Skip to main content

Advertisement

SpringerLink
Log in

The economic efficiency of energy-consuming equipment: a DEA approach

  • Original Article
  • Published:
Energy Efficiency Aims and scope Submit manuscript

Abstract

The market for an energy-consuming device offers a range of models that will meet consumers’ needs for an energy service with different levels of energy efficiency. A more efficient model is likely to have greater up-front costs, but the increased efficiency will eventually translate into energy cost savings over the device’s lifespan. Cost-effectiveness indicators (namely, net benefit and benefit-cost ratio) can be used to assess whether a more efficient model can be a better alternative for consumers. However, whereas these indicators express to what extent the additional benefits outweigh the additional costs, they do not indicate how efficiently each model allocates capital and energy to provide the energy service. They, therefore, lack the economic efficiency dimension of the problem. This paper introduces a data-oriented, non-parametric approach to evaluate such efficiency for a set of alternative models of an energy-consuming device. It relies on data envelopment analysis (DEA) to calculate relative efficiency coefficients. The coefficients establish an input efficient frontier for the energy service provided and indicate the models that provide the energy service at the least cost. DEA is further extended to calculate the highest cost-effectiveness achievable and indicate the most cost-effective alternatives. The approach proves useful to support consumers’ decision-making when shopping for energy-consuming equipment, to guide manufacturers when benchmarking the models they produce, and to inform energy efficiency policy-making and program designing.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3

Similar content being viewed by others

Notes

  1. Examples of energy-consuming devices and the corresponding energy services they provide are air-conditioners for space cooling, furnaces for space heating, boilers for water heating, clothes washers for clothes washing, air compressors for air compressing, and pumps for water pumping.

  2. More on applications of DEA to energy and environmental studies can be found in Zhou et al. (2008).

  3. Capital here refers to total equipment-related costs. It includes purchase, shipment, and installation costs, as well as any non-energy-related operating costs. For the sake of comparability, these costs should not include any costs associated with features, utilities, or services that are not available in all models under assessment.

  4. The reference model is usually one that is less energy-efficient and less costly than the model being assessed. Typically, it will be the least costly alternative in the market that provides the energy service at the highest energy efficiency and, consequently, with the lowest energy consumption.

  5. See, for example, Short et al. (1995), Elliot et al. (1997), Wroblewski et al. (1997), Mahlia et al. (2002), Lee et al. (2003), EPA (2008), Nikolaidis et al. (2009), McNeil and Bojda (2012), and the Technical Support Documents the U.S. Department of Energy publishes as part of its energy efficiency standard rulemakings. (https://www1.eere.energy.gov/buildings/appliance_standards/standards_test_procedures.html)

  6. See section “Estimating the economic efficiency of energy-consuming devices with DEA” for a discussion on weak efficiency.

  7. This is illustrated in section “Illustrative case”.

  8. More on DEA concepts and applications can be found in Cooper et al. (2011b). For literature reviews of DEA, see Gattoufi et al. (2004b) and Emrouznejad et al. (2008).

  9. The term “virtual” refers to the fact that a benchmark production unit for a non-efficient one may not be an actual unit but rather a hypothetical one that incorporates characteristics from other efficient units in the frontier.

  10. An input distance function characterizes a DMU by looking at a minimal proportional contraction of its inputs, given its outputs. An output distance function considers a maximal proportional expansion of the DMU’s outputs, given its inputs (definition adapted from Coelli et al. (2005)).

  11. According to Sengupta (2003), cost-oriented efficiency models can be used when outputs are not easily quantified or not measurable at all. They, therefore, provide a more general framework than a production efficiency approach.

  12. The reduced format of Eq. (3c) operates as a convexity constraint that drives the linear program to solve for solutions with non-decreasing returns to scale. However, since in this case all DMUs produce the same amount of energy service, they all operate at the same scale and the constraint has no effect on the DMU’s efficiency. For more on returns to scale in DEA see, for example, Golany and Yu (1997) or Cooper et al. (2011b).

