Skip to main content
Disciplines
Automotive Business IT + Informatics Construction + Real Estate Electrical Engineering + Electronics Energy + Sustainability Insurance + Risk Finance + Banking Management + Leadership Marketing + Sales Mechanical Engineering + Materials
Events
DE
EN
Books
Journals
Topic Page
Marketing
Start single access now
Access for companies
EXTENDED SEARCH
Log in
Top
Published in:
Editors’ Introduction Read chapter Read first chapter

2021 | OriginalPaper | Chapter

DEA Models Without Inputs or Outputs: A Tour de Force

Author : Giannis Karagiannis

Published in: Advances in Efficiency and Productivity Analysis

Publisher: Springer International Publishing

Log in

Activate our intelligent search to find suitable subject content or patents.

search-config
loading …

Abstract

In this paper we review DEA models without outputs or inputs and models with a single constant input or output and we explore their properties and relations. Then we summarize their potential usefulness in several applications, including (a) multiple criteria decision-making (MCDM) such as supplier selection and ABC inventory classification, (b) construction of composite indicators (environmental, sustainability, subjective well being, etc.), (c) ratio analysis, and (d) spatial efficiency. We further consider the cases of optimistic versus pessimistic composite indicators and of intra- and inter-group composite indicators. We also explore the usefulness of these models in other topics of performance evaluation such as cross efficiency, efficiency based on common weights, and productivity analysis. Lastly, we consider their aggregation across DMUs rules.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

inform now
previous chapter Individual Efficient Frontiers in Performance Analysis
next chapter U.S. Banking in the Post-Crisis Era: New Results from New Methods
Footnotes
1
The value of inputs or outputs is set usually to one but this is not necessary, it has only to be the same for all DMUs.
 
2
In MCDM analysis, alternatives can be seen as DMUs and attributes or criteria for evaluating the alternatives as inputs or outputs, with the former corresponding to the less-is-better type criteria and the latter to the more-is-better type criteria.
 
3
As Lovell and Pastor (1999, p. 51) claimed, “considering a single constant input (output) is equivalent to considering multiple constant inputs (outputs).”
 
4
It is only the slacks that render a DMU inefficient in this case as in regard to ordinal factors DEA model.
 
5
In their set-up, there are two players in the game: one player is the DMU under evaluation who attempts to max (min) its gain (loss) and the other player is a central evaluator who wants to min (max) its loss (gains). On the other hand, there are two strategy spaces in the game: one is related to the weights in the multiplier form of the DEA model and the other to the index h, which selects a competitive DMU.
 
6
Interestingly, the three models that have been used for site evaluation, namely the VRS input-oriented model without outputs in (1) used by Adolphson et al. (1991), the VRS input-oriented model with a single constant output in (7) used by Desai and Storbeck (1990), the CRS input-oriented model with a single constant output in (6) used Thompson et al. (1986), and the CRS output-oriented model with a single constant output in (8) used by Takamura and Tone (2003) are equivalent to each other and result in the same assessment results.
 
7
See van Puyenbroeck (2018) for a discussion on the output orientation of the BoD model.
 
8
Melyn and Moesen (1991) were the first to use the name BoD model but they did so for (11) not for (9), as it is common now days.
 
9
For the BoD and the inverted BoD models, the primal formulation corresponds to the multiplier form and the dual to the envelopment form.
 
10
This simply means that the aforementioned result also holds for an input-oriented model with a single constant input, i.e., the BoD model.
 
