We’re sorry, something doesn't seem to be working properly.

Please try refreshing the page. If that doesn't work, please contact support so we can address the problem.

Two-phase Matheuristic for the vehicle routing problem with reverse cross-docking | SpringerLink

Two-phase Matheuristic for the vehicle routing problem with reverse cross-docking

Abstract

Cross-dockingis a useful concept used by many companies to control the product flow. It enables the transshipment process of products from suppliers to customers. This research thus extends the benefit of cross-docking with reverse logistics, since return process management has become an important field in various businesses. The vehicle routing problem in a distribution network is considered to be an integrated model, namely the vehicle routing problem with reverse cross-docking (VRP-RCD). This study develops a mathematical model to minimize the costs of moving products in a four-level supply chain network that involves suppliers, cross-dock, customers, and outlets. A matheuristic based on an adaptive large neighborhood search (ALNS) algorithm and a set partitioning formulation is introduced to solve benchmark instances. We compare the results against those obtained by optimization software, as well as other algorithms such as ALNS, a hybrid algorithm based on large neighborhood search and simulated annealing (LNS-SA), and ALNS-SA. Experimental results show the competitiveness of the matheuristic that is able to obtain all optimal solutions for small instances within shorter computational times. For larger instances, the matheuristic outperforms the other algorithms using the same computational times. Finally, we analyze the importance of the set partitioning formulation and the different operators.

This is a preview of subscription content, access via your institution.

References

  1. 1.

    Farahani, R.Z., Rezapour, S., Drezner, T., Fallah, S.: Competitive supply chain network design: an overview of classifications, models, solution techniques and applications. Omega 45, 92–118 (2014)

    Article  Google Scholar 

  2. 2.

    Rezaei, S., Kheirkhah, A.: Applying forward and reverse cross-docking in a multi-product integrated supply chain network. Prod. Eng. 11(4–5), 494–509 (2017)

    Google Scholar 

  3. 3.

    Belle, J.V., Valckenaers, P., Cattrysse, D.: Cross-docking: state of the art. Omega 40(6), 827–846 (2012)

    Article  Google Scholar 

  4. 4.

    Lee, Y.H., Jung, J.W., Lee, K.M.: Vehicle routing scheduling for cross-docking in the supply chain. Comput. Ind. Eng. 51(2), 247–256 (2006)

    Article  Google Scholar 

  5. 5.

    Liao, C.J., Lin, Y., Shih, S.C.: Vehicle routing with cross-docking in the supply chain. Expert Syst. Appl. 37(10), 6868–6873 (2010)

    Article  Google Scholar 

  6. 6.

    Yu, V.F., Jewpanya, P., Redi, A.A.N.P.: Open vehicle routing problem with cross-docking. Comput. Ind. Eng. 94, 6–17 (2016)

    Article  Google Scholar 

  7. 7.

    Gunawan, A., Widjaja, A.T., Vansteenwegen, P., Yu, V.F.: Adaptive large neighborhood search for vehicle routing problem with cross-docking. In: 2020 IEEE Congress on Evolutionary Computation (CEC), pp. 1–8 (2020)

  8. 8.

    Gunawan, A., Widjaja, A.T., Vansteenwegen, P., Yu, V.F.: A matheuristic algorithm for the vehicle routing problem with cross-docking. Appl. Soft Comput., vol. 103 (2021)

  9. 9.

    Gunawan, A., Widjaja, A.T., Vansteenwegen, P., Yu, V.F.: A matheuristic algorithm for solving the vehicle routing problem with cross-docking. In: Kotsireas, I.S., Pardalos, P.M. (eds.) Proceedings of the 2020 Learning and Intelligent Optimization Conference (LION) 2020, Lecture Notes in Computer Science, vol. 12096, pp. 9–15. Springer (2020)

  10. 10.

    Kaboudani, Y., Ghodsypour, S.H., Kia, H., Shahmardan, A.: Vehicle routing and scheduling in cross docks with forward and reverse logistics. Operational Research 20(3), 1589–1622 (2020)

    Article  Google Scholar 

  11. 11.

    Rogers, D.S., Tibben-Lembke, R.S.: An examination of reverse logistics practices. J. Bus. Logist. 22(2), 129–148 (2001)

    Article  Google Scholar 

  12. 12.

    Shen, B., Li, Q.: Impacts of returning unsold products in retail outsourcing fashion supply chain: a sustainability analysis. Sustainability 7(2), 1172–1185 (2015)

    Article  Google Scholar 

  13. 13.

    Widjaja, A.T., Gunawan, A., Jodiawan, P., Yu, V.F.: Incorporating a reverse logistics scheme in a vehicle routing problem with cross-docking network: A modelling approach. In: Proceedings of the 2020 IEEE 7th International Conference on Industrial Engineering and Applications (ICIEA), pp. 854–858 (2020)

  14. 14.

    Ruiz-Benítez, R., Ketzenberg, M., van der Laan, E.A.: Managing consumer returns in high clockspeed industries. Omega 43, 54–63 (2014)

    Article  Google Scholar 

  15. 15.