  13. “Other models” will typically refer to all other existing models of the energy-consuming device in the market. One can also consider extending the set of existing models with additional theoretical models that will work as benchmarks (or standards) for the models available in the market. This may be of particular interest to policy analysis. For more on the benefits and limitations from incorporating standards in DEA, see Golany and Roll (1994).

  14. An inefficient DMU can be referred to different points in the efficiency frontier depending on the preferences of the decision-maker. See Lins et al. (2004) for a summary of approaches to refer inefficient DMUs to the efficiency frontier and for a multi-objective linear programming model that allows an inefficient DMU to be projected onto any point of the efficiency frontier.

  15. Equation 4c, similarly to Eq. (3c), is presented in its reduced form and does not explicit the outputs from the DMUs. Further, in a standard slack-based program, this expression would include an output slack. However, because in this application all DMUs provide the same amount of energy service as output, all output slacks are zero.

  16. If an inefficient model has only one or no fully efficient peers, the reference capital and energy for the inefficient model to become efficient should be the capital and energy calculated from Eqs. (5a) and (5b).

  17. This is illustrated in “Illustrative case” section.

  18. The second term of the right side of Eq. (7) is the cost-efficiency score of the model. For more on the use of DEA to calculate allocative- and cost-efficiency scores, see Cooper et al. (2011a) or Coelli et al. (2005).

  19. Productivity is measured by the ratio of outputs to inputs. Since all models provide the same energy service, the ones that provide the energy service with the least costs clearly present the highest productivity. In addition, it can be demonstrated that these models are also the ones with the greatest difference between energy cost savings and additional capital when compared to the most efficient least expensive model.

  20. Example of other works that have extended DEA to calculate cost-effectiveness indicators with DMUs’ inputs and outputs different than the cost and benefit components of cost-effectiveness indicators are Kuosmanen and Kortelainen (2007), where a “DEA-type framework” is used to calculate a competitive advantage coefficient based on net-benefits and Kortelainen and Kuosmanen (2007), where an eco-efficiency measure—also based on net-benefits—is calculated for consumer durables.

  21. Transformation developed upon Bisschop (2012), who relied on Charnes and Cooper (1962) to setup a step-by-step approach for the transformation process.

  22. The benefit-cost ratio is calculated relative to model m 0 = (k 0, g 0), and therefore, m 0 is not part of this program. Consequently, k* > k 0, and there is no risk in letting u* ≥ 0 as u* will never be zero.

  23. See "Appendix: Original data" for the original version of the data used in the illustrative case.

  24. All non-energy-related operating costs—namely, maintenance and repair costs—are assumed to be zero for the eight models.

  25. A line linking “m5” to “m5′” in Fig. 2 would extend through the origin. Note in this figure the intersection of the axes is at point (400, 51).

  26. This is a proxy to the average electricity rate projected by the U.S. Department of Energy (DOE 2014) to be paid by commercial consumers in the USA over the next 10 years ($0.101 per kWh).

  27. The linear program in Box 2 was used to maximize the benefit-cost ratio.

  28. Using a different reference model to calculate the cost-effectiveness indicators would lead to different results. Table 6 presents cost-effectiveness indicators calculated relative to models “m1,” “m5,” and “m8.” Interesting to note, due to the definition of net-benefit and benefit-cost ratio, whereas the former preserves the ranking across models, the latter does not.

References

  • Baker, R. C., & Talluri, S. (1997). A closer look at the use of data envelopment analysis for technology selection. Computers & Industrial Engineering, 32(1), 101–108.

    Article  Google Scholar 

  • Baxter, L. W., et al. (1986). An efficiency analysis of household energy use. Energy Economics, 8(2), 62–73.

    Article  Google Scholar 

  • Bisschop, J. (2012). AIMMS—optimization modeling. Bellevue: Paragon Decision Technology B.V.

    Google Scholar 

  • Blum, H., Atkinson, B., & Lekov, A. B. (2013). A methodological framework for comparative assessments of equipment energy policy measures. Energy Efficiency, 6(1), 65–90.

