The research on the optimization of a low-carbon multimodal transportation path under uncertainty can have an important theoretical and practical significance in the high-quality development situation. This paper investigates the low-carbon path optimization problem under dual uncertainty. A hybrid robust stochastic optimization (HRSO) model is established considering the transportation cost, time cost and carbon emission cost. In order to solve this problem, a catastrophic adaptive genetic algorithm (CA-GA) based on Monte Carlo sampling is designed and tested for validity. The multimodal transportation schemes and costs under different modes are compared, and the impacts of uncertain parameters are analyzed by a 15-node multimodal transportation network numerical example. The results show that: (1) the uncertain mode will affect the decision-making of multimodal transportation, including the route and mode; (2) robust optimization with uncertain demand will increase the total cost of low-carbon multimodal transportation due to the pursuit of stability; (3) the influence of time uncertainty on the total cost is significant and fuzzy, showing the trend of an irregular wave-shaped change, like the ups and downs of the mountains. The model and algorithm we proposed can provide a theoretical basis for the administrative department and logistic services providers to optimize the transportation scheme under uncertainty.

The third party logistics (3PL) suppliers selection is a key issue in sustainable operation of fourth party logistics (4PL). A two-stage auction mechanism is designed for the selection of 3PL suppliers. Different from previous studies, the paper considers risk preference of 4PL integrators during the auction and uses the prospect theory to establish the auction scoring function of 4PL integrators. First, a first score sealed auction (FSSA) mechanism is used to solve the selection problem. However, the results show that FSSA is not an ideal method. Hence, the English auction (EA) mechanism is combined with the FSSA mechanism to form a two-stage auction. The FSSA is taken as the first stage auction, and the EA is taken as the second stage auction, and the two-stage auction mechanism is constructed. The two-stage auction can improve the utility of the 4PL integrator and the auction efficiency. In addition, for the degree of disclosure of attribute weights in the scoring function, two states, complete information and incomplete information is designed. In case analysis, the validity of the designed two-stage auction mechanism is verified. The 4PL integrator can obtain higher utility under the risk-neutral auction than the risk-averse auction. The complete information auction does not make the 4PL integrator obtain higher utility than the incomplete information auction.

By delving into low-carbon transportation research, we can address the imperative for the high-quality development of transportation services, while simultaneously advancing the realization of the dual-carbon objective. This study focuses on optimizing multimodal transport routes under varying carbon tax frameworks, taking into account the demand uncertainty that arises from unforeseen events such as abrupt restocking or seasonal fluctuations. We formulate a dual-objective 0-1 path optimization model under both a unified carbon tax mechanism and a piecewise progressive carbon tax scheme. The model aims to minimize total cost and carbon emissions in the face of stochastic demand. Utilizing Monte Carlo simulation and the laws of large numbers, we convert the model to maximize the expected value of the uncertain objective. An enhanced non-dominated sorting genetic algorithm is then developed to solve this model, yielding solutions that more effectively meet our objectives. This algorithm is designed to expand the search space, mitigating the “"premature convergence” issue and thereby generating superior individuals and solutions. Finally, we assess the applicability of our model and algorithm to transportation challenges within the context of the dual-carbon initiative through a numerical example. We also explore the influence of different carbon tax mechanisms on total cost and emissions, as well as their applicability and efficacy in the face of demand uncerainty. The findings indicate that companies can achieve emission reductions with minimal cost increases under dual-target cost scenarios, ideal for dual carbon transportation contexts. Moreover, carbon tax rates significantly impact emission control, with segmented progressive taxes proving more effective, especially in high-demand uncertainty. Decision-makers should consider technological capabilities to set optimal tax rates and thresholds, fostering corporate enthusiasm. This research informs policy and decision-making for authorities and firms.