One of the most important problem in supply chain management is the design of distribution systems which can reduce the transportation costs and meet the customer's demand at the minimum time. In recent years, cross-docking (CD) centers have been considered as the place that reduces the transportation and inventory costs. Meanwhile, neglecting the optimum location of the centers and the optimum routing and scheduling of the vehicles mislead the optimization process to local optima. Accordingly, in this research, the integrated vehicle routing and scheduling problem in cross-docking systems is modeled. In this new model, the direct shipment from the manufacturers to the customers is also included. Besides, the vehicles are assigned to the cross-dock doors with lower cost. Next, to solve the model, a novel machine-learning-based heuristic method (MLBM) is developed, in which the customers, manufacturers and locations of the cross-docking centers are grouped through a bi-clustering approach. In fact, the MLBM is a filter based learning method that has three stages including customer clustering through a modified bi-clustering method, sub-problems’ modeling and solving the whole model. In addition, for solving the scheduling problem of vehicles in cross-docking system, this paper proposes exact solution as well as genetic algorithm (GA). GA is also adapted for large-scale problems in which exact methods are not efficient. Furthermore, the parameters of the proposed GA are tuned via the Taguchi method. Finally, for validating the proposed model, several benchmark problems from literature are selected and modified according to new introduced assumptions in the base models. Different statistical analysis methods are implemented to assess the performance of the proposed algorithms. 
A novel learning based approach for a new integrated location-routing and scheduling problem within cross-docking considering direct shipment