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Polarity in DEA Models

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  • Agrell, Per J.
  • Bogetoft, Peter
  • Tind, Jorgen

Abstract

This article discusses models in data envelopment analysis (DEA) relaxing the standard convexity assumptions. The basic model treats mutually incomparable pairs of sets to be generated by a procedure proposed earlier. Each pair consists of a consumption set and a production set of feasible input-output combinations. Two fundamental operations by the procedure are based on intersection and convex hull generation in the input-output space. A polarity analysis is performed which, subject to the usual assumptions about free disposability and nonnegativity, appears fruitful to do in the framework of blocking and antiblocking sets. It is shown how this leads to an interchange of the above operations extending some classical results from convex analysis. The last part of the paper presents a pair of linear programming models calculating a Farrell productivity index based on a preceeding application of the procedure. This is a generalization of the classical linear programming models in DEA subject to standard assumptions about convexity.

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Bibliographic Info

Paper provided by Royal Veterinary and Agricultural University, Food and Resource Economic Institute in its series Unit of Economics Working papers with number 24188.

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Date of creation: 2000
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Handle: RePEc:ags:rvaewp:24188

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Web page: http://www.foi.life.ku.dk/
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Related research

Keywords: Data Envelopment Analysis; polarity; Research Methods/ Statistical Methods;

References

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  1. Evers, J.J.M. & Rockafellar, R.T. & Ruys, P.H.M. & Weddepohl, H.N. & Westermann, L.R.J., 1978. "Convex analysis and mathematical economics," Research Memorandum 71, Tilburg University, Faculty of Economics and Business Administration.
  2. Banker, Rajiv D., 1984. "Estimating most productive scale size using data envelopment analysis," European Journal of Operational Research, Elsevier, vol. 17(1), pages 35-44, July.
  3. Niels Christian Petersen, 1990. "Data Envelopment Analysis on a Relaxed Set of Assumptions," Management Science, INFORMS, vol. 36(3), pages 305-314, March.
  4. Peter Bogetoft, 1996. "DEA on Relaxed Convexity Assumptions," Management Science, INFORMS, vol. 42(3), pages 457-465, March.
  5. Charnes, A. & Cooper, W. W. & Rhodes, E., 1978. "Measuring the efficiency of decision making units," European Journal of Operational Research, Elsevier, vol. 2(6), pages 429-444, November.
  6. R. D. Banker & A. Charnes & W. W. Cooper, 1984. "Some Models for Estimating Technical and Scale Inefficiencies in Data Envelopment Analysis," Management Science, INFORMS, vol. 30(9), pages 1078-1092, September.
  7. Peter Bogetoft & Joseph M. Tama & Jørgen Tind, 2000. "Convex Input and Output Projections of Nonconvex Production Possibility Sets," Management Science, INFORMS, vol. 46(6), pages 858-869, June.
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