Cross efficiency model of network DEA and its application on low carbon efficiency evaluation of multimodal transport

The transportation industry is the main source of carbon dioxide (CO2) emissions, and the development of multimodal transport is conducive to reducing transportation carbon emissions. In order to evaluate the low carbon efficiency of multimodal transport, this article proposes a cross efficiency data envelopment analysis (DEA) method for complex network structures from the perspective of fairness, and takes China's rail-water intermodal transport as an example for research. The proposed method includes two secondary goal models that reduce the unreasonable differences between self-evaluation and peer-evaluation and treat all stages within the network system equally. Then, the improved entropy weight method is used to aggregate the cross efficiency. In addition, a numerical example is given to verify the effectiveness of the proposed method. The results of the case study show that the efficiency of Tangshan Port and Rizhao Port is relatively high, and others should learn from the successful experiences and develop improvement strategies based on their own characteristics. The conclusions can provide reference for transportation enterprise management and policy formulation, and the proposed method can be widely applied to the performance analysis of enterprise network, industrial chain, and supply chain.