Modeling multimodal network design problem under uncertainty conditions: A case study of cement transportation in Iran

goods can have a significant impact on reducing logistics costs and increasing customer satisfaction. Therefore, the purpose of this paper is to develop a mixed integer linear programming model for a rail - road transportation network design. In this model, due to the strategic nature of decision making of modeling the logistics network design, customer demand, as well as transport costs, is uncertain. a bi-objective scenario-based two-stage stochastic programming model is proposed for the design of multimodal transportation network design problem. The first objective function focuses on minimizing costs from the economic point of view and the second objective focuses on reducing risk decision making and incorporates min-max relative regret in in robust optimization framework. In the proposed scenario-based two stage stochastic model, the first-level variables determine the optimal locations for the establishment of multimodal terminals and the second-level variables determine the amount of cargo loaded by each of the multimodal rail-road transportation and road transportation modes. The performance of the proposed mathematical model is analyzed computationally through a real case study for multimodal transportation network design for Cement transportation of Iran. In this study the model decides about the number and location of multimodal terminals from the railway stations in the Iran’s railway network as well as the allocation of load flows and the determination of the amount of cement carried by the road network and the multimodal rail-road network of the country.