An advanced data analytic approach for reallocating green gas emissions in cap-and-trade context

Reza Farzipoor Saen*, Zohreh Moghaddas, Majid Azadi

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


The swift economic growth experienced by nations has exacerbated the challenge of global warming over the years. Cap-and-trade stands out as the most effective approach for managing and reducing greenhouse gas emissions. This study aims to construct a data envelopment analysis model to redistribute authorized emissions among decision-making units (DMUs). Notably, the model accounts for the intricate relationship between the production of desirable and undesirable outputs within the cap-and-trade framework. Furthermore, the model adapts the current mathematical modelling by addressing undesirable output as an inherent by-product of the desirable output. Emphasis is placed on maximizing the collective efficiency scores of all DMUs. Additionally, to confront the presence of multiple potential optimal solutions in the cap-and-trade context, the model computes the efficiency interval of DMUs. Finally, the paper showcases the model's capabilities by presenting a comprehensive case study, demonstrating its practical application and effectiveness in addressing emissions reallocation within the cap-and-trade system.

Original languageEnglish
JournalAnnals of Operations Research
Early online date28 Feb 2024
Publication statusE-pub ahead of print - 28 Feb 2024

Bibliographical note

Copyright © 2024, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature. This version of the article has been accepted for publication, after peer review and is subject to Springer Nature’s AM terms of use [], but is not the Version of Record and does not reflect post-acceptance improvements, or any corrections. The Version of Record is available online at:


  • Cap-and-trade
  • Data envelopment analysis (DEA)
  • Efficiency
  • Reallocation
  • Undesirable outputs


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