Skip to main content
SpringerLink
Log in

Importance for DEA of zeros in data, multipliers, and solutions

  • Published:
Journal of Productivity Analysis Aims and scope Submit manuscript

Abstract

Some prominent literature in the DEA field has displayed the following three problems involving zeros: (1) The structural role of zeros in data has not necessarily been recognized; in fact, without explanation, arbitrary, small positive numbers have been substituted for such zeros. (2) It is not well recognized that the artificial, non-Archimedean construct is not necessarily needed to exclude zero multipliers and to identify positive slacks. (3) Because of degeneracy, optimal solutions are not necessarily unique; this lack of uniqueness is especially important in interpretation of the multipliers and slacks.

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

Similar content being viewed by others

References

  • Afriat, S.N. (1972). “Efficiency Estimation of Production Functions.”International Economic Review 13(3), 568–598.

    Google Scholar 

  • Ahn, T., A. Charnes, and W.W. Cooper (1988). “Efficiency Characteristics in Different DEA Models.”Socio-Economic Planning Sciences 22, 253–257.

    Google Scholar 

  • Ali, I., and L.M. Seiford. (1990). “Translation Invariance in Data Envelopment Analysis.”Operations Research Letters 9, 403–405.

    Google Scholar 

  • Banker, R.D. (1984). “Estimating Most Productive Scale Size Using Data Envelopment Analysis.”European Journal of Operational Research 17, 35–44.

    Google Scholar 

  • Banker, R.D., A. Charnes, and W.W. Cooper. (1984). “Some Models for Estimating Technical and Scale Efficiencies in Data Envelopment Analysis.”Management Science 30, 1078–1092.

    Google Scholar 

  • Banker, R.D., and R.M. Thrall. (1992). “Estimation of Returns to Scale Using Data Envelopment Analysis.”European Journal of Operational Research 66, 74–84.

    Google Scholar 

  • Barr, R.S. L.M. Seiford, and T.F. Siems. (1992). “An Envelopment-Analysis, Approach to Measuring the Managerial Quality of Banks.”Final Program, EURO XII/TIMS XXXI Joint International Conference Operational Research/Management Science, Helsinki.

  • Bessent, A., W. Bessent, J. Elam, and T. Clark. (1988). “Efficiency Frontier Determination by Constrained Facet Analysis.”Operations Research 36, 785–796.

    Google Scholar 

  • Byrnes, P., R. Fare, and S. Grosskopf. (1984). “Measuring Productive Efficiency: An Application to Illinois Strip Mines.”Management Science 30, 671–681.

    Google Scholar 

  • Charnes, A., and W.W. Cooper. (1989).Data Envelopment Analysis. University of Texas, Austin: Center for Cybernetic Studies, CCS Research Report No. 626.

    Google Scholar 

  • Charnes, A., and W.W. Cooper. (1990).DEA Usages and Interpretations. University of Texas, Austin: Graduate School of Business.

    Google Scholar 

  • Charnes, A., and W.W. Cooper. (1985). “Preface to Topics in Data Envelopment Analysis.” In R.G. Thompson and R.M. Thrall (eds.),Normative Analysis in Policy Decisions, Public and Private Vol. 2 ofAnnals of Operations Research, (P. Hammer, ed.-in-chief), Basel: J.C. Basel AG, pp. 59–94.

    Google Scholar 

  • Charnes, A., W.A. Cooper, Z.M. Huang, and D.B. Sun. (1989a).Relations between Half-Space and Finitely Generated Cones in Polyhedral Cone-Ratio DEA Models. Center for Cybernetic Studies, CCS Research Report No. 636, University of Texas, Austin.

  • Charnes, A., W.W. Cooper, Z.M. Huang, and D.B. Sun. (1990). “Polyhedral Cone-Ratio, DEA Models with an Illustrative Application to Large Commercial Banks.”Journal of Econometrics 46, 73–91.

    Google Scholar 

  • Charnes, A., W.W. Cooper, and E. Rhodes. (1978). “Measuring the Efficiency of Decision-Making Units.”European Journal of Operational Research 2, 429–444.

    Google Scholar 

  • Charnes, A., W.W. Cooper, and E. Rhodes. (1979). “Measuring the Efficiency of Decision-Making Units.”European Journal of Operations Research 3, 339.

    Google Scholar 

  • Charnes, A., W.W. Cooper, and L. Seiford. (1983).An Empirical DEA Production Function, Center for Cybernetic Studies, University of Texas, Austin, CCS Project Research Report, 1981. Reissued as CCS Report 459,Pareto-Optimality, Efficiency Analysis and Empirical Production Functions, with additional authors B. Golany and J. Stutz.

  • Charnes, A., W.W. Cooper, L. Seiford, and J. Stutz. (1982). “A Multiplicative Model for Efficiency Analysis.”Socio-Economic Planning Sciences 16, 223.

