Polarity in DEA Models

Per Agrell (), Peter Bogetoft and Jorgen Tind

No 24188, Unit of Economics Working Papers from Royal Veterinary and Agricultural University, Food and Resource Economic Institute

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.

Keywords: Research; Methods/; Statistical; Methods (search for similar items in EconPapers)
Pages: 20
Date: 2000
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Persistent link: https://EconPapers.repec.org/RePEc:ags:rvaewp:24188

DOI: 10.22004/ag.econ.24188

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