Allocating a fixed cost across decision-making units with undesirable outputs: A bargaining game approach

Feng Li, Ali Emrouznejad, Qingyuan Zhu*, Gang Kou

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


Allocating a fixed cost among a set of peer decision-making units (DMUs) is one of the most important applications of data envelopment analysis. However, almost all existing studies have addressed the fixed cost allocation (FCA) problem within a traditional framework while ignoring the existence of undesirable outputs. Undesirable outputs are neither scarce in various production activities in real world applications nor trivial in efficiency evaluation and subsequent decision making. Motivated by this observation, this article attempts to explicitly extend the traditional FCA problem to situations in which DMUs are necessarily involved with undesirable outputs. To this end, we first investigate the efficiency evaluation of DMUs considering undesirable outputs based on the joint weak disposability assumption. Then, flexible FCA schemes are considered to revisit the efficiency evaluation process. The results show that feasible allocation schemes exist such that all DMUs can be simultaneously efficient. Furthermore, we define the comprehensive satisfaction degree and develop a satisfaction degree bargaining game approach to determine a unique FCA scheme. Finally, the proposed approach is tested with an empirical study of banking activities based on real conditions.

Original languageEnglish
JournalJournal of the Operational Research Society
Early online date5 Oct 2021
Publication statusE-pub ahead of print - 5 Oct 2021

Bibliographical note

This is an Accepted Manuscript version of the following article, accepted for publication in Journal of the Operational Research Society . Feng Li, Yue Wang, Ali Emrouznejad, Qingyuan Zhu & Gang Kou (2021) Allocating a fixed cost across decision-making units with undesirable outputs: A bargaining game approach, Journal of the Operational Research Society. It is deposited under the terms of the Creative Commons Attribution-NonCommercial License (, which permits non-commercial re-use, distribution, and reproduction in any medium, provided the original work is properly cited.

Funding: This research was financially supported by the National Natural Science Foundation of China (Nos. 71901178, 71904084, 71725001 and 71910107002), the Natural Science Foundation 25 for Jiangsu Province (No. BK20190427), the Social Science Foundation of Jiangsu Province (No. 19GLC017), and the Fundamental Research Funds for the Central Universities (No. NR2019003).


  • bargaining game
  • comprehensive satisfaction degree
  • data envelopment analysis (DEA)
  • fixed cost allocation (FCA)
  • undesirable outputs


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