An Interval Fuzzy Programming Approach to Solve a Green Intermodal Routing Problem for Timber Transportation Under Uncertain Information

Abstract

This study investigates an intermodal routing problem for transporting wood from a storage yard of the timber harvest area to a timber mill, in which the transfer nodes in the intermodal transportation network have multiple service time windows. To improve the environmental sustainability of timber transportation, a carbon tax policy is employed in the routing to reduce the carbon emissions. Uncertain information on the capacities and carbon emission factors of the transportation activities in the intermodal transportation network is modeled using interval fuzzy numbers to enhance the feasibility of the routing optimization in the actual timber transportation. Based on the above consideration, an interval fuzzy nonlinear optimization model is established to handle the specific routing problem. Model defuzzification and linearization are then conducted to obtain an equivalent formulation that is crisp and linear to make the global optimum solution attainable. A numerical experiment is conducted to verify the feasibility of the proposed model, and it reveals the influence of the optimization level and service time windows on the routing optimization, and it confirms that intermodal transportation is suitable for timber transportation. This experiment also analyzes the feasibility of a carbon tax policy in reducing the carbon emissions of timber transportation, and it finds that the performance of this policy is determined by the optimization level given by the timber mill and is not always feasible in all cases. For the case where a carbon tax policy is infeasible, this study proposes a bi-objective optimization that can use Pareto solutions to balance the economic and environmental objectives as an alternative. The bi-objective optimization further shows the relationship between lowering the transportation costs, reducing the carbon emissions, and enhancing the reliability on capacity and budget by improving the optimization level. The conclusions provide managerial insights that can help the timber mill and intermodal transportation operator organize cost-efficient, low-carbon, and reliable intermodal transportation for timber distribution, and support sustainable forest logistics.