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An integrated design methodology based on the use of group AHP-DEA approach for measuring lean tools efficiency with undesirable output

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Abstract

The selection of lean tools is one of the crucial factors for decision makers and practitioners in a competitive environment. A few efforts have been made based on problem selection. Conversely, numerical studies have been done on analytical hierarchy process (AHP)–data envelopment analysis (DEA) as well as DEA-undesirable variables separately. Thus, there is a shortage of lean practitioners as well as the methods involved. The present research aims at integrating AHP and DEA with desirable and undesirable factors to evaluate the lean tools and techniques and to rank the aspect of efficacy. We suggest a logical procedure to measure the efficacy of lean tools on leanness and to prioritize them as decision makers. In this extensive research, we apply the integrated multicriteria decision-making approach, including the hybrid groups AHP and DEA models with desirable and undesirable variables, to assess the relative efficiency of lean manufacturing tools and techniques. Case studies are used to demonstrate the lean implementation in companies while being validated by a panel of experts. The integration of these approaches has created synergy and shown to be even more powerful. Thus, the proposed integrated AHP-DEA model can evaluate and rank different alternatives while considering desirable and undesirable variables in the production processes.

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Authors and Affiliations

  1. Department of Industrial Engineering, Gachsaran Branch, Gachsaran, Iran

    Alireza Anvari

  2. Department of Mechanical and Manufacturing Engineering, UPM, Serdang, Malaysia

    Norzima Zulkifli

  3. Department of Industrial Engineering, Science and Research Branch, Kerman, Iran

    Shahryar Sorooshian

  4. Department of Industrial Engineering, Najafabad Branch, Najafabad, Iran

    Omid Boyerhassani

Authors
  1. Alireza Anvari
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  2. Norzima Zulkifli
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  3. Shahryar Sorooshian
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  4. Omid Boyerhassani
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Corresponding author

Correspondence to Alireza Anvari.

Appendices

Appendix A

1.1 Calculating the consistency ratio

Table 12 Rating weights of criteria by the comparison matrix
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Table 13 Geometric average of rating weights of criteria by the comparison matrix
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Table 14 Normalization of rating weights of criteria by the comparison matrix
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Table 15 Weight importance of the criteria
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Table 16 Weights criteria multiplied by Geometric average of matrix
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Table 17 Calculating weighted sum vector by weights criteria multiplied by geometric average of matrix
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Table 18 Calculation of the consistency vector
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Appendix B

2.1 Prioritization of the thirteen alternatives under four criteria by AHP Method

Table 19 Scores of 13 alternatives by decision makers under all criteria
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Table 20 DMUs data—weights of criteria multiplied by weights geometric average of alternatives matrix
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Table 21 Normalization of rating weights of alternatives based on all criteria and prioritizing alternatives
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Table 22 Final ranking of 13 alternatives
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Appendix C

3.1 BCC-DEA method-without considering AHP, weighting, and undesirable variables.

Table 23 Scores of 13 alternatives by decision makers under all criteria
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Table 24 DMUs data—geometric average of alternatives based on all criteria
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3.2 BCC Method by Lingo Software

Tool (0.7725496)

Maximize 3.2453u1 + w

Subject to

  1. 1.

    3.5195v1 + 4.4163v2 + 4.162766v3 = 1

  2. 2.

    3.2453u1 − 3.5195v1 − 4.4163v2 − 4.162766v3 + w ≤ 0

  3. 3.

    3.5944u1 − 2.5508v1 − 3.9487v2 − 4.742881v3 + w ≤ 0

  4. 4.

    2.7866u1 − 4.6779v1 − 3.5652v2 − 2.352158v3 + w ≤ 0

  5. 5.

    4.2823u1 − 3.8981v1 − 4.6179v2 − 3.063887v3 + w ≤ 0

  6. 6.

    2.9302u1 − 2.8252v1 − 3.7585v2 − 4.317359v3 + w ≤ 0

  7. 7.

    2.5508u1 − 2.3522v1 − 3.1777v2 − 3.981071v3 + w ≤ 0

  8. 8.

    2.3522u1 − 3.3659v1 − 3.9487v2 − 4.416333v3 + w ≤ 0

  9. 9.

    2.0477u1 − 1.6438v1 − 2.9302v2 − 5.348051v3 + w ≤ 0

  10. 10.

    4.2273u1 − 4.6179v1 − 4.5144v2 − 2.402248v3 + w ≤ 0

  11. 11.

    3.7585u1 − 4.7818v1 − 3.8981v2 − 2.168943v3 + w ≤ 0

  12. 12.

    4.0723u1 − 3.2271v1 − 3.6801v2 − 2.352158v3 + w ≤ 0

  13. 13.

    1.8206u1 − 2.6052v1 − 2.8252v2 − 3.437543v3 + w ≤ 0

  14. 14.

    2.7663u1 − 1.6438v1 − 3.4713v2 − 4.828651v3 + w ≤ 0

  15. 15.

    u1 > =0

  16. 16.

    v1 > =0

  17. 17.

    v2 > =0

  18. 18.

    v3 > =0

  19. 19.

    w > =0

Similarly, this formula has been applied for the other alternatives (tools and techniques). As a result Table 24 shows scores of each alternatives.

Table 25 Ranking of thirteen alternatives under four criteria using the BCC-DEA method
Full size table

Appendix D

Table 26 The ten questions put to experts for the purpose of measuring method validation
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A panel comprising of twelve experts was selected in order to validate the method and results. All members of the panel were interviewed personally and were informed of the objectives and the process of lean tools selection

A panel of experts as the more professional group in LM uses the linguistic variables to assess the method. The linguistic evaluations are converted into crisp numbers. The results of this validation are illustrated in Fig. 4.

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Anvari, A., Zulkifli, N., Sorooshian, S. et al. An integrated design methodology based on the use of group AHP-DEA approach for measuring lean tools efficiency with undesirable output. Int J Adv Manuf Technol 70, 2169–2186 (2014). https://doi.org/10.1007/s00170-013-5369-z

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