Modeling a Carbon-Efficient Road–Rail Intermodal Routing Problem with Soft Time Windows in a Time-Dependent and Fuzzy Environment by Chance-Constrained Programming

Abstract

This study explores a road–rail intermodal routing problem. To improve the carbon efficiency of transportation, reducing CO2 emissions is considered by the routing. Soft time windows are incorporated into the routing to optimize the timeliness of the first-mile pickup and last-mile delivery services in intermodal transportation. The routing is further modeled in a time-dependent and fuzzy environment where the average truck speeds of the road depend on the truck departure times and are simultaneously considered fuzzy along with rail capacities. The fuzzy truck speed leads to the fuzziness of three aspects, including speed-dependent CO2 emissions of the road, a timetable-constrained transfer process from road to rail, and delivery time window violation. This study formulates the routing problem under the above considerations and carbon tax regulation as a combination of transportation path planning problem and truck departure time and speed matching problem. A fuzzy nonlinear optimization model is then established for the proposed routing problem. Furthermore, chance-constrained programming with general fuzzy measure is used to conduct the defuzzification of the model to make the problem solvable, and linearization techniques are adopted to linearize the model to enhance the efficiency of problem-solving. Finally, this study presents an empirical case to demonstrate the effectiveness of the designed approach. This case study evaluates the performance of carbon tax regulation by comparing it with multi-objective optimization. It also focuses on sensitivity analysis to discuss the influence of the optimistic–pessimistic parameter and confidence level on the optimization results. Several managerial insights are revealed based on the case study.

Chance-Constrained Optimization for a Green Multimodal Routing Problem with Soft Time Window under Twofold Uncertainty

“…The Chinese government and industry are focused on optimizing the transportation structure dominated by roads by encouraging the transfer of long-distance freight flows from roads to railways and waterways that are acknowledged as sustainable transportation modes. The aim of optimizing the transportation structure is to establish a multimodal transportation system that can integrate the various advantages of different transportation modes [2]. With the motivation of this national policy, multimodal transportation in China has developed rapidly since 2015.…”

Solving a Multimodal Routing Problem with Pickup and Delivery Time Windows under LR Triangular Fuzzy Capacity Constraints

“…The operational-level multimodal routing plays a crucial role in improving the operations and management of multimodal transportation systems [1] and is a promising approach to fully strengthen the advantages of multimodal transportation over unimodal transportation. In China, by enhancing the service level to attract more freight sources, multimodal routing enables multimodal transportation to replace road-dominated transportation that is low efficiency and energy-consuming to optimize the transportation structure [2]. Due to its great significance in practice, the multimodal routing problem (MRP) has been widely discussed in the research field of transportation planning [3] and is one of the six research topics in the decision support of multimodal transportation (policy support, terminal network design, multimodal service network design, multimodal routing, drayage operations, and ICT innovations) [4].…”

“…However, the majority of relevant studies focus more on the delivery than the pickup when modeling the time window and assume that containers are released at a fixed time [13,16] or there is the earliest release time [17]. Currently, quite a few works simultaneously model the two types of time windows, in which Sun et al [2] and Zhang et al [18] use the soft time window. Although these studies discuss the pickup and delivery time windows, their modeling still has the disadvantage of the soft time windows indicated above.…”

“…Contrary to stochastic programming, based on the fuzzy set theory [25], Sun et al [8], Li et al [13], and Lu et al [26] use triangular fuzzy numbers to model capacity uncertainty and establish the fuzzy chance-constrained programming (FCCP) models to deal with their MRPs. A group of studies by Sun et al [2,16,27] model trapezoidal fuzzy capacities and propose FCCP models for specific MRPs.…”

“…Under the above situation, fuzzy programming based on the use of fuzzy numbers to model uncertainty [29,30] is an alternative for MRP under capacity uncertainty. However, References [2,8,13,16,26,27] use regular fuzzy numbers when modeling uncertain capacity and only analyze the influence of the confidence level introduced by fuzzy programming approaches on the MRP. In these studies, the influence of the uncertainty level of the fuzzy capacity on the MRP is not considered.…”