Supply-chain management and optimization aims at reducing costs and inventories. One way to increase the supply-chain efficiency is to use cross-docking for consolidating shipments from different suppliers. Cross-docking is a warehousing strategy used in logistics that consists on moving goods from suppliers to customers through a cross-dock facility. The employment of this strategy must be carefully evaluated because sometimes transportation requests can be better directly moved from source-sites to destination. A realistic problem studying the convenience of direct delivery, avoiding some cross-docking transfers, is here discussed. An efficient methodology for finding (near)optimal solutions is also described. The methodology is based on the use of column generation embedded into an incomplete branch-and-price tree. The approach provides (near)optimal solutions by solving the column generation sub-problems without necessarily considering all unexplored nodes in the search-tree. Finally, we show computational results on numerous test problems and on four configurations of the addressed case study. (C) 2015 Elsevier Ltd. All rights reserved.