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A New Linear Programming Method for Weights Generation and Group Decision Making in the Analytic Hierarchy Process

Author

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  • Seyed Saeed Hosseinian

    (Shahed University)

  • Hamidreza Navidi

    (Shahed University)

  • Abas Hajfathaliha

    (Shahed University)

Abstract

This paper proposes a new linear programming method entitled by LP-GW-AHP for weights generation in analytic hierarchy process (AHP) which employs concepts from data envelopment analysis. We propose four specially constructed linear programming (LP) models which are used to derive weight vector from a pair-wise comparison matrix or a group of them. We can use both interval and relative importance weights for each decision maker in LP-GW-AHP. In this method, solving only one LP model is enough for local weights derivation from pair-wise comparison matrices. Five numerical examples are examined to illustrate the potential applications of the LP-GW-AHP method. We show that not only derived weights of the new method have slight differences than Saaty’s eigenvector weights but sometimes they are better than eigenvector method weights in the fitting performance index as well. LP-GW-AHP is compared with a method which has been recently proposed for the weights derivation in the group AHP and it becomes obvious that LP-GW-AHP provides better weights. The simple additive weighting method is utilized to aggregate local weights without the need to normalize them.

Suggested Citation

  • Seyed Saeed Hosseinian & Hamidreza Navidi & Abas Hajfathaliha, 2012. "A New Linear Programming Method for Weights Generation and Group Decision Making in the Analytic Hierarchy Process," Group Decision and Negotiation, Springer, vol. 21(3), pages 233-254, May.
    • Handle: RePEc:spr:grdene:v:21:y:2012:i:3:d:10.1007_s10726-009-9182-x
    DOI: 10.1007/s10726-009-9182-x
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    References listed on IDEAS

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    Cited by:

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    2. Vijay Pereira & Umesh Bamel, 2023. "Charting the managerial and theoretical evolutionary path of AHP using thematic and systematic review: a decadal (2012–2021) study," Annals of Operations Research, Springer, vol. 326(2), pages 635-651, July.
    3. Kao, Chiang & Liu, Shiang-Tai, 2022. "Group decision making in data envelopment analysis: A robot selection application," European Journal of Operational Research, Elsevier, vol. 297(2), pages 592-599.
    4. Kamvysi, Konstantina & Gotzamani, Katerina & Andronikidis, Andreas & Georgiou, Andreas C., 2014. "Capturing and prioritizing students’ requirements for course design by embedding Fuzzy-AHP and linear programming in QFD," European Journal of Operational Research, Elsevier, vol. 237(3), pages 1083-1094.
    5. Kamvysi, Konstantina & Andronikidis, Andreas & Georgiou, Andreas C. & Gotzamani, Katerina, 2023. "A quality function deployment framework for service strategy planning," Journal of Retailing and Consumer Services, Elsevier, vol. 73(C).
    6. Paweł Karczmarek & Witold Pedrycz & Adam Kiersztyn, 2021. "Fuzzy Analytic Hierarchy Process in a Graphical Approach," Group Decision and Negotiation, Springer, vol. 30(2), pages 463-481, April.

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