Article  Google Scholar 

  • Pecin D, Pessoa A, Poggi M, Uchoa E, Santos H (2017) Limited memory rank-1 cuts for vehicle routing problems. Oper Res Lett 45(3):206–209

    Article  Google Scholar 

  • Pessoa A, Sadykov R, Uchoa E, Vanderbeck F (2019) A generic exact solver for vehicle routing and related problems. In: Lodi A, Nagarajan V (eds) Integer programming and combinatorial optimization. Springer International Publishing, Cham, pp 354–369

    Chapter  Google Scholar 

  • Pessoa A, Sadykov R, Uchoa E, Vanderbeck F (2020) A generic exact solver for vehicle routing and related problems. Math Program 183(1):483–523. https://doi.org/10.1007/s10107-020-01523-z

    Article  Google Scholar 

  • Picard JC, Queyranne M (1978) The time-dependent traveling salesman problem and its application to the tardiness problem in one-machine scheduling. Oper Res 26(1):86–110

    Article  Google Scholar 

  • Ramadhan F, Imran A (2019) An adaptation of the record-to-record travel algorithm for the cumulative capacitated vehicle routing problem. In: 2019 IEEE international conference on industrial engineering and engineering management (IEEM), IEEE, pp 238–242

  • Ribeiro GM, Laporte G (2012) An adaptive large neighborhood search heuristic for the cumulative capacitated vehicle routing problem. Comput Oper Res 39(3):728–735

    Article  Google Scholar 

  • Roberti R, Mingozzi A (2014) Dynamic ng-path relaxation for the delivery man problem. Transp Sci 48(3):413–424

    Article  Google Scholar 

  • Sadykov R, Uchoa E, Pessoa A (2021) A bucket graph-based labeling algorithm with application to vehicle routing. Transp Sci 55(1):4–28. https://doi.org/10.1287/trsc.2020.0985

    Article  Google Scholar 

  • Salehipour A, Goos P, Sorensen K, Braysy O (1983) The traveling repairman problem. In: Proceedings of the 21st annual conference of the Belgian operational research society (ORBEL’83)

  • Smiti N, Dhiaf MM, Jarboui B, Hanafi S (2020) Skewed general variable neighborhood search for the cumulative capacitated vehicle routing problem. Int Trans Oper Res 27(1):651–664

    Article  Google Scholar 

  • Sze JF, Salhi S, Wassan N (2017) The cumulative capacitated vehicle routing problem with min–sum and min–max objectives: an effective hybridisation of adaptive variable neighbourhood search and large neighbourhood search. Transp Res Part B Methodol 101:162–184

    Article  Google Scholar 

  • Wang X, Choi TM, Li Z, Shao S (2020) An effective local search algorithm for the multidepot cumulative capacitated vehicle routing problem. IEEE Tran Syst Man Cybern Syst 50(12):4948–4958. https://doi.org/10.1109/TSMC.2019.2938298

    Article  Google Scholar 

Download references

Acknowledgements

The research was partially supported by the following Grants: CAPES – Finance Code 001, CNPq 313601/2018-6, Faperj E-26/202.887/2017, and CAPES PrInt UFF No 88881.

Author information

Authors and Affiliations

  1. Departamento de Engenharia de Produção, Universidade Federal Fluminense, Rua Passo da Pàtria, 156, Bloco E - sala 440, São Domingos, Rio de Janeiro, Niterói, 24210-240, Brazil

    Caio Marinho Damião, João Marcos Pereira Silva & Eduardo Uchoa

Authors
  1. Caio Marinho Damião
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. João Marcos Pereira Silva
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Eduardo Uchoa
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to João Marcos Pereira Silva.

Ethics declarations

Conflict of interest

The authors declare that they have no conflict of interest.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Appendices

Appendix

Some optimal solutions

We depict two optimal solutions for the sake of curiosity. The edges are represented with a line width that is proportional to the number of customers that remain to be visited in the route, reflecting the cost of that edge in the solution.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Damião, C.M., Silva, J.M.P. & Uchoa, E. A branch-cut-and-price algorithm for the cumulative capacitated vehicle routing problem. 4OR-Q J Oper Res 21, 47–71 (2023). https://doi.org/10.1007/s10288-021-00498-7

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10288-021-00498-7

Keywords

Mathematics Subject Classification

Search

Navigation