Estimating most productive scale size decomposition in a fuzzy network data envelopment analysis model: assessing the sustainability and resilience of the supply chain

This paper estimates the Most Productive Scale Size (MPSS) in the NDEA model to appraise the sustainability and resilience of the supply chains. As the corresponding input and output criteria are not always accurately measurable, we also introduce the fuzzy version of our proposed NDEA model and apply the proposed model in a case study involving 10 Iranian supply chains of Companies Producing Soft Drinks (CPSDs). The considered-three-echelon supply chains include suppliers, manufacturers, and distributors. Mathematical analysis proves that the MPSS of the considered supply chain can be decomposed as the sum of the MPSS values of the individual stages. Thus, the supply chain is overall MPSS if and only if it is MPSS in every three stages. The results of this study reveal that the Behnoush supply chain is overall MPSS in all three stages, including supplier, manufacturer, and distributor, for any α ∈ {0.1,0.5, 1}. A sensitivity analysis has been performed to measure the impact of each criterion on the entire supply chain performance. The sensitivity analysis results indicate that the social and resilience criteria significantly impact the performance and ranking of supply chains. Finally, we discuss how to improve the sustainability and resilience of non-MPSS supply chains.