A two-stage DEA model with partial impacts between inputs and outputs: application in refinery industries

Mohammad Nemati, Reza Kazemi Matin*, Mehdi Toloo

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

13 Citations (Scopus)


Conventional data envelopment analysis (DEA) methods are useful for estimating the performance measure of decision making units (DMUs) that each DMU uses multiple inputs to produce multiple outputs without considering any partial impacts between inputs and outputs. Nevertheless, there are some real-world situations where DMUs may possess several production lines with a two-stage network structure that each production line use inputs according to their needs. The current paper extends the recent work by Ma (Expert Syst Appl Int J 42:4339–4347, 2015) to consider partial impact between inputs and outputs for two-stage network production systems. Toward this end, we consider several input–output bundles in each stage for production lines. We formulate a couple of new mathematical programming models in the DEA framework with the aim of considering partial impact between inputs and outputs for calculating aggregate, overall, and subunit efficiencies along with resource usage by production lines for a two-stage production system Finally, an application in refinery industries is provided as an example to illustrate the potential application of the proposed method.

Original languageEnglish
Pages (from-to)285-312
Number of pages28
JournalAnnals of Operations Research
Issue number1
Publication statusPublished - Dec 2020
Externally publishedYes


  • Data envelopment analysis (DEA)
  • Free intermediate measures
  • Partial impact
  • Two-stage network DEA

ASJC Scopus subject areas

  • Decision Sciences(all)
  • Management Science and Operations Research

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