Two-echelon, multi-commodity supply chain network design with mode selection, lead-times and inventory costs

We have formulated the problem as a mixed integer programming model, which integrates the above mentioned decisions and intends to minimize total costs of the network including transportation, lead-times, and inventory holding costs for products, as well as opening and operating costs for facilities. Moreover, we have developed an efficient Lagrangian based heuristic solution algorithm for solving the real-sized problems in reasonable computational time.