LLM-Assisted Virtual Expert Weight Elicitation in Pharmaceutical Supply Chains: A Z-Number Multi-Agent Framework

Abstract

The elicitation of criteria weights in spatial and logistical Multi-Criteria Decision Making (MCDM) typically relies on panels of human domain experts. However, in specialized high-stakes contexts such as pharmaceutical inventory management, expert availability is scarce, expensive, and subject to cognitive biases. This study proposes a novel methodological framework that offers a structured alternative to traditional human panels by employing a Multi-Agent System (MAS) of Large Language Models (LLMs) to generate subjective weights. We introduce a rigorous Z-number-based fuzzy AHP approach in which LLMs, acting as autonomous virtual experts, defined as Agents LLM1, LLM2, and LLM3, perform iterative pairwise comparisons. The methodology strictly separates internal logical consistency, verified via Consistency Ratios (CR) on crisp matrices, from confidence modeling, which is handled via Z-numbers. The LLM-derived weights were aggregated over k=3 iterations to mitigate stochasticity and hybridized with objective CRITIC weights to rank nine Vendor Managed Inventory (VMI) policies. Results indicate strong ranking invariance across all agents and hybridization ratios (ρ=1.0). Beyond numerical stability, the framework demonstrates "behavioral isomorphism" with human ethical standards, explicitly enforcing a "safety-first" constraint. This suggests that LLM-driven frameworks exhibit "dominance stability," positioning them as robust cognitive simulators that align optimization metrics with domain-specific priorities such as patient safety.