This study explores an operational‐level container routing problem in the road‐rail multimodal service network. In response to the demand for an environmentally friendly transportation, we extend the problem into a green version by using both emission charging method and bi‐objective optimization to optimize the CO₂ emissions in the routing. Two uncertain factors, including capacity uncertainty of rail services and travel time uncertainty of road services, are formulated in order to improve the reliability of the routes. By using the triangular fuzzy numbers and time‐dependent travel time to separately model the capacity uncertainty and travel time uncertainty, we establish a fuzzy chance‐constrained mixed integer nonlinear programming model. A linearization‐based exact solution strategy is designed, so that the problem can be effectively solved by any exact solution algorithm on any mathematical programming software. An empirical case is presented to demonstrate the feasibility of the proposed methods. In the case discussion, sensitivity analysis and bi‐objective optimization analysis are used to find that the bi‐objective optimization method is more effective than the emission charging method in lowering the CO₂ emissions for the given case. Then, we combine sensitivity analysis and fuzzy simulation to identify the best confidence value in the fuzzy chance constraint. All the discussion will help decision makers to better organize the green multimodal transportation.

The implementation of China’s Belt and Road Initiative macro strategy has promoted exchanges and cooperation between China and Europe and countries along the route. The operation of the China Railway Express provides a new transportation platform for China–Europe trade. The sustainable development of the China Railway Express has a great significance in terms of promoting the growth of China–Europe trade and meeting the demand for freight in Asia and Europe. Its time-saving advantage over shipping and its economic advantage over air transport cannot be ignored. This paper is based on the discrete selection model of stochastic utility theory. The paper constructs a multi-logit model based on generalized cost functions, including economics, timeliness, reliability, convenience, safety, and environmental protection. To calculate the market share of the China Railway Express and China–Europe Shipping, the paper conducts a quantitative analysis of the market competitiveness of the China Railway Express. Then, the sensitivity analysis and elastic analysis are carried out on the China Railway Express freight rate, the Chinese road freight rate, the China Railway Express service fee, the China Railway Express travelling speed, the China Railway Express sending operation time at the departure station, the China Railway Express transportation time error, the China Railway Express transportation frequency, and the China Railway Express carbon emissions per unit. Finally, based on the analysis results, suggestions for promoting the sustainable development of the China Railway Express are given.

Bi-objective optimization for multi-modal transportation routing planning problem based on Pareto optimality

With the remarkable development of international trade, global commodity circulation has grown significantly. To accomplish commodity circulation among various regions and countries, multi-modal transportation scheme has been widely adopted by a large number of companies. Meanwhile, according to the relevant statistics, the international logistics costs reach up to approximate 30-50% of the total production cost of the companies. Lowering the transportation costs has become one of the most important sources for a company to raise profits and maintain competitiveness in the global market. Thus, how to optimize freight routes selection to move commodities through the multi-modal transportation network has gained great concern of both the decision makers of the companies and the multi-modal transport operators. In this study, we present a systematical review on the multi-modal transportation freight routing planning problem from the aspects of model formulation and algorithm design. Following contents are covered in this review: (1) distinguishing the formulation characteristics of various optimization models; (2) identifying the optimization models in recent studies according to the formulation characteristics; and (3) discussing the solution approaches that are developed to solve the optimization models, especially the heuristic algorithms.

The sustained and steady development of China’s economy has led to the rapid improvement of the logistics. At the same time, the rise of the e-commerce mode has given rise to a huge demand for express delivery and the express industry has entered a period of boom. Fortunately, China’s high-speed rail network has been networked, and the development of a high-speed rail express train has entered the test stage. After the high-speed rail express train is put into use, it could effectively relieve the pressure of highway transportation and significantly reduce transport pollution. To make better use of high-speed rail transport resources and give full play to its green and efficient advantages, this study established a two-stage model of a high-speed rail express train operation plan. In the first stage, a train candidate set generation model aiming for the minimum total cost of train operation was established that considered the high-speed line carrying capacity, section flow capacity, and OD requirement satisfaction constraints, which reduces the scale of train spare parts and improves the efficiency of solution. In addition, a column generation algorithm was designed to solve the model. In the second stage, an accurate flow distribution model aiming for the optimal economic efficiency was established, and then the high-speed express train operation plan was designed completely. The computational results are encouraging and demonstrate the effectiveness of the model and solution method.

We explore a freight routing problem wherein the aim is to assign optimal routes to move commodities through a multimodal transportation network. This problem belongs to the operational level of service network planning. The following formulation characteristics will be comprehensively considered: (1) multicommodity flow routing; (2) a capacitated multimodal transportation network with schedule-based rail services and time-flexible road services; (3) carbon dioxide emissions consideration; and (4) a generalized costs optimum oriented to customer demands. The specific planning of freight routing is thus defined as a capacitated time-sensitive multicommodity multimodal generalized shortest path problem. To solve this problem systematically, we first establish a node-arc-based mixed integer nonlinear programming model that combines the above formulation characteristics in a comprehensive manner. Then, we develop a linearization method to transform the proposed model into a linear one. Finally, a computational experiment from the Chinese inland container export business is presented to demonstrate the feasibility of the model and linearization method. The computational results indicate that implementing the proposed model and linearization method in the mathematical programming software Lingo can effectively solve the large-scale practical multicommodity multimodal transportation routing problem.