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Enhanced Russell Measure Model for Two-Stage Systems with Undesirable Outputs: An Envelopment-Multiplier Approach

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  • Keyvan Asanimoghaddam

    (University of Guilan, Department of Applied Mathematics, Faculty of Mathematical Sciences)

  • Maziar Salahi

    (University of Guilan, Department of Applied Mathematics, Faculty of Mathematical Sciences)

  • Rita Shakouri

    (Technical and Vocational University (TUV), Department of Computer Engineering, Faculty of Electrical and Computer Engineering)

Abstract

The main objective of this study is to introduce the Enhanced Russell Measure (ERM) model for evaluating two-stage systems producing undesirable outputs. It utilizes an external evaluation approach, which involves calculating overall system efficiency and determining individual stage efficiencies using the multiplier (dual) model after linearization. Additionally, conceptual constraints are applied to ensure that efficiency values remain within the range of 0 to 1 and that the relationship between the overall efficiency and the efficiency of the stages is maintained. It effectively overcomes the limitations of traditional models, enhancing the accuracy of efficiency analyses. When applied to data on railway systems of 22 European countries in 2016–2017, the model successfully resolves the issue of efficiency values exceeding 1, and each efficient stage identified within the ERM linear envelopment model did not require improvement. It also provides more accurate calculations of individual stage efficiencies, allowing for better comparisons of complex system performance.

Suggested Citation

  • Keyvan Asanimoghaddam & Maziar Salahi & Rita Shakouri, 2025. "Enhanced Russell Measure Model for Two-Stage Systems with Undesirable Outputs: An Envelopment-Multiplier Approach," SN Operations Research Forum, Springer, vol. 6(4), pages 1-22, December.
    • Handle: RePEc:spr:snopef:v:6:y:2025:i:4:d:10.1007_s43069-025-00580-4
    DOI: 10.1007/s43069-025-00580-4
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