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This paper presents a new generalized vehicle routing problem with a cross-dock. Basic features of the examined problem are the many-to-many relationship between the suppliers and customers, and the use of different vehicle fleets for performing the inbound and outbound routes. An adaptive memory programming method has been developed coupled with a Tabu Search algorithm. For generating new provisional solutions, elite subroutes with varying lengths are identified from the reference solutions and are used as building blocks, while multiple strategies are applied to maintain an effective interplay between diversification and intensification. Various computational experiments are conducted on existing as well as on new data sets with diverse features, regarding the geographic distribution of the nodes and the density of supplier-customer links. Overall, the proposed method performed very well and new best solutions have been found. Lastly, new insights regarding the impact of split options are reported.

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