Obviating some of the theoretical barriers of analytical hierarchy process by a revised eigenvector method: a case study in sustainable supplier selection

In recent decades, Group Decision-Making (GDM) has emerged as a potent strategy for addressing pivotal decisions within organizations. A fundamental step in GDM methodologies, such as the Analytical Hierarchy Process (AHP), involves deriving priorities from Pairwise Comparison Matrices (PCMs). The Eigenvector Method (EM) has conventionally served as the prevailing means for weight determination in AHP. Nonetheless, inherent limitations mar its effectiveness, primarily stemming from its non-linearity and susceptibility to inconsistency-related issues. To redress these shortcomings, this paper advances a novel approach by first introducing a Linear Programming (LP) methodology grounded in EM principles for priority derivation. Subsequently, the paper introduces three distinctive LP models, which utilize an enhanced set of constraints derived from revised EM constraints, to ascertain both weights and priorities within the PCM. Notably, these models yield accurate weights for Perfectly Consistent PCM (PCPCM) and effectively determine optimal local priorities for inconsistent PCMs, closely aligned with EM-derived priority vectors. Comparative analysis between the proposed models and existing counterparts underscores the superiority of the former, particularly in weight determination. The proposed models, showcased through a comprehensive case study, exhibit significant advantages in enhancing GDM through the AHP technique, thereby substantiating their practical applicability. Key contributions of this paper include the novel proposition of a LP approach grounded in EM for priority derivation, and the introduction of three innovative models for weights and priority determination. These models are subsequently adapted for GDM within the AHP framework. Moreover, the proposed models stand resilient against the issue of rank reversal, even with the addition or removal of unrelated choices. Additionally, their adaptability extends to the group AHP (GAHP) method, encompassing interval and fuzzy weights. In summation, this paper underscores the evolution of GDM methodologies, propelling the field towards enhanced precision and applicability. The introduced models not only address existing limitations but also lay the foundation for novel avenues of research and practice in multi-criteria decision-making paradigms.