    Zuluaga, J.P.S., Thiell, M., Perales, R.C.: Reverse cross-docking. Omega 66, 48–57 (2017)

    Article  Google Scholar 

  16. 16.

    Gunawan, A., Widjaja, A.T., Vansteenwegen, P., Yu, V.F.: Vehicle routing problem with reverse cross-docking: An adaptive large neighborhood search algorithm. In: Lalla-Ruiz, E, Mes, M, Voß, S (eds.) Proceedings of the 11th International Conference on Computational Logistics (ICCL) 2020, Lecture Notes in Computer Science, vol. 12433, pp. 167–182. Springer (2020)

  17. 17.

    Gunawan, A., Widjaja, A.T., Gan, B., Yu, V.F., Jodiawan, P.: Vehicle routing problem for multi-product cross-docking. In: Proceedings of the 10th International Conference on Industrial Engineering and Operations Management (IEOM) 2020, pp. 66–77 (2020)

  18. 18.

    Wen, M., Larsen, J., Clausen, J., Cordeau, J.F., Laporte, G.: Vehicle routing with cross-docking. Journal of the Operational Research Society 60(12), 1708–1718 (2009)

    Article  Google Scholar 

  19. 19.

    Tarantilis, C.D.: Adaptive multi-restart tabu search algorithm for the vehicle routing problem with cross-docking. Optim. Lett. 7(7), 1583–1596 (2013)

    MathSciNet  Article  Google Scholar 

  20. 20.

    Grangier, P., Gendreau, M., Lehuédé, F., Rousseau, L.-M.: A matheuristic based on large neighborhood search for the vehicle routing problem with cross-docking. Computers & Operations Research 84, 116–126 (2017)

    MathSciNet  Article  Google Scholar 

  21. 21.

    Morais, V.W.C., Mateus, G.R., Noronha, T.F.: Iterated local search heuristics for the vehicle routing problem with cross-docking. Expert Syst. Appl. 41 (16), 7495–7506 (2014)

    Article  Google Scholar 

  22. 22.

    Wang, J., Jagannathan, A.K.R., Zuo, X., Murray, C.C.: Two-layer simulated annealing and tabu search heuristics for a vehicle routing problem with cross docks and split deliveries. Computers & Industrial Engineering 112, 84–98 (2017)

    Article  Google Scholar 

  23. 23.

    Dondo, R., Cerdá, J.: The heterogeneous vehicle routing and truck scheduling problem in a multi-door cross-dock system. Computers & Chemical Engineering 76, 42–62 (2015)

    Article  Google Scholar 

  24. 24.

    Grangier, P., Gendreau, M., Lehuédé, F., Rousseau, L.-M.: The vehicle routing problem with cross-docking and resource constraints. J. Heuristics, pp. 1–31 (2019)

  25. 25.

    Baniamerian, A., Bashiri, M., Tavakkoli-Moghaddam, R.: Modified variable neighborhood search and genetic algorithm for profitable heterogeneous vehicle routing problem with cross-docking. Appl. Soft Comput. 75, 441–460 (2019)

    Article  Google Scholar 

Download references

Acknowledgements

This research is supported by the Singapore Ministry of Education (MOE) Academic Research Fund (AcRF) Tier 1 grant. The work of Vincent F. Yu was partially supported by the Ministry of Science and Technology of Taiwan under grant MOST 108-2221-E-011-051-MY3 and the Center for Cyber-Physical System Innovation from The Featured Areas Research Center Program within the framework of the Higher Education Sprout Project by the Ministry of Education (MOE) in Taiwan.

Author information

Affiliations

Authors

Corresponding author

Correspondence to Aldy Gunawan.

Additional information

Publisher’s note

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

Appendix A: Supplier delivery process constraints

Appendix A: Supplier delivery process constraints

The constraints occurring in the supplier delivery process are formulated as follows.