Literature
Adolphson, D. L., Cornia, G. C., & Walters, L. C. (1991). A unified framework for classifying DEA models. In Operational research ’90 (pp. 647–657). New York: Pergamon Press.
Athanassopoulos, A. D., & Storbeck, J. E. (1995). Non-parametric models for spatial efficiency. Journal of Productivity Analysis, 6, 225–245.CrossRef
Banker, R. D. (1980). A game theoretic approach to measuring efficiency. European Journal of Operational Research, 5, 262–268.CrossRef
Bardhan, I., Bowlin, W. F., Cooper, W. W., & Sueyoshi, T. (1996). Models and measures of efficiency dominance in DEA: Part II: free disposal hull and Russell measure approaches. Journal of the Operational Research Society of Japan, 39, 333–344.CrossRef
Bernini, C., Guizzardi, A., & Angelini, G. (2013). DEA-like model and common weights approach for the construction of a subjective community well-being indicator. Social Indicators Research, 114, 405–424.CrossRef
Bowen, H. P., & Moesen, W. (2011). Composite competitiveness indicators with endogenous versus predetermined weights: An application to the world economic forum’s global competiveness index. Competitiveness Review: An International Business Journal, 21, 129–151.CrossRef
Cai, Y., & Wu, W. (2001). Synthetic financial evaluation by a method combining DEA with AHP. International Transactions in Operational Research, 8, 603–609.CrossRef
Caporaletti, L. E., Dula, J. H., & Womer, N. K. (1999). Performance evaluation based on multiple attributes with nonparametric frontiers. Omega, 27, 637–645.CrossRef
Cesaroni, G., Kerstens, K., & van de Woestyne, I. (2019). Short- and long-run plant capacity notions: definitions and comparison. European Journal of Operational Research, 275, 387–397.CrossRef
Charles, V., & Kumar, M. (2014). Satisficing data envelopment analysis: an application to SERVQUAL efficiency. Measurement, 51, 71–80.CrossRef
Charles, V., Fare, R., & Grosskpf, S. (2016). A translation invariant pure DEA model. European journal of Operational Research, 249, 390–392.CrossRef
Charnes, A., Cooper, W. W., & Rhodes, E. (1981). Evaluating program and managerial efficiency: an application of data envelopment analysis to program follow through. Management Science, 27, 668–697.CrossRef
Cherchye, L., Lovell, C. A. K., Moesen, W., & van Puyenbroeck, T. (2007). One market, one number? A composite indicator assessment of EU internal market dynamics. European Economic Review, 51, 749–779.CrossRef
Cherchye, L., Moesen, W., Rogge, N., & van Puyenbroeck, T. (2007a). An introduction to “benefit of the doubt” composite indicators. Social Indicators Research, 82, 111–145.CrossRef
Cherchye, L., Lovell, C. A. K., Moesen, W., & van Puyenbroeck, T. (2007b). One market, one number? A composite indicator assessment of EU internal market dynamics. European Economic Review, 51, 749–779.CrossRef
Cherchye, L., Moesen, W., Rogge, N., van Puyenbroeck, T., Saisana, M., Saltelli, A., Liska, R., & Tarantola, S. (2008). Creating composite indicators with DEA and robustness analysis: the case of the technology achievement index. Journal of Operational Research Society, 59, 239–253.CrossRef
Cook, W. D., & Kress, M. (1990). A data envelopment model for aggregating preference rankings. Management Science, 36, 1302–1310.CrossRef
Cook, W. D., Chai, D., Doyle, J. R., & Green, R. H. (1998). Hierarchies and groups in DEA. Journal of Productivity Analysis, 10, 177–198.CrossRef
Cooper, W. W., Ruiz, J. L., & Sirvent, I. (2009). Selecting non-zero weights to evaluate effectiveness of basketball players with DEA. European Journal of Operational Research, 195, 563–574.CrossRef
de Witte, K., & Rogge, N. (2010). To publish or not to publish: on the aggregation and drivers of research performance. Scientometrics, 85, 657–680.CrossRef
