This paper studies multiple cross-dockings where the loads are transferred from origins (suppliers) to destinations (customers) through cross-docking facilities. Products are no longer stored in intermediate depots and incoming shipments consolidate based on customer demands and immediately deliver them to their destinations. In this paper, each cross-docking has a covering radius that customers can be served by at least one cross-docking provided. In addition, this paper considers the breakdown of trucks. We present a two-stage model for the location of cross-docking centers and scheduling inbound and outbound trucks in multiple cross-dockings. We work on minimizing the transportation cost in a network by loading trucks in the supplier locations and route them to the customers via cross-docking facilities. The objective in the first stage is to minimize transportation cost of delivering the products from suppliers to open cross-docks and cross-docks to the customers and in the second-stage, the objective is to minimize the makespans of open cross-dockings and the total weighted summation of completion time. Due to the difficulty of obtaining the optimum solution in medium and large-scale problems, we propose four types of metaheuristic algorithms, i.e., genetic, simulated annealing, differential evolution and hybrid algorithms. The result showed that simulated annealing is the best algorithm between four algorithms.
