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.
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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.
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Appendix A: Supplier delivery process constraints
Appendix A: Supplier delivery process constraints
The constraints occurring in the supplier delivery process are formulated as follows.
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.
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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 90, 915–949 (2022). https://doi.org/10.1007/s10472-021-09753-3
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DOI: https://doi.org/10.1007/s10472-021-09753-3