Network scheduling problem with cross-docking and loading constraints

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.