مدل برنامه ریزی خطی برای اندازه گیری عملکرد بهره وری انرژی اقتصاد گسترده

Data envelopment analysis (DEA) has recently gained popularity in energy efficiency analysis. A common feature of the previously proposed DEA models for measuring energy efficiency performance is that they treat energy consumption as an input within a production framework without considering undesirable outputs. However, energy use results in the generation of undesirable outputs as by-products of producing desirable outputs. Within a joint production framework of both desirable and undesirable outputs, this paper presents several DEA-type linear programming models for measuring economy-wide energy efficiency performance. In addition to considering undesirable outputs, our models treat different energy sources as different inputs so that changes in energy mix could be accounted for in evaluating energy efficiency. The proposed models are applied to measure the energy efficiency performances of 21 OECD countries and the results obtained are presented.

With high energy prices and the concern about global warming and sustainable development, energy efficiency has become a vital part of the energy strategy in many countries (Ang, 2006). Researchers have developed appropriate indicators for monitoring economy-wide energy efficiency trends over time or comparing energy efficiency performances across countries/regions. A number of national energy agencies and international organizations have developed their energy efficiency measurement and monitoring systems. See, for example, International Energy Agency (IEA), 2004a and International Energy Agency (IEA), 2007, EECA (2006), NRC (2006), OEERE (2007) and ODYSSEE (2007). The foremost issue in the measurement of energy efficiency performance is to define the term “energy efficiency” (Patterson, 1996; Ang, 2006). There exist various definitions of energy efficiency, among which “the ratio of energy services to energy input” is a popular one. The definition given in the Directive 2006/32/EC of the European Council and the Parliament on energy end-use efficiency and energy services is a general one, namely energy efficiency is “a ratio between an output of performance, service, goods or energy, and an input of energy”. Different definitions of energy efficiency would lead to different indicators being used to monitor changes in energy efficiency, which can yield very different results and policy implications (Berndt, 1978).1 At the economy-wide level, since there is no single meaningful measure for energy services across all energy-consuming sectors and as such various approaches to measuring energy efficiency performance have been proposed in the literature. A common practice to measure economy-wide energy efficiency performance is to first decompose the change in energy consumption or aggregate energy intensity into a number of contributing factors, and then aggregate the effects of energy intensity changes at energy end-use or sub-sector level to give a composite energy efficiency performance index (Ang, 2006). The decomposition of energy consumption or aggregate energy intensity can be implemented by the index decomposition analysis (IDA) technique (Ang and Zhang, 2000; Ang 2004; Liu and Ang, 2007). This IDA-based approach has been adopted by a number of countries including Canada, New Zealand and the United States to track economy-wide energy efficiency trends over time (EECA, 2006; NRC, 2006; OEERE, 2007). It has been found that IDA-based energy efficiency studies mainly dealt with the measurement of energy efficiency changes over time in a specific entity, such as a country or a specific energy-consuming sector. Few of them dealt with the benchmarking of energy efficiency performance across different entities. In contrast, data envelopment analysis (DEA) has recently been widely applied to evaluate the energy efficiency performances of different entities. DEA, proposed by Charnes et al. (1978), is a well-established non-parametric frontier approach to evaluating the relative efficiency of a set of comparable entities featured with multiple inputs and outputs. The recent literature survey by Zhou et al. (2008a) found a rapid increase in the number of studies using DEA in the broad area of energy and environmental analysis. In energy efficiency studies, DEA has also gained in popularity. For instance, Boyd and Pang (2000) discussed the relationship between productivity and energy efficiency, and Ramanathan (2000) used DEA to compare the energy efficiencies of alternative transport modes. More recently, Onut and Soner (2006) applied DEA to assess the energy efficiencies of five-star hotels in Turkey. Hu and Wang (2006) and Hu and Kao (2007) developed a total-factor energy efficiency index by using DEA. Azadeh et al. (2007) proposed an integrated DEA approach to assessing the energy efficiency of energy-intensive manufacturing sectors. Wei et al. (2007) investigated the energy efficiency change of China's iron and steel sectors by using DEA-based Malmquist index approach. Mukherjee (2008) presented several DEA models for measuring the energy efficiency of manufacturing sectors. Lee (2008) combined regression analysis with DEA to study the energy efficiency of government buildings. A common feature of the DEA models in the above-mentioned studies is that they model energy consumption as an input within a production framework where both energy and other non-energy inputs are used to produce good or desirable outputs. However, energy use also results in the generation of some undesirable outputs, e.g. CO2 emissions, as by-products of producing desirable outputs. The measurement of energy efficiency without considering undesirable outputs does not seem to provide an equitable score for energy efficiency benchmarking and comparisons. It would therefore be appropriate to evaluate the economic-wide energy efficiencies within a joint production framework where both desirable and undesirable outputs are considered simultaneously. This paper presents several DEA-type linear programming models within a joint production framework for measuring economy-wide energy efficiency performance. In addition to considering undesirable outputs, our models treat different energy sources as different inputs so that changes in energy mix could be accounted for in evaluating energy efficiency. The rest of this paper is organized as follows. Section 2 proposes the models for measuring energy efficiency performance. In Section 3, we present an empirical application study on measuring the energy efficiency performance of 21 OECD countries. Section 4 concludes this study.

DEA has recently been widely applied to measure energy efficiency performance at different application levels. A common feature of previous DEA-related energy efficiency studies is that they model energy consumption as an input within a production framework without considering undesirable outputs. In real cases, energy use results in the generation of undesirable outputs as by-products of producing desirable outputs. However, none of previous studies attempt to evaluate energy efficiency within a join production framework of both desirable and undesirable outputs. The main purpose of this paper is to fill this gap by providing several DEA-type linear programming models for measuring economy-wide energy efficiency performance. Using the environmental DEA technology concept, we develop three alternative energy efficiency performance indexes. The first index, i.e. EEPI1, attempts to proportionally reduce the energy inputs to the frontier of the best practice. Since it does not consider the energy mix effects, the index could be treated as a purely technical efficiency index in energy consumption. To account for the energy mix effects in evaluating energy efficiency, we further developed EEPI2 based on a non-radial DEA-type model and EEPI3 based on a slacks-based DEA-type model. Each of these two indexes has its own features but they are not fully independent of each other. Using the proposed models, we finally present an empirical application study on measuring the energy efficiency performance of 21 OECD countries. Although our study mainly focuses on the measurement of economy-wide energy efficiency, given data availability, the proposed models could also be applied to measure the energy efficiency performance of lower-level entities such as electricity generation plants.