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Zero weights and non-zero slacks: Different solutions to the same problem
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Authors
Advisor(s)
Abstract(s)
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; nonradial
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.
Description
Keywords
Data Envelopment Analysis (DEA) Weight restrictions Non-radial models Efficient facets analysis
Pedagogical Context
Citation
PORTELA, Maria; THANASSOULIS, Emmanuel - Zero weights and non-zero slacks: Different solutions to the same problem. Annals of Operations Research. ISSN 0254-5330. Vol. 145 (2006), p. 129–147
Publisher
Springer Verlag