    Article  Google Scholar 

  • Boyd, G. A., & Pang, J. X. (2000). Estimating the linkage between energy efficiency and productivity. Energy Policy, 28(5), 289–296.

    Article  Google Scholar 

  • Boyd, G., et al. (1993). Energy intensity improvements in steel minimills. Contemporary Policy Issues, 11(3), 88–100.

    Article  Google Scholar 

  • Charnes, A., & Cooper, W. W. (1962). Programming with linear fractional functionals. Naval Research Logistics Quarterly, 9(3–4), 181–186.

    Article  MATH  MathSciNet  Google Scholar 

  • Charnes, A., Cooper, W. W., & Rhodes, E. (1978). Measuring the efficiency of decision-making units. European Journal of Operational Research, 2(6), 429–444.

    Article  MATH  MathSciNet  Google Scholar 

  • Charnes, A., et al. (1985). Foundation of data envelopment analysis for Pareto-Koopmans efficient empirical production functions. Journal of Econometrics, 30(1–2), 91–107.

    Article  MATH  MathSciNet  Google Scholar 

  • Chauhan, N. S., Mohapatra, P. K. J., & Pandey, K. P. (2006). Improving energy productivity in paddy production through benchmarking—an application of data envelopment analysis. Energy Conversion and Management, 47(9–10), 1063–1085.

    Article  Google Scholar 

  • Chen, T. Y., & Yu, O. S. (1997). Performance evaluation of selected US utility commercial lighting demand-side management programs. Energy Engineering: Journal of the Association of Energy Engineering, 94(4), 50–66.

    Google Scholar 

  • Coelli, T. J., Prasada Rao D. S., O'Donnell C. J., et al. (2005). An introduction to efficiency and productivity analysis. New York: Springer Science + Business Media.

  • Cook, W. D., & Zhu, J. (2005). Modeling performance measurement: applications and implementation issues in DEA. New York, NY, USA: Springer Science + Business Media.

    Google Scholar 

  • Cooper, W.W., Seiford, L.M., Zhu, J. (2011a). Data envelopment analysis: history, models, and interpretations. In W.W. Cooper, L.M. Seiford, J. Zhu (Eds.), Handbook on data envelopment analysis (International series in operations research & management science, Vol. 164). New York: Springer.

  • Cooper, W. W., Seiford, L. M., & Zhu, J. (2011b). Handbook on data envelopment analysis (International series in operations research & management science, Vol. 164). New York: Springer.

    Google Scholar 

  • DOE (2014). Electricity supply, disposition, prices, and emissions. In Annual energy outlook, interactive table viewer. U.S. Energy Information Administration, U.S. Department of Energy, Washington, DC, USA. http://www.eia.gov/oiaf/aeo/tablebrowser/#release=AEO2014&subject=3-AEO2014&table=8-AEO2014&region=0-0&cases=ref2014-d102413a.

  • Doyle, J. R., & Green, R. H. (1991). Comparing products using data envelopment analysis. Omega International Journal of Management Science, 19(6), 631–638.

    Article  Google Scholar 

  • Doyle, J. R., & Green, R. H. (1994). Strategic choice and data envelopment analysis: comparing computers across many attributes. Journal of Information Technology, 9(1), 61–69.

    Article  Google Scholar 

  • Elliot, R.N., Laitner, S., Pye, M. (1997). Considerations in the estimation of costs and benefits of industrial energy efficiency projects. Energy conversion engineering conference 1997. IECEC-97 proceedings of the 32 nd intersociety energy conversion engineering congress vol 3: 2143–2147. Honolulu, HI, USA.

  • Emrouznejad, A., Parker, B. R., & Tavares, G. (2008). Evaluation of research in efficiency and productivity: a survey and analysis of the first 30 years of scholarly literature in DEA. Journal of Socio-Economic Planning Sciences, 42(3), 151–157.

    Article  Google Scholar 

  • EPA (2008). Understanding cost-effectiveness of energy efficiency programs: best practices, technical methods, and emerging issues for policy-makers. National Action Plan for Energy Efficiency. Energy and Environmental Economics, Inc. and Regulatory Assistance Project.

