The range-adjusted measure (RAM) is an effective method for efficiency evaluation in non-radial data envelopment analysis (DEA). However, two steps are required to fully rank decision-making units (DMUs) using the traditional RAM approach when multiple DMUs are efficient. The first step is to identify the efficient DMUs using a RAM model, and the second step is to measure the super-efficiency of these efficient DMUs with a Super-RAM model. We propose an integrated RAM model that combines RAM and Super-RAM. This novel model can not only measure efficiency and super-efficiency in a single step, but also handle undesirable outputs. The proposed model is applied to evaluate the performance of China's regional cold chain logistics systems considering carbon emissions. The results demonstrate the advantages of the novel integrated RAM model with undesirable outputs. Additionally, the top ten regional cold chain logistics systems in China, ranked by performance, are Anhui, Qinghai, Hebei, Ningxia, Hainan, Gansu, Inner Mongolia, Shanxi, Jilin, and Guangxi.