Developing a Fuzzy Network DEA Model with Linking Constraints to Evaluate Overall and Stage-Level Efficiency of Supply Chains under Uncertainty: An Application in Automotive Manufacturing

Abstract

Traditional data envelopment analysis (DEA) models for assessing supply chain efficiency treat stages independently, ignore links between them, and overlook data uncertainty. This study presents a fuzzy network data envelopment analysis (FNDEA) model to assess the overall efficiency of a three-stage supply chain (supplier, manufacturer, and distributor) under uncertainty. Input, output, and intermediate product variables are modeled as triangular fuzzy numbers. To solve the fuzzy model, the α-cut approach is used, transforming it into two deterministic linear programs with lower (optimistic) and upper (pessimistic) bounds. By applying compatibility constraints on the flow of intermediate products, the model simultaneously accounts for dependencies between stages and presents the efficiency of each stage and the overall efficiency of the chain as intervals. The model is implemented on data from 10 real supply chains, and efficiency is calculated at five α-cut levels of 0, 0.25, 0.5, 0.75, and 1. The results show that the proposed model identifies inefficient steps and provides improvement paths at different levels of uncertainty. This approach allows managers to base decisions on efficiency intervals rather than definite numbers and to conduct more robust analyses in uncertain environments.