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Using slacks-based model to solve inverse DEA with integer intervals for input estimation

Author

Listed:
  • Atefeh Younesi

    (University of Cádiz)

  • Farhad Hosseinzadeh Lotfi

    (Islamic Azad University)

  • Manuel Arana-Jiménez

    (University of Cádiz)

Abstract

This paper deals with an inverse data envelopment analysis (DEA) based on the non-radial slacks-based model in the presence of uncertainty employing both integer and continuous interval data. To this matter, suitable technology and formulation for the DEA are proposed using arithmetic and partial orders for interval numbers. The inverse DEA is discussed from the following question: if the output of $$DMU_o$$ D M U o increases from $$Y_o$$ Y o to $$\beta _o$$ β o , such the new DMU is given by $$(\alpha _o^*,\beta )$$ ( α o ∗ , β ) belongs to the technology, and its inefficiency score is not less than t-percent, how much should the inputs of the DMU increase? A new model of inverse DEA is offered to respond to the previous question, whose interval Pareto solutions are characterized using the Pareto solution of a related multiple-objective nonlinear programming (MONLP). Necessary and sufficient conditions for input estimation are proposed when output is increased. A functional example is presented on data to illustrate the new model and methodology, with continuous and integer interval variables.

Suggested Citation

  • Atefeh Younesi & Farhad Hosseinzadeh Lotfi & Manuel Arana-Jiménez, 2023. "Using slacks-based model to solve inverse DEA with integer intervals for input estimation," Fuzzy Optimization and Decision Making, Springer, vol. 22(4), pages 587-609, December.
    • Handle: RePEc:spr:fuzodm:v:22:y:2023:i:4:d:10.1007_s10700-022-09403-1
    DOI: 10.1007/s10700-022-09403-1
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    References listed on IDEAS

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    1. Jahanshahloo, G.R. & Soleimani-damaneh, M. & Ghobadi, S., 2015. "Inverse DEA under inter-temporal dependence using multiple-objective programming," European Journal of Operational Research, Elsevier, vol. 240(2), pages 447-456.
    2. R. D. Banker & A. Charnes & W. W. Cooper, 1984. "Some Models for Estimating Technical and Scale Inefficiencies in Data Envelopment Analysis," Management Science, INFORMS, vol. 30(9), pages 1078-1092, September.
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    Cited by:

    1. Mehdi Soltanifar & Madjid Tavana & Vincent Charles & Mojtaba Ghiyasi & Hamid Sharafi, 2025. "A novel inverse data envelopment analysis model with negative ratio data," Operational Research, Springer, vol. 25(2), pages 1-34, June.
    2. Mojtaba Ghiyasi & Ning Zhu, 2025. "Inverse data envelopment analysis for parallel production systems: an analysis in four types of Chinese banks," International Journal of System Assurance Engineering and Management, Springer;The Society for Reliability, Engineering Quality and Operations Management (SREQOM),India, and Division of Operation and Maintenance, Lulea University of Technology, Sweden, vol. 16(1), pages 29-37, January.
    3. Li-Huan Liao & Lei Chen & Junchao Wang, 2024. "A New Resource Allocation Multiple Criteria Decision-Making Method in a Two-Stage Inverse Data Envelopment Analysis Framework for the Sustainable Development of Chinese Commercial Banks," Sustainability, MDPI, vol. 16(4), pages 1-13, February.

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