de Witte, K., & Rogge, N. (2011). Accounting for exogenous influences in performance evaluations of teachers. Economics of Education Review, 30, 641–653.CrossRef
Desai, A., & Storbeck, J. E. (1990). A data envelopment analysis for spatial efficiency. Computers, Environment and Urban Systems, 14, 145–156.CrossRef
Despic, O., Despic, M., & Paradi, J. C. (2007). DEA-R: ratio-based comparative efficiency model, its mathematical relation to DEA and its use in applications. Journal of Productivity Analysis, 28, 33–44.CrossRef
Despotis, D. K. (2005). A reassessment of the human development index via data envelopment analysis. Journal of Operational Research Society, 56, 969–980.CrossRef
Doyle, J. R., & Green, R. H. (1991). Comparing products using data envelopment analysis. Omega, 19, 631–638.CrossRef
Doyle, J. R., & Green, R. H. (1994). Efficiency and cross efficiency in DEA: derivation, meanings and uses. Journal of Operational Research Society, 45, 567–578.CrossRef
Doyle, J. R., Green, R. H., & Cook, W. D. (1995). Upper and lower bound evaluation for multiattribute objects: Comparison models using linear programming. Organizational Behavior and Human Decision Processes, 64, 261–273.CrossRef
Färe, R., & Grosskopf, S. (2003). Nonparametric productivity analysis with undesirable outputs: comment. American Journal of Agricultural Economics, 85, 1070–1074.CrossRef
Fernandez-Castro, A.S. and P.C. Smith. Towards a general non-parametric model of corporate performance, Omega, 1994, 22, 237-49.
Fernandez-Castro, A. S., & Smith, P. C. (2000). Lancaster’s characteristics approach revisited: product selection using non-parametric methods. Managerial and Decision Economics, 23, 83–91.CrossRef
Ferrier, G. D., & Trivitt, J. S. (2013). Incorporating quality in the measurement of hospital efficiency: a double DEA approach. Journal of Productivity Analysis, 40, 337–355.CrossRef
Fusco, E. (2015). Enhancing Non-compensatory composite indicators: a directional proposal. European Journal of Operational Research, 242, 620–630.CrossRef
Fӓre, R., & Karagiannis, G. (2014). Benefit-of-the-doubt aggregation and the diet problem. Omega, 47, 33–35.CrossRef
Fӓre, R., & Karagiannis, G. (2017). The denominator rule for share-weighting aggregation. European Journal of Operational Research, 260, 1175–1180.CrossRef
Fӓre, R., & Karagiannis, G. (2020). The denominator rule and a theorem by Janos Aczel. European Journal of Operational Research, 282, 398–400.CrossRef
Fӓre, R., Karagiannis, G., Hassanasab, M., & Margaritis, D. (2019). A benefit-of-the-doubt model with reverse indicators. European Journal of Operational Research, 278, 394–400.CrossRef
Gaaloul, H., & Khalfallah, S. (2014). Application of the “Benefit-of-the-Doubt” approach for the construction of a digital access indicator: a revaluation of the “Digital Access Index”. Social Indicators Research, 118, 45–56.CrossRef
Garcia-Romero, A., Santin, D., & Sicilla, G. (2016). Another brick in the wall: a new ranking of academic journal in economics using FDH. Scientometrics, 107, 91–101.CrossRef
Gomes, E. G., de Abreu, U. G. P., de Mello, J. C. C. B. S., de Carvalho, T. B., & de Zen, S. (2012). Unitary input DEA model to identify beef cattle production systems typologies. Pesquisa Operacional, 32, 389–406.CrossRef
Green, R. H., Doyle, J. R., & Cook, W. D. (1996). Preference voting and project ranking using DEA and cross evaluation. European Journal of Operational Research, 90, 461–472.CrossRef
Greenberg, R., & Nunamaker, T. (1987). A Generalized multiple criteria model for control and evaluation of nonprofit organizations. Financial Accountability and Management, 3, 331–342.CrossRef
Guardiola, J., & Picazo-Tadeo, A. (2014). Building weighted-domain composite indices of life satisfaction with data envelopment analysis. Social Indicators Research, 117, 257–274.CrossRef
