Fixed-sum data envelopment analysis efficiency evaluation with network parallel structure under decentralized and centralized scenarios

Abstract

Network data envelopment analysis (DEA) approach can evaluate decision-making units (DMUs) with network structure. However, in the real world, the total amount of some inputs/outputs is fixed, which is called fixed-sum inputs/outputs. Few studies focus on fixed-sum DEA (FSDEA) evaluation issues with considering the internal network structure of DMUs. Existing studies on fixed-sum research mainly discuss series structures, parallel structures are often neglected although they are common in reality. In this study, we propose a novel fixed-sum DEA efficiency evaluation model for parallel structures, based on generalized equilibrium efficient frontier DEA. Furthermore, depending on whether there’s a centralized decision maker, we propose models in decentralized scenario and centralized scenario to construct the efficient frontier. Then, to calculate efficiencies of overall DMUs and sub-DMUs, efficiency evaluation models in decentralized scenario and centralized scenario are proposed based on the established efficient frontier respectively. Finally, we demonstrate the practical application of the proposed models by evaluating the industrial performance of the three major industries in each province in China for the year 2020. Through this application, we aim to compare the efficiency differences between provinces and provide insights for improving their industrial performance.