Zero weights and non-zero slacks: Different solutions to the same problem |
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Authors: | Maria Conceição A Silva Portela Emmanuel Thanassoulis |
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Institution: | (1) Universidade Católica, Portuguesa, Centro Regional do Porto, R. Diogo Botelho, 1327, 4169-005 Porto, Portugal;(2) Aston Business School, Aston Triangle, B4 7ET, Birmingham, UK |
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Abstract: | This paper re-assesses three independently developed approaches that are aimed at solving the problem of zero-weights or non-zero
slacks in Data Envelopment Analysis (DEA). The methods are weights restricted, non-radial and extended facet DEA models. Weights
restricted DEA models are dual to envelopment DEA models with restrictions on the dual variables (DEA weights) aimed at avoiding
zero values for those weights; non-radial DEA models are envelopment models which avoid non-zero slacks in the input-output
constraints. Finally, extended facet DEA models recognize that only projections on facets of full dimension correspond to
well defined rates of substitution/transformation between all inputs/outputs which in turn correspond to non-zero weights
in the multiplier version of the DEA model. We demonstrate how these methods are equivalent, not only in their aim but also
in the solutions they yield. In addition, we show that the aforementioned methods modify the production frontier by extending
existing facets or creating unobserved facets. Further we propose a new approach that uses weight restrictions to extend existing
facets. This approach has some advantages in computational terms, because extended facet models normally make use of mixed
integer programming models, which are computationally demanding. |
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Keywords: | Data Envelopment Analysis (DEA) Weight restrictions Non-radial models Efficient facets analysis |
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