Hadi-Vencheh, A. (2010). An improvement to the multiple criteria ABC inventory classification. European Journal of Operational Research, 201, 962–965.CrossRef
Hashimoto, A. (1997). A ranked voting system using a DEA/AR exclusion model: a note. European Journal of Operational Research, 97, 600–604.CrossRef
Huang, C., Dai, C., & Guo, M. (2015). A hybrid approach using two-level DEA for financial failure prediction and integrated SE-DEA and GCA for indicators selection. Applied Mathematics and Computation, 251, 431–441.CrossRef
Kamakura, W. A., Ratchford, B. T., & Agrawal, J. (1988). Measuring market efficiency and welfare loss. Journal of Consumer Research, 15, 289–302.CrossRef
Kao, C., & Hung, H. T. (2003). Ranking university libraries with a posteriori weights. Libri, 53, 282–289.CrossRef
Kao, C., & Lin, Y. C. (2004). Evaluation of the university libraries in Taiwan: total measure versus ratio measure. Journal of Operational Research Society, 55, 1256–1265.CrossRef
Kao, C., Wu, W. Y., Hsieh, W. J., Wang, T. Y., Lin, C., & Chen, L. H. (2008). Measuring the national competitiveness of Southeast Asian countries. European Journal of Operational Research, 187, 613–628.CrossRef
Kao, C., Liu, S. T., & Pao, H. L. (2012). Assessing improvement in management research in Taiwan. Scientometrics, 92, 75–87.CrossRef
Karagiannis, G. (2017). On aggregate composite indicators. Journal of Operational Research Society, 68, 741–746.CrossRef
Karagiannis, R., & Karagiannis, G. (2018). Intra- and inter-group composite indicators using the BoD model. Socio-economic Planning Sciences, 61, 44–51.CrossRef
Karagiannis, G., & Lovell, C. A. K. (2016). Productivity measurement in radial DEA models with a single constant input. European Journal of Operational Research, 251, 323–328.CrossRef
Karagiannis, G., & Paleologou, S. M. (2014). Towards a composite public sector performance indicator. In: Paper presented in the 2014 Asia Pacific productivity conference, Brisbane, July 2-4, 2014.
Karagiannis, G., & Paschalidou, G. (2017). Assessing research effectiveness: A comparison of alternative nonparametric models. Journal of the Operational Research Society, 68, 456–468.CrossRef
Keeney, R. L., & Raiffa, H. (1976). Decisions with multiple objectives. New York: Wiley.
Koopmans, T. C. (1957). Three essays on the state of economic science. New York: McGraw-Hill.
Kuosmanen, T. (2005). Weak disposability in nonparametric production analysis with undesirable outputs. American Journal of Agricultural Economics, 87, 1077–1082.CrossRef
Kuosmanen, T., & Podinovski, V. (2009). Weak disposability in nonparametric production analysis: Reply to Färe and Grosskopf. American Journal of Agricultural Economics, 91, 539–545.CrossRef
Lauer, J. A., Lovell, C. A. K., Murray, C. J. L., & Evans, D. B. (2004). World health system performance revisited: the impact of varying the relative importance of health system goals. BMC Health Services Research.
Lewis, H. F., & Sexton, T. R. (2004). Data envelopment Analysis with reverse inputs and outputs. Journal of Productivity Analysis, 21, 113–132.CrossRef
Lee, H., & Kim, C. (2014). Benchmarking of service quality with data envelopment analysis. Expert Systems with Applications, 41, 3761–3768.CrossRef
Lins, M. P. E., Gomes, E. G., Soares de Mello, J. C. C. B., & de Mello, A. J. R. S. (2003). Olympic ranking based on a zero sum gains DEA model. European Journal of Operational Research, 148, 312–322.CrossRef
Liu, W. B., Zhang, D. Q., Meng, W., Li, X. X., & Xu, F. (2011). A study of DEA models without explicit inputs. Omega, 39, 472–480.CrossRef
Lovell, C. A. K., & Pastor, J. T. (1997). Target setting: an application to a bank branch network. European Journal of Operational Research, 98, 290–299.CrossRef
