Integrated Multi-Level Intermodal Network Design Problem: A Sustainable Approach, Based on Competition of Rail and Road Transportation Systems

Rail transportation system is a green mode that saves energy and reduces the negative impacts. Integrating road and rail systems, known as intermodal transportation, contributes to a sustainable business environment. In this article, based on a sequential game, an integrated multi-level intermodal network design problem (IMINDP) is addressed. On the upper level, a government as the Stackelberg leader with environmental, economic, and social concerns decides whether or not to establish intermodal terminals and rail corridors, considering budget limitation and minimization of both internal and external costs. On the lower level, freight shippers as the Stackelberg followers decide how to transport their freight shipments through rail, road, and intermodal networks, considering rail accessibility, capacity constraints and internal costs minimization. A mathematical programming model is developed to formulate the shippers’ best response to the decisions adopted by the government. Due to NP-hard nature of the problem, a three-level solution approach, based on the Genetic Algorithm (GA) and novel heuristic indicators, is proposed. An exhaustive enumeration algorithm is presented to achieve the optimal solutions as benchmarks for evaluating the solutions obtained by the proposed solution approach. An experimental analysis based on a real-world case indicates the great efficiency of the proposed solution approach. According to the results, a decrease in available budget of infrastructure construction leads to an increase in total external and internal costs imposed on the government. It is also inferred that external transportation costs internalization, as an effective pricing policy, plays a significant role in the strategic network design decisions.