Data envelopment analysis cross-like efficiency model for non-homogeneous decision-making units: The case of United States companies' low-carbon investment to attain corporate sustainability

Traditional data envelopment analysis (DEA) models assume directly comparability among decision-making units (DMUs). However, this assumption is not necessarily applied in practice; DMUs do not always utilize similar inputs to produce similar outputs. Sometimes, a DMU may not choose to produce a certain output (e.g., a steel plant may not produce tool steels) or cannot produce the certain output for some certain reasons. Meanwhile, DMUs may choose different resources to achieve the general productions or services (e.g., papermaker mills consume different raw materials to produce paper). How to compare a DMU to other units objectively becomes an issue when evaluating efficiency in the absence of homogeneity. In this study, a cross-like efficiency model for the DEA of non-homogeneous DMUs is established to handle the aforementioned issue. The proposed method can even assign unique rankings to DMUs with missing outputs or inputs. Furthermore, prior information on the appropriate bound for the share of resources is not needed. The proposed model is applied to an existing data set used in previous studies. 39 companies on S&P 500 corporations in 2013 are also studied with this model. It is confirmed that investors focus on the company's green thoughts and long-term sustainability by the empirical investigation. Furthermore, this study shows that the Information Technology sector has the highest low-carbon investment performance among the nine sectors investigated. The measurement of low-carbon technology investment can be an available benchmark for a specific industry to attain corporate sustainability.