Lovell, C. A. K., & Pastor, J. T. (1999). Radial DEA models without inputs or without outputs. European Journal of Operational Research, 118, 46–51.CrossRef
Mahlberg, B., & Obersteiner, M. (2001). Re-measuring the HDI by data envelopment analysis. In: IIASA interim report IR-01-069, Luxemburg.
Melyn, W., & Moesen, W. (1991). Towards a synthetic indicator for macroeconomic performance: unequal weighting when limited information is available, Public Economics Research Paper Nr 17. Katholieke Universiteit Leuven.
Mizobuchi, H. (2014). Measuring world better life frontier: a composite indicator for OECD better life index. Social Indicators Research, 118, 987–1007.CrossRef
Molinos-Senante, M., Gomez, T., Caballero, R., & Sala-Garrido, R. (2017). Assessing the quality of service to consumers provided by water utilities: a synthetic index approach. Ecological Indicators, 78, 214–220.CrossRef
Morais, P., & Camanho, A. S. (2011). Evaluation of performance of European cities with the aim to promote quality of life improvements. Omega, 39, 398–409.CrossRef
Morey, M. R., & Morey, R. C. (1999). Mutual fund performance appraisals: A multi-horizon perspective with endogenous benchmarking. Omega, 27, 241–258.CrossRef
Mozaffari, M. R., Gerami, J., & Jablonsky, J. (2014). Relationship between DEA models without explicit inputs and DEA-R models. Central European Journal of Operational Research, 22, 1–12.CrossRef
Murias, P., de Miguel, J. C., & Rodriguez, D. (2008). A composite indicator for university quality assessment: the case of Spanish higher education system. Social Indicators Research, 89, 129–146.CrossRef
Murthi, B. P. S., Choi, Y. K., & Desai, P. (1997). Efficiency of mutual funds and portfolio performance measurement: a non-parametric approach. European Journal of Operational Research, 98, 408–418.CrossRef
Nakabayashi, K., & Tone, K. (2006). Egoist’s dilemma: a DEA game. Omega, 34, 135–148.CrossRef
Nakabayashi, K., Sahoo, B. K., & Tone, K. (2009). Fair allocation based on two criteria: A DEA game view of “add them up and divide by two”. Journal of the Operational Research Society of Japan, 52, 131–146.CrossRef
Ng, W. L. (2007). A simple classifier for multiple criteria ABC analysis. European Journal of Operational Research, 177, 344–353.CrossRef
Ng, W. L. (2008). An efficient and simple model for multiple criteria supplier selection problem. European Journal of Operational Research, 186, 1059–1067.CrossRef
O’Donnell, C. J., & Nguyen, K. (2013). An econometric approach to estimating support prices and measures of productivity change in public hospitals. Journal of Productivity Analysis, 40, 323–335.CrossRef
OECD. (2008). Handbook on constructing composite indicators: Methodology and user guide. Paris.
Prieto, A. M., & Zofio, J. L. (2001). Evaluating effectiveness in public provision of infrastructure and equipment: The case of Spanish municipalities. Journal of Productivity Analysis, 15, 41–58.CrossRef
Ramanathan, R. (2006a). ABC inventory classification with multiple-criteria using weighted linear optimization. Computers and Operations Research, 33, 695–700.CrossRef
Ramanathan, R. (2006b). Data envelopment analysis for weight derivation and aggregation in the analytical hierarchy process. Computers and Operations Research, 33, 1289–1307.CrossRef
Ramanathan, R., & Yunfeng, J. (2009). Incorporating cost and environmental factors in quality function deployment using data envelopment analysis. Omega, 37, 711–723.CrossRef
Rogge, N. (2018). On aggregating benefit of the doubt composite indicators. European Journal of Operational Research, 264, 364–369.CrossRef
Ruiz, J. L., Pastor, D., & Pastor, J. T. (2013). Assessing professional tennis players using data envelopment analysis (DEA). Journal of Sports Economics, 14, 276–302.CrossRef
Sahoo, B. K., & Acharya, D. (2010). An alternative approach to monetary aggregation in DEA. European Journal of Operational Research, 204, 672–682.CrossRef
