Journal of Productivity Analysis

, Volume 40, Issue 3, pp 285–292 | Cite as

Modeling CRS bounded additive DEA models and characterizing their Pareto-efficient points

  • Jesus T. Pastor
  • Juan Aparicio
  • Juan F. Monge
  • Diego Pastor
Article

Abstract

Dealing with weighted additive models in Data Envelopment Analysis guarantees that any projection of an inefficient unit belongs to the strong efficient frontier, among other interesting properties. Recently, constant returns to scale (CRS) range-bounded models have been introduced for defining a new additive-type efficiency measure (see Cooper et al. in J Prod Anal 35(2):85–94, 2011). This paper continues such earlier work further, considering a more general setting. In particular, we show that under free disposability of inputs and outputs, CRS bounded additive models require a double set of slacks. The second set of slacks allows us to properly characterize all the Pareto-efficient points associated to the bounded technology. We further introduce the CRS partially-bounded additive models.

Keywords

Data envelopment analysis Additive models Bounded technology 

JEL Classifications

C51 C61 

References

  1. Ali AI, Seiford LM (1993) The mathematical programming approach to efficiency analysis. In: Fried H, Lovell CAK, Schmidt SS (eds) The measurement of productive efficiency: techniques and applications. Oxford University Press, Inc, New YorkGoogle Scholar
  2. Banker RD, Charnes A, Cooper WW (1984) Some models for estimating technical and scale inefficiencies in data envelopment analysis. Manage Sci 30:1078–1092CrossRefGoogle Scholar
  3. Charnes A, Cooper WW, Rhodes E (1978) Measuring the efficiency of decision making units. Eur J Oper Res 2:429–444CrossRefGoogle Scholar
  4. Charnes A, Cooper WW, Golany B, Seiford L, Stutz J (1985) Foundations of data envelopment analysis for pareto-koopmans efficient empirical production functions. J Econ 30:91–107Google Scholar
  5. Cooper WW, Pastor JT, Borras F, Aparicio J, Pastor D (2011) BAM: a bounded adjusted measure of efficiency for use with bounded additive models. J Prod Anal 35(2):85–94CrossRefGoogle Scholar
  6. Hollingsworth B, Smith P (2003) Use of ratios in data envelopment analysis. Appl Econ Lett 10:733–735CrossRefGoogle Scholar
  7. Lovell CAK, Pastor JT (1995) Units invariant and translation invariant DEA models. Oper Res Lett 18:147–151CrossRefGoogle Scholar
  8. Ray SC (2004) Data envelopment analysis. Theory and techniques for economics and operations research. Cambridge University Press, CambridgeCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2012

Authors and Affiliations

  • Jesus T. Pastor
    • 1
  • Juan Aparicio
    • 1
  • Juan F. Monge
    • 1
  • Diego Pastor
    • 2
  1. 1.Center of Operations Research (CIO)Miguel Hernandez University of ElcheElcheSpain
  2. 2.Division Educacion Fisica y DeportivaMiguel Hernandez University of ElcheElcheSpain

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