A Two-Step Centralized Model via Data Envelopment Analysis for Allocating Aggregate Carbon Emissions Abatements

Carbon emissions gradually gains importance along with the adoption of the Kyoto Protocol. Data envelopment analysis (DEA) is among the best techniques to measure the environmental performance of a production process with carbon emissions. In the existing literature, only inefficient decision making units (DMUs) are required to reduce their undesirable outputs while efficient DMUs are free from the responsibility. This is not acceptable from a practical point of view. In this paper, we develop a two-step approach to reallocate aggregate carbon emissions abatements. First, we use a directional distance function DEA model to compute the potential carbon reductions. Second, by setting lower and upper bounds of reductions for all DMUs, a centralized model is proposed to reallocate the total amount of carbon abatements among all DMUs in a way that overall inefficiency of DMUs are minimized. In our allocation scheme, both inefficient and efficient DMUs are required to reduce their carbon emissions. We perform sensitivity analyses related to the selection of lower and upper bounds of carbon abatements. The proposed approaches are applied to compute and reallocate potential carbon abatements for Organization for Economic Cooperation and Development (OECD) countries