  • Färe, R., & Primont, D. (1995). Multi-output production and duality: theory and applications. Norwell: Kluwer Academic Publishers.

    Book  Google Scholar 

  • Farrell, M. J. (1957). The measurement of productive efficiency. Journal of the Royal Statistical Society, 120(III), 253–281.

    Article  Google Scholar 

  • Fernandez-Castro, A. S., & Smith, P. C. (2002). Lancaster’s characteristics approach revisited: product selection using non-parametric methods. Managerial and Decision Economics, 23(2), 83–91.

    Article  Google Scholar 

  • Gattoufi, S., et al. (2004a). Epistemology of data envelopment analysis and comparison with other fields of OR/MS for relevance to applications. Journal of Socio-Economic Planning Sciences, 38(2–3), 123–140.

    Article  Google Scholar 

  • Gattoufi, S., Oral, M., & Reisman, A. (2004b). Data envelopment analysis literature: a bibliography update (1951–2001). Journal of Socio-Economic Planning Sciences, 38(2–3), 159–229.

    Google Scholar 

  • Golany, B., & Roll, Y. (1994). Incorporating standards via DEA. In A. Charnes, W. W. Cooper, A. Y. Lewin, & L. M. Seiford (Eds.), Data envelopment analysis: theory, methodology, and application. New York: Springer.

    Google Scholar 

  • Golany, B., & Tamir, E. (1995). Evaluating efficiency-effectiveness-equality trade-offs: a data envelopment analysis approach. Management Science, 41(7), 1172–1184.

    Article  MATH  Google Scholar 

  • Golany, B., & Yu, G. (1997). Estimating returns to scale in DEA. European Journal of Operational Research, 103(1), 28–37.

    Article  MATH  Google Scholar 

  • Hu, J. L., & Kao, C. H. (2007). Efficient energy-saving targets for APEC economies. Energy Policy, 35(1), 373–382.

    Article  Google Scholar 

  • Hu, J. L., & Wang, S. C. (2006). Total-factor energy efficiency of regions in China. Energy Policy, 34(17), 3206–3217.

    Article  Google Scholar 

  • Khouja, M. (1995). The use of data envelopment analysis for technology selection. Computers & Industrial Engineering, 28(1), 123–132.

    Article  Google Scholar 

  • Kortelainen, M., & Kuosmanen, T. (2007). Eco-efficiency analysis of consumer durables using absolute shadow prices. Journal of Productivity Analysis, 28(1–2), 57–69.

    Article  Google Scholar 

  • Kuosmanen, T., & Kortelainen, M. (2007). Valuing environmental factors in cost-benefit analysis using data envelopment analysis. Ecological Economics, 62(1), 56–65.

    Article  Google Scholar 

  • Lee, W.-S. (2008). Benchmarking the energy efficiency of government buildings with data envelopment analysis. Energy and Buildings, 40(5), 891–895.

    Article  Google Scholar 

  • Lee, W. L., Yik, F. W. H., & Jones, P. (2003). A strategy for prioritising interactive measures for enhancing energy efficiency of air-conditioned buildings. Energy, 28(8), 877–893.

    Article  Google Scholar 

  • Lins, M. P. E., Angulo-Meza, L., & Silva, A. C. M. (2004). A multi-objective approach to determine alternative targets in data envelopment analysis. The Journal of the Operational Research Society, 55(10), 1090–1101.

    Article  MATH  Google Scholar 

  • Mahlia, T. M. I., Masjuki, H. H., & Choudhury, I. A. (2002). Theory of energy efficiency standards and labels. Energy Conversion and Management, 43(6), 743–761.

    Article  Google Scholar 

  • McNeil, M. A., & Bojda, N. (2012). Cost-effectiveness of high-efficiency appliances in the U.S. residential sector: a case study. Energy Policy, 45, 33–42.

    Article  Google Scholar 

  • Nikolaidis, Y., Pilavachi, P. A., & Chletsis, A. (2009). Economic evaluation of energy saving measures in a common type of Greek building. Applied Energy, 86(12), 2550–2559.