Sayed, H., Hamed, R., Abdelhamid, A. H., & Hosny, S. H. (2015). Using meta-goal programming for a new Human Development Indicator with distinguishable country ranks. Social Indicators Research, 123, 1–27.CrossRef
Sayed, H., Hamed, R., Hosny, S. H., & Abdelhamid, A. H. (2018). Avoiding ranking contradictions in human development index using goal programming. Social Indicators Research, 138, 405–442.CrossRef
Seydel, J. (2006). Data envelopment analysis for decision support. Industrial Management and Data Systems, 106, 81–95.CrossRef
Stigler, G. J. (1945). The cost of subsistence. Journal of Farm Economics, 27, 303–314.CrossRef
Takamura, Y., & Tone, K. (2003). A comparative site evaluation study for relocating Japanese government agencies out of Tokyo. Socio-economic Planning Sciences, 37, 85–102.CrossRef
Thompson, R. G., Singleton, F. D., Jr., Thrall, R. M., & Smith, B. A. (1986). Comparative site evaluation for locating a high-energy physics lab in Texas. Interfaces, 16, 35–49.CrossRef
van Puyenbroeck, T. (2018). On the output orientation of the benefit-of-the-doubt model. Social Indicators Research, 139, 415–431.CrossRef
Vidoli, F., Fusco, E., & Mazziota, C. (2015). Non-compensability in composite indicators: a robust directional frontier model. Social Indicators Research, 122, 635–652.CrossRef
Wang, Y. M., & Chin, K. S. (2009). A new data envelopment analysis method for priority determination and group decision making in the analytic hierarchy process. European Journal of Operational Research, 195, 239–250.CrossRef
Weber, C. A., & Desai, A. (1996). Determination of paths to vendor market efficiency using parallel coordinates representation: A negotiation tool for buyers. European Journal of Operational Research, 90, 142–155.CrossRef
Wei, C. K., Chen, L. C., Li, R. K., & Tsai, C. H. (2011). A study of developing an input-oriented ratio-based comparative efficiency model. Experts Systems with Applications, 38, 2473–2477.CrossRef
Whittaker, G., Barnhart, B., Färe, R., & Grosskopf, S. (2015). Application of index number theory to the construction of a water quality index: Aggregated nutrient loadings related to the areal extent of hypoxia in the northern Gulf of Mexico. Ecological Indicators, 49, 162–168.CrossRef
Xu, F., Zhang, D., Yang, G., & Liu, W. (2013). Game perspectives of DEA models and their duals. Journal of Applied Mathematics.
Yang, G., Shen, W., Zhang, D., & Liu, W. (2014). Extended utility and DEA models without explicit input. Journal of Operational Research Society, 65, 1212–1220.CrossRef
Zanella, A., Camanho, A. S., & Dias, T. G. (2013). Benchmarking countries’ environmental performance. Journal of Operational Research Society, 64, 426–438.CrossRef
Zanella, A., Camanho, A. S., & Dias, T. G. (2015a). Undesirable outputs and weighting schemes in composite indicators based on data envelopment analysis. European Journal of Operational Research, 245, 517–530.CrossRef
Zanella, A., Camanho, A. S., & Dias, T. G. (2015b). The assessment of cities’ livability integrating human wellbeing and environmental impact. Annals of Operation Research, 226, 695–726.CrossRef
Zhou, P., & Fan, L. (2007). A note on multi-criteria ABC inventory classification using weighted linear optimization. European Journal of Operational Research, 182, 1488–1491.CrossRef
Zhou, P., Ang, B. W., & Poh, K. L. (2007). A mathematical programming approach to constructing composite indicators. Ecological Economics, 291–297.
Metadata
Title
DEA Models Without Inputs or Outputs: A Tour de Force
Author
Giannis Karagiannis
Copyright Year
2021
Book
Advances in Efficiency and Productivity Analysis

Print ISBN: 978-3-030-47105-7

Electronic ISBN: 978-3-030-47106-4

Copyright Year: 2021

DOI
https://doi.org/10.1007/978-3-030-47106-4_10