Designing a multi-objective mathematical model of routing-locating in multiple cross-dock systems using soft time window

Cross docking is an appropriate method to reduce the warehouse space requirements, inventory management costs, and turnaround times for customer orders .This paper focuses on the optimization of the transportation cost and the planning of the movement of inbound and outbound trucks with multi cross dock and two different types of objective functions of minimizing total cost, minimize the number of transportation into the network inside the supply chain.. Since the paper model is a linear programming integer of zero and since these models belong to the NP-hard class, their solving time severely increases with increasing the problem dimensions. In this paper, to solve the model meta-heuristic algorithms have been used. The algorithms used in solving the model are Multiple Objective Simulated Annealing (MOSA) and Multiple Objective Ant Colony (MOACO) Algorithm. Finally, the model has been solved using two algorithms and computational experiments reported carefully to illustrate and compare designing and computational.