    Google Scholar 

  • Charnes, A., W.W. Cooper, L. Seiford, and J. Stutz. (1983). “Invariant Multiplicative Efficiency and Piecewise Cobb-Douglas Envelopments.”Operations Research Letters 2, 101.

    Google Scholar 

  • Charnes, A., W.W. Cooper, and R.M. Thrall. (1986). “Classifying and Characterizing Efficiencies and Inefficiencies in Data Envelopment Analysis.”Operations Research Letters 5, 105–110.

    Google Scholar 

  • Charnes, A., W.W. Cooper, and R.M. Thrall. (1991). “A Structure for Classifying and Characterizing Efficiencies and Inefficiencies in Data Envelopment Analysis.”Journal of Productivity Analysis 2, 197–237.

    Google Scholar 

  • Charnes, A.W., W.W. Cooper, Q.L. Wei, and Z.M. Huang. (1989b). “Cone Ratio Date Envelopment Analysis and Multi-Objective Programming.”International Journal of Systems Science 20, 1099–1118.

    Google Scholar 

  • Clark. J.A. (1988). “Economies of Scale and Scope at Depository Financial Institutions: A Review of the Literature.”Economic Review, Federal Reserve of Kansas City, Kansas City, Sep./Oct., pp. 16–33.

  • Fare, R., S. Grosskopf, and C.A. Knox Lovell. (1985).The Measurement of Efficiency of Production, Boston: Kluwer-Nijhoff.

    Google Scholar 

  • Fare, R., and W. Hunsaker. (1986). “Notions of Efficiency and Their Reference Sets.”Management Science 32, 237–243.

    Google Scholar 

  • Fare, R., and C.A. Knox Lovell. (1988). “Aggregation and Efficiency.” In W. Eichhorn, (ed.),Measurement in Economics. Heidelberg: Physica-Verlag, pp. 639–647.

    Google Scholar 

  • Farrell, M.J. (1957). “The Measurement of Productive Efficiency.”Journal of the Royal Statistical Society Series A 120, 251–281.

    Google Scholar 

  • Federal Reserve Bank of Kansas City. (1990). “Farm Real Estate Values, Nonirrigated Land and Irrigated Land.” unpublished survey for years 1976–1988.

  • Ferrier, G.S., and C.A.K. Lovell (1990). “Measuring Cost Efficiency in Banking: Econometric and Linear Programming Evidence.”Journal of Econometrics 46, 229–243.

    Google Scholar 

  • Fixler, D.J., and K.D. Zieschang. (1991). “Pricing Imputation Problems in Commercial Banking.”EURO XI, Final Program, 11th European Congress on Operational Research, RWTH Aachen.

  • Karlin, S. (1959).Mathematical Methods and Theory in Games, Programming, and Economics. Reading, MA: Addison-Wesley.

    Google Scholar 

  • Seiford, L.H. (1990). “A Bibliography of Data Envelopment Analysis (1978–1986).”DEA Bibliography., 5.0, University of Massachusetts Amherst.

    Google Scholar 

  • Seiford, L.M. and R.M. Thrall. (1990). “Recent Developments in DEA: The Mathematical Approach to Frontier Analysis.”Journal of Econometrics 46, 7–38.

    Google Scholar 

  • Shephard, R.W. (1970).Theory of Cost and Production Functions. Princeton, NJ: Princeton University Press.

    Google Scholar 

  • Thompson, R.G., L.N. Langemeier, C-T. Lee, E. Lee, and R.M. Thrall. (1990). “The Role of Multiplier Bounds in Efficiency Analysis with an Application to Kansas Farming.”Journal of Econometrics 46, 93–108.

    Google Scholar 

  • Thompson, R.G., F.D. Singleton, Jr, R.M. Thrall, and B.A. Smith. (1986). “Comparative Site Evaluations for Locating High Energy Physics, Lab in Texas.”TIMS Interfaces 16, 35–49.

    Google Scholar 

  • Thompson, R.G., and R.M. Thrall. (1993). “Polyhedral Assurance Regions with Linked Constraints.”Computational Economics Conference. Boston: Kluwer Academic Publishers.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Decision and Information Sciences, University of Houston, 77204-6282, Houston, Texas

    Russell G. Thompson & P. S. Dharmapala

  2. Jesse H. Jones Graduate School of Adminisration, Rice University, P.O. Box 1892, 77251, Houston, Texas

    Robert M. Thrall

Authors
  1. Russell G. Thompson
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. P. S. Dharmapala
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Robert M. Thrall
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

The editor for this paper was R. Robert Russell.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Thompson, R.G., Dharmapala, P.S. & Thrall, R.M. Importance for DEA of zeros in data, multipliers, and solutions. J Prod Anal 4, 379–390 (1993). https://doi.org/10.1007/BF01073546

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01073546

Keywords

Search

Navigation