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This paper addresses the multi-objective optimization for the road–rail intermodal routing problem that aims to minimize the total costs and carbon dioxide emissions of the routes. To achieve high timeliness of the entire transportation process, pickup and delivery services are simultaneously improved based on the employment of fuzzy soft time windows to measure their service levels. The modeling of road–rail intermodal routing considers fixed schedules of rail and time flexibility of road to match the real-world transportation scenario, in which travel times and carbon dioxide emission factors of road services are considered to be time-varying. To improve the feasibility of the routing, uncertainty of travel times and carbon dioxide emission factors of road services and capacities of rail services are incorporated into the problem. By applying trapezoidal fuzzy numbers to formulate the uncertainty, we propose a fuzzy multi-objective nonlinear optimization model for the routing problem that integrates the truck departure time planning for road services. After processing the model with fuzzy chance-constrained programming and linearization, we obtain an auxiliary equivalent crisp linear model and solve it by designing an interactive fuzzy programming approach with the Bounded Objective Function method. Based on an empirical case study, we demonstrate the validity of the proposed approach and discuss the effects of improving the confidence levels and service levels on the optimization results. The case analysis reveals several managerial insights that help to realize an efficient transportation organization by making effective trade-offs among lowering costs, reducing emissions, improving service levels, and enhancing feasibility.

complex and intelligent systems

Green road–rail intermodal routing problem with improved pickup and delivery services integrating truck departure time planning under uncertainty: an interactive fuzzy programming approach