Developing a cross-docking network design model under uncertain environment

Cross-docking is a logistic concept, which plays an important role in supply chain management by decreasing inventory holding, order packing, transportation costs and delivery time. Paying attention to these concerns, and importance of the congestion in cross docks, we present a mixed-integer model to optimize the location and design of cross docks at the same time to minimize the total transportation and operating costs. The model combines queuing theory for design aspects, for that matter, we consider a network of cross docks and customers where two M/M/c queues have been represented to describe operations of indoor trucks and outdoor trucks in each cross dock. To prepare a perfect illustration for performance of the model, a real case also has been examined that indicated effectiveness of the proposed model.