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

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.