$$ L \sum\limits_{v \in V} \sum\limits_{i \in S \cup 0, i \neq j} x_{ij}^{\prime\prime\prime v} \geq \sum\limits_{i \in O} r_{ij}^{\prime\prime} + \sum\limits_{i \in C} r_{ij}^{\prime} - \sum\limits_{v \in V} \sum\limits_{i \in O} A_{ij}^{\prime\prime v} \forall j \in S $$
(75)
$$ \sum\limits_{i \in O} r_{ij}^{\prime\prime} + \sum\limits_{i \in C} r_{ij}^{\prime} - \sum\limits_{v \in V} \sum\limits_{i \in O} A_{ij}^{\prime\prime v} \geq \epsilon - L \Bigg(1-\sum\limits_{v \in V} \sum\limits_{i \in S \cup 0, i \neq j} x_{ij}^{\prime\prime\prime v}\Bigg) \forall j \in S $$
(76)
$$ \sum\limits_{i \in S} \sum\limits_{j \in S, j \neq i} x_{ij}^{\prime\prime\prime v} \leq L \sum\limits_{j \in S} x_{0j}^{\prime\prime\prime v} \forall v \in V \\ $$
(77)
$$ \sum\limits_{i \in S \cup 0, i \neq l} x_{il}^{\prime\prime\prime v} = \sum\limits_{j \in S \cup 0, j \neq l} x_{lj}^{\prime\prime\prime v} \forall l \in S, \forall v \in V \\ $$
(78)
$$ \sum\limits_{v \in V} \sum\limits_{i \in S \cup 0} x_{ij}^{\prime\prime\prime v} \leq 1 \forall j \in S \\ $$
(79)
$$ \sum\limits_{v \in V} A_{j}^{\prime\prime\prime v} \geq \Bigg(\sum\limits_{i \in O} r_{ij}^{\prime\prime} + \sum\limits_{i \in C} r_{ij}^{\prime} - \sum\limits_{v \in V} \sum\limits_{i \in O} A_{ij}^{\prime\prime v}\Bigg) - L \Bigg(1 - \sum\limits_{v \in V} \sum\limits_{i \in S \cup 0} x_{ij}^{\prime\prime\prime v}\Bigg) \forall j \in S \\ $$
(80)
$$ \sum\limits_{v \in V} A_{j}^{\prime\prime\prime v} \leq \Bigg(\sum\limits_{i \in O} r_{ij}^{\prime\prime} + \sum\limits_{i \in C} r_{ij}^{\prime} - \sum\limits_{v \in V} \sum\limits_{i \in O} A_{ij}^{\prime\prime v}\Bigg) + L \Bigg(1 - \sum\limits_{v \in V} \sum\limits_{i \in S \cup 0} x_{ij}^{\prime\prime\prime v}\Bigg) \forall j \in S \\ $$
(81)
$$ L \sum\limits_{i \in S \cup 0, i \neq j} x_{ij}^{\prime\prime\prime v} \geq A_{j}^{\prime\prime\prime v} \forall j \in S, \forall v \in V \\ $$
(82)
$$ q_{0}^{\prime\prime\prime v} = \sum\limits_{j \in S} A_{j}^{\prime\prime\prime v} \forall v \in V \\ $$
(83)
$$ q_{i}^{\prime\prime\prime} \geq q_{0}^{\prime\prime\prime v} - A_{i}^{\prime\prime\prime v} - L (1-x_{0i}^{\prime\prime\prime v}) \forall i \in S, \forall v \in V \\ $$
(84)
$$ q_{i}^{\prime\prime\prime} \leq q_{0}^{\prime\prime\prime v} - A_{i}^{\prime\prime\prime v} + L (1-x_{0i}^{\prime\prime\prime v}) \forall i \in S, \forall v \in V \\ $$
(85)
$$ q_{j}^{\prime\prime\prime} \geq q_{i}^{\prime\prime\prime} - A_{j}^{\prime\prime\prime v} - L (1 - x_{ij}^{\prime\prime\prime v}) \forall i,j \in S, \forall v \in V \\ $$
(86)
$$ q_{j}^{\prime\prime\prime} \leq q_{i}^{\prime\prime\prime} - A_{j}^{\prime\prime\prime v} + L (1 - x_{ij}^{\prime\prime\prime v}) \forall i,j \in S, \forall v \in V \\ $$
(87)
$$ q_{0}^{\prime\prime\prime v} \leq q \forall v \in V \\ $$
(88)
$$ u_{j}^{\prime\prime\prime} \geq u_{i}^{\prime\prime\prime} + 1 - |S|\Bigg(1-\sum\limits_{v \in V} x_{ij}^{\prime\prime\prime v}\Bigg) \forall i,j \in S \\ $$
(89)

Constraints (75) and (76) ensure that if either there exist outlets’ returned products or there are some returned products from customers that are not sent to any outlet (including the defective products), then the supplier that supplies the product will be visited. Constraint (77) ensures that for every vehicle used in this process, it always starts its trip from the cross-dock. Constraint (78) ensures the outflow and inflow of a vehicle in each supplier node. Constraint (79) ensures that each supplier is visited at most once. The amount of products delivered to each supplier is calculated in constraints (80) and (81), while ensuring no split delivery occurs as in constraint (82). Constraints (83) to (87) track the total load inside a vehicle. Constraint (88) ensures that the total amount of products delivered to all suppliers in a vehicle does not exceed vehicle capacity. Constraint (89) is the sub-tour elimination constraint.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Gunawan, A., Widjaja, A.T., Vansteenwegen, P. et al. Two-phase Matheuristic for the vehicle routing problem with reverse cross-docking. Ann Math Artif Intell (2021). https://doi.org/10.1007/s10472-021-09753-3

Download citation

Keywords

  • Vehicle routing problem
  • Cross-docking
  • Reverse logistics
  • Matheuristic
  • Adaptive large neighborhood search

Mathematics Subject Classification (2010)

  • 90B06
  • 90C59