Advertisement

Hyper Sensitivity Analysis of Productivity Measurement Problems

  • L. Churilov
  • M. Sniedovich
Part of the International Series in Operations Research & Management Science book series (ISOR, volume 43)

Abstract

In this paper we introduce a method for conducting a Hyper Sensitivity Analysis (HSA) of productivity and efficiency measurement problems. HSA is an intuitive generalization of conventional sensitivity analysis where the term “hyper” indicates that the sensitivity analysis is conducted with respect to functions rather than numeric values. The concept of HSA is suited for situations where several candidates for the function quantifying the utility of (input, output) pairs are available. Both methodological and technical issues arising in the area of multiple criteria productivity measurement in the context of such an analysis are examined.

Keywords

hyper sensitivity analysis productivity efficiency DEA multiple objective programming composite concave programming. 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Althin R., Fare R., and Grosskopf S. Profitability and Productivity Changes: An Application to Swedish Pharmacies. Annals of Operations Research, 1996; 66: 219–230CrossRefGoogle Scholar
  2. Avkiran N.K. Productivity Analysis in the Services Sector with Data Envelopment Analysis. Queensland, Australia: N.K. Avkiran Publishers, 1999Google Scholar
  3. Bjurek H. Essays on Efficiency and Productivity Change with Applications to Public Service Production. Ekonomiska Studier 52, School of Economics and Commercial Law, University of Gothenburg, 1994Google Scholar
  4. Bouyssou D. Using DEA as a Tool for MCDM: Some Remarks. Journal of the Operational Research Society, 1999; 50: 974–978Google Scholar
  5. Byrne A., Sniedovich M., and Churilov L. Handling Soft Constraints via Composite Concave Programming. Journal of the Operational Research Society, 1998; 49: 870–877Google Scholar
  6. Caves D.W., Christensen L.R., and Diewert W.E. The Economic Theory of Index Numbers and the Measurement of Input, Output, and Productivity. Econometrica 1982; 50: 1393–1414CrossRefGoogle Scholar
  7. Charnes A., Cooper W.W., and Thrall R.M. Classifying and Characterizing Efficiencies and Inefficiencies in Data Envelopment Analysis. Operations Research Letters, 1986; 5(3):105–110CrossRefGoogle Scholar
  8. Churilov L. Global Optimization through Composite Linearization. PhD Thesis, Department of Mathematics and Statistics, The University of Melbourne, Australia, 1998Google Scholar
  9. Churilov L., Ralph D., and Sniedovich M. A Note on Composite Concave Quadratic Programming. Operations Research Letters, 1998; 23: 163–169CrossRefGoogle Scholar
  10. Churilov L., Bomze I., Sniedovich M., and Ralph D. Hyper Sensitivity Analysis of Portfolio Optimization Problems. Submitted for publication. 1999Google Scholar
  11. Coelli T., Prasada Rao D.S., and Battese G. An Introduction to Efficiency and Productivity Analysis. Boston, USA: Kluwer Academic Publishers, 1998CrossRefGoogle Scholar
  12. Davis H. Productivity Accounting. USA: The Wharton School Industrial Research Unit, University of Pennsylvania, 1951 (reprint 1978).Google Scholar
  13. Domingo A. and Sniedovich M. Experiments with Dynamic Programming Algorithms for Nonseparable Problems. European Journal of Operations Research 1993; 67(2): 172–187CrossRefGoogle Scholar
  14. French S. Decision Theory — An Introduction to the Mathematics of Rationality. New York: John Wiley and Sons, 1988Google Scholar
  15. Fried H.O., Knox Lovell C.A., and Schmidt S.S. The Measurement of Productive Efficiency: Techniques and Applications. New York, USA: Oxford University Press, 1993Google Scholar
  16. Fuentes H., Grifell-Tatje E., and Perelman S. “A Parametric Distance Function Approach for Malmquist Index Estimation”. Working Paper, CREPP 98/03, Centre de Recherche en Economie Publique et en Economie de la Population, Universite de Liege, Belgium, 1998 Google Scholar
  17. Gal T. Postoptimality Analyses, Parametric Programming and Related Topics. Berlin, Germany: de Gruyter, 1995Google Scholar
  18. Hillier F.C. and Lieberman G.J. Introduction to Operations Research. 5th edition. New York, USA: McGraw-Hill, 1990Google Scholar
  19. Joro T., Korhonen P., and Wallenius J. Structural Comparison of Data Envelopment Analysis and Multiple Objective Linear Programming. Management Science 1998; vol.44, No.7: 962–970CrossRefGoogle Scholar
  20. Macalalag E. and Sniedovich M. Generalized Linear Programming and Sensitivity Analysis Techniques. Naval Research Logistics 1996; 43: 397–413CrossRefGoogle Scholar
  21. Schrage L. Optimization Modeling with LINDO. New York: The Scientific Press, 5th edition, 1997Google Scholar
  22. Shamir R. The Efficiency of the Simplex Method, a Survey. Management Science 1987; 33: 301–334CrossRefGoogle Scholar
  23. Sink D.S. Productivity Management: Planning, Measurement and Evaluation, Control and Improvement. New York: John Wiley & Sons, 1989.Google Scholar
  24. Sniedovich M. C-programming and the Minimization of Pseudolinear and Additive Concave functions. Operations Research Letters 1986; 5(4): 185–189CrossRefGoogle Scholar
  25. Sniedovich M. Algorithmic and Computational Aspects of Composite Concave Programming. International Transactions in Operations Research 1994; 1(1): 75–84CrossRefGoogle Scholar
  26. Steuer R. Multiple Criteria Optimization: Theory, Computation, and Application. New York: John Wiley & Sons, 1986Google Scholar
  27. Stewart TJ. Relationship between Data Envelopment Analysis and Multicriteria Decision Analysis. Journal of the Operational Research Society 1996; 47: 654–665Google Scholar

Copyright information

© Springer Science+Business Media New York 2002

Authors and Affiliations

  • L. Churilov
    • 1
  • M. Sniedovich
    • 2
  1. 1.School of Business SystemsMonash UniversityAustralia
  2. 2.Department of Mathematics and StatisticsThe University of MelbourneAustralia

Personalised recommendations