Cross-docking is a logistic strategy which can increase rates of consolidation, and reduce distribution and storage costs and delivery times. The optimization literature on cross-docking has mostly focused on the modeling and solution of problems considering a single cross-docking facility. Networks with multiple cross-docks remain rather unexplored and the few papers that deal with the problem do this by simplifying the geometry of the goods. We intend to shorten this gap by proposing a mixed-integer linear programming model for optimizing distribution and delay costs for the transportation of goods in open networks with multiple cross-docks considering the three-dimensional aspects of the cargo. Also, we propose a logic-based Benders decomposition strategy which allow for the solution of larger instances when compared with those that can be handled by a branch-and-cut MIP solver. Experiments showed that the decomposition can handle instances with two times more nodes and five times more boxes than a direct use of the solver. Also, the framework is flexible enough to accommodate other features of practical cases.

交叉对接是一种物流策略，可以提高整合率，并减少分销和存储成本以及交付时间。有关交叉坞站的优化文献主要集中在考虑单个交叉坞站设施的问题的建模和解决方案上。带有多个交叉坞站的网络仍未得到很好的探索，处理该问题的几篇论文通过简化商品的几何形状来做到这一点。我们打算通过提出一种混合整数线性规划模型来缩短这一差距，该模型可以优化在考虑到货物的三维方面的，具有多个交叉码头的开放网络中货物运输的分配和延误成本。还，我们提出了一种基于逻辑的Benders分解策略，与分支剪切MIP求解器可以处理的那些实例相比，它可以解决更大的实例。实验表明，与直接使用求解器相比，分解可以处理的实例的节点数和盒数增加了两倍。而且，该框架具有足够的灵活性以适应实际案例的其他功能。