10.57647/mathsci.2025.1901.04

Fixed Cost Allocation with a Minimum Distance to Fair Allocation in Fuzzy Data Envelopment Analysis

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  • Elahe Sarfi1,
  • Esmat Noroozi2,
  • Farhad Hosseinzadeh Lotfi3,
  • Mohammadreza Shahriari4,
  • Tofigh Allahviranloo5,
  • Sovan Samanta*5,6,7,
  • Leo Mrsic7,8,
  1. Department of Mathematics, Damghan Branch, Islamic Azad University, Damghan, Iran
  2. Department of Mathematics, East Tehran Branch, Islamic Azad University, Tehran, Iran
  3. Department of Mathematics, Science and Branch, Islamic Azad University, Tehran, Iran
  4. Department of Industrial Management, South Tehran Branch, Islamic Azad University, Tehran, Iran
  5. Research Center of Performance and Productivity Analysis, Istinye University, Istanbul, Turkiye
  6. Department of Mathematics, Tamralipta Mahavidyalaya, WB-721636, India
  7. Department of Technical Sciences, Algebra Bernays University, Gradiscanska 24, 10000 Zagreb, Croatia
  8. Rudolfovo Science and Technology Centre Novo Mesto, Slovenia

Received: 2025-01-21

Revised: 2025-03-09

Accepted: 2025-03-26

Published in Issue 2025-03-31

Copyright (c) 2025 Elahe Sarfi, Esmat Noroozi, Farhad Hosseinzadeh Lotfi, Mohammadreza Shahriari, Tofigh Allahviranloo, Sovan Samanta, Leo Mrsic (Author)

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This work is licensed under a Creative Commons Attribution 4.0 International License.

How to Cite

Sarfi, E., Noroozi, E., Hosseinzadeh Lotfi, F., Shahriari, M., Allahviranloo, T., Samanta, S., & Mrsic, L. (2025). Fixed Cost Allocation with a Minimum Distance to Fair Allocation in Fuzzy Data Envelopment Analysis. Mathematical Sciences, 19(1 (March 2025). https://doi.org/10.57647/mathsci.2025.1901.04
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Abstract

Resource allocation in Data Envelopment Analysis (DEA) has been extensively studied, yet most works focus on redistributing available resources rather than allocating unavoidable fixed costs among decision-making units (DMUs). This study addresses the important problem of fixed cost allocation, aiming to ensure that inefficient DMUs can become efficient while keeping allocations as fair as possible, thereby providing a practical decision-making tool in real-world contexts such as banking and manufacturing.
We propose a new linear DEA-based model that allocates fixed costs so as to transform an inefficient DMU into an efficient one, with the objective of minimizing the deviation from fair allocation. The model is then generalized to a fuzzy environment by incorporating triangular fuzzy numbers for inputs, outputs, and costs, and validated using benchmark datasets from Cook and Kress and Wang et al. The results demonstrate that the proposed models can successfully enhance the efficiency of targeted DMUs while producing allocations close to fairness, and the fuzzy extension proves robust in handling imprecise data. The key novelties of this research are (i) introducing a linear efficiency-improving allocation model with minimum distance to fairness, (ii) extending the allocation problem to fuzzy DEA by considering fuzzy costs alongside fuzzy inputs and outputs, and (iii) showing that this integrated framework has not been addressed before in the literature, thereby offering a novel, practical, and equitable approach for fixed cost allocation in DEA.

Keywords

  • Data Envelopment Analysis,
  • Efficiency,
  • Allocation,
  • Fair allocation,
  • Triangular fuzzy number
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