Supply chain management entails controlling and integrating different processes between suppliers and consumers. Distribution strategy is an important process in the supply chain. The distribution strategy used by a company has distinct features according to the type of its products and its production system, for example direct shipment, milk-runs, warehousing and cross docking. The cross docking strategy consists of synchronizing the unloading of inbound loads with the consolidation and loading the outbound loads. This process may involve one or more cross dockings. The objective is to reduce distribution costs by eliminating or reducing the inventory and improving the use of the handling and transport capacity. Moreover, a distribution system may have to consider decisions about the product delivery routes (vehicle routing problem). Although vehicle routing and cross docking decisions may be strongly related, to the best of our knowledge in the literature, there is only one paper dealing with both problems in an integrated way. In this paper, the authors addressed a distribution system of perishable products with only one depot. However, there are practical situations in which two or more depots are interconnected and other features need to be considered. In our project, we will focus on a distribution system based on a retailer network that has two depots operating in accordance with the cross docking strategy. They receive loads from different suppliers, which are unloaded and consolidated in new freights that are immediately delivered directly to their destination stores. In search of a more efficient system, we intend to consider the possibility of delivery by routes in the cross docking problem, i.e., direct delivery and delivery to various customers in a given route are both feasible. This approach aims to reduce transport costs and the length of time goods remain in the depots. We will develop a mathematical model whose solution will provide operational planning for the distribution activities with practical aspects that do not appear in the literature and consider the integrated vehicle routing and cross-docking problem. Both problems are difficult to solve, therefore we will propose a matheuristic and/or heuristic method to solve the integrated problem.
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