Modelling energy and carbon emission performance: A constrained performance index measure

Abstract Energy and carbon emission performance evaluation is a focus topic in the field of environmental protection and energy utilization. However, the current studies are not high in identifying economic output inefficiency and neglect to control target energy carbon emission intensity (ECI), which may cause evaluation bias. Hence, this paper presents a constrained performance index measure (CPIM) model to solve the issues. The proposed model takes the performance index measure and can identify more numbers of positive economic output inefficiency compared to the directional distance function (DDF) model. Besides, the ECI constraint is presented and imposed into the proposed model to restrict the target ECI of decision making units. The numerical example from China’s provincial dataset demonstrates and confirms the validity and merit of the proposed model through the measure and constraint comparison among different models. Then, it is found that most provinces exist certain economic output inefficiency and the center regions have a worst score of energy carbon emission performance index due to the rapid development of their secondary industry by using the proposed model. Several valuable modeling directions and questions related to performance index measure and energy pollution emission constraints are provided for future research.