The decomposition of efficiency in parallel network production models

Antonio Peyrache, Maria C. A. Silva

Research output: Contribution to journalArticlepeer-review



Kao (2012) proposed a method to decompose DMU efficiency into sub-unit efficiencies for parallel production systems. We provide a numerical example showing that the proposed method can yield negative sub-unit efficiency scores under variable returns to scale, against common sense and standard postulates requiring this score to be non-negative. As a solution, we propose a decomposition based on the directional distance function that does not suffer from this problem. In particular, we recognize that the overall inefficiency of the DMU is composed of the sub-units technical inefficiencies and a reallocation inefficiency component. The proposed method can be also applied to non-convex technologies, therefore providing a more general method to implement such a decomposition. Given the connection between the directional distance function and slack-based efficiency measurement, the method can easily be extended to this case as well.
Original languageEnglish
Article number103084
Number of pages6
Publication statusPublished - Sept 2024


  • Data envelopment analysis
  • Directional distance function
  • Free disposal hull
  • Inefficiency
  • Networks


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