Zero weights and non-zero slacks: different solution to the same problem

Maria C.A. Silva Portela, Emmanuel Thanassoulis

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish
Pages (from-to)129-147
Number of pages19
JournalAnnals of Operations Research
Issue number1
Publication statusPublished - Jul 2006


  • dataenvelopment analysis (DEA)
  • efficient facets analysis
  • non-radial models
  • weight restrictions


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