A generalized fuzzy Multiple-Layer NDEA: An application to performance-based budgeting

Abstract

Network data envelopment analysis (NDEA) is capable of considering operations and interdependence of a system’s component processes to measure efficiencies. There are numerous performance evaluation applications in which some indicators have hierarchical structures with a considerable number of sub-indicators. This problem of ignoring the hierarchical structure of indicators weakens the discrimination power of NDEA models and may result in inaccurate efficiency scores. In this paper we propose a generalized fuzzy Multiple-Layer NDEA (GFML-NDEA) model and GFML-NDEA-based composite indicators (GFML-NDEA-CI) to incorporate the hierarchical structures of indicators in the ambit of the particular two-stage NDEA models. To demonstrate the usefulness of the GFML-NDEA-CI model proposed, its application was tested by evaluating the efficiency of the performance-based budgeting (PBB) system in 14 governmental agencies in Iran. The comparative analysis results obtained from the GFML-NDEA-CI (multi-layer) model with those from the single-layer fuzzy NDEA-CI model indicate that the number of efficient decision-making units (DMUs) in the one-layer model is eight, whereas it is solely one DMU in the multi-layer model. The discrimination power of the multi-layer model proposed is significantly increased by observing that standard deviation of efficiency scores are increased by 41%, 61%, and 84% for possibility levels 0, 0.5, and 1, respectively. This is obtained while reducing information entropy, thus suggesting that the proposed model yields more reliable scores.