Multi-valued measures in DEA in the presence of undesirable outputs

Mehdi Toloo*, Jana Hančlová

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

19 Citations (Scopus)


Data envelopment analysis (DEA) evaluates the relative efficiency of a set of comparable decision making units (DMUs) with multiple performance measures (inputs and outputs). Classical DEA models rely on the assumption that each DMU can improve its performance by increasing its current output level and decreasing its current input levels. However, undesirable outputs (like wastes and pollutants) may often be produced together with desirable outputs in final products which have to be minimized. On the other hands, in some real-world situations, we may encounter some specific performance measures with more than one value which are measured by various standards. In this study, we referee such measures as multi-valued measures which only one of their values should be selected. For instance, unemployment rate is a multi-valued measure in economic applications since there are several definitions or standards to measure it. As a result, selecting a suitable value for a multi-valued measure is a challenging issue and is crucial for successful application of DEA. The aim of this study is to accommodate multi-valued measures in the presence of undesirable outputs. In doing so, we formulate two individual and summative selecting directional distance models and develop a pair of multiplier- and envelopment-based selecting approaches. Finally, we elaborate applicability of the proposed method using a real data on 183 NUTS 2 regions in 23 selected EU-28 countries.

Original languageEnglish
Article number102041
JournalOmega (United Kingdom)
Publication statusPublished - Jul 2020
Externally publishedYes


  • DEA (Data envelopment analysis)
  • Directional output distance function
  • NUTS 2 (Nomenclature des unités territoriales statistiques)
  • Optimistic and pessimistic approaches
  • Selecting models
  • Undesirable outputs

ASJC Scopus subject areas

  • Strategy and Management
  • Management Science and Operations Research
  • Information Systems and Management

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