Sharif Digital Repository

A novel bi-objective three-echelon supply chain problem is formulated in this paper in which cross-dock facilities to transport the products are modeled as an M/M/m queuing system. The proposed model is validated using the epsilon constraint method when applied to solve some small-size problems. Since the problem belongs to the class of NP-hard and that it is of a bi-objective type, a multi-objective particle swarm optimization (MOPSO) algorithm with a new solution structure that satisfies all of the constraints is developed to find Pareto solutions. As there is no benchmark available in literature, three other multi-objective meta-heuristic algorithms called non-dominated ranking genetic...