    Article  Google Scholar 

  • Odeck, J., & Hjalmarsson, L. (1996). The performance of trucks—an evaluation using data envelopment analysis. Transportation Planning and Technology, 20(1), 49–66.

    Article  Google Scholar 

  • Onut, S., & Soner, S. (2006). Energy efficiency assessment for the Antalya Region hotels in Turkey. Energy and Buildings, 38(8), 964–971.

    Article  Google Scholar 

  • Sengupta, J. K. (2003). New efficiency theory—with applications of data envelopment analysis. Berlin, Germany: Springer.

    MATH  Google Scholar 

  • Short, W., Packey, D. J., & Holt, T. (1995). A manual for the economic evaluation of energy efficiency and renewable energy technologies (Report NREL/TP-462-5173). Golden: National Renewable Energy Laboratory.

    Book  Google Scholar 

  • Staat, M. R., Bauer, H. H., & Hammerschmidt, M. (2002). Structuring product markets: an approach based on customer value. Marketing Educators’ Conference Proceedings, 13(1), 205–212.

    Google Scholar 

  • Womer, N. K., et al. (2006). Benefit-cost analysis using data envelopment analysis. Annals of Operations Research, 145(1), 229–250.

    Article  MATH  Google Scholar 

  • Wroblewski, R.G., et al. (1997). An analysis of motor system optimization options—a question of diminishing return on investment. Proceedings from the Nineteenth Industrial Energy Technology Conference ESL-IE-97-04-17: 2143-2147. Houston, TX, USA.

  • Zhou, P., & Ang, B. W. (2008). Linear programming models for measuring economy-wide energy efficiency performance. Energy Policy, 36(8), 2911–2916.

    Article  Google Scholar 

  • Zhou, P., Ang, B. W., & Poh, K. L. (2008). A survey of data envelopment analysis in energy and environmental studies. European Journal of Operational Research, 189(1), 1–18.

    Article  MATH  MathSciNet  Google Scholar 

Download references

Acknowledgments

This work was supported by the Assistant Secretary for Energy Efficiency and Renewable Energy, Office of Building Technology, State, and Community Programs, of the U.S. Department of Energy under Contract No. DE-AC02-05CH11231. The author acknowledges Luiz F. L. Legey, Universidade Federal do Rio de Janeiro, Brazil, for his thoughtful comments on a draft version of this paper and three anonymous reviewers for their valuable feedback on earlier versions of the paper.

Highlights

• When comparing alternative models of an energy-consuming device, it is important to account for their economic efficiency.

• Data envelopment analysis (DEA) can be used to estimate technical and allocative efficiency scores for a set of alternative models of an energy-consuming device.

• DEA efficiency scores delineate the input efficient frontier for the energy service provided and identify the models that provide the energy service at the least cost.

• DEA technical and allocative efficiency scores and cost-effectiveness metrics are complementary indicators of the economic performance of energy-consuming devices.

Author information

Authors and Affiliations

  1. Energy Efficiency Standards Group, Energy Analysis and Environmental Impacts Department, Environmental Energy Technologies Division, Lawrence Berkeley National Laboratory, 1 Cyclotron Rd, Berkeley, CA, 94720, USA

    Helcio Blum

Authors
  1. Helcio Blum
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Helcio Blum.

Appendix: Original data

Appendix: Original data

The illustrative case develops upon a set of seven models of 1 hp electric motors, operating at full load for 6,000 h per year, during 10 years, in commercial sector in the USA. Some of the former motor prices and energy efficiency were modified to shed light on issues that may arise when using cost-effectiveness indicators and DEA efficiency scores to compare economic performance across different models of the same type of equipment. The original parameters, as well as the corresponding efficient frontier are presented in Box 5.

Box 5: Original version of the data used in the illustrative case

figure a

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Blum, H. The economic efficiency of energy-consuming equipment: a DEA approach. Energy Efficiency 8, 281–298 (2015). https://doi.org/10.1007/s12053-014-9283-5

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12053-014-9283-5

Keywords

Search

Navigation