Research On Efficiency Evaluation Of DMUs With Fixed-sum Outputs

In real life,we often encounter some Decision Making Units(DMUs)whose outputs' sum are fixed.The traditional Data Envelopment Analysis(DEA)methods assume that DMUs' input or output are independent so that it is not suitable for evaluating the efficiency of DMUs with fixed-sum outputs.How to evaluate the performance of DMUs with fixed-sum outputs is a hot and challenging question in DEA field.At present,the generalized equilibrium efficient frontier data envelopment analysis(GEEFDEA)approach is a more effective approach for evaluating the efficiency of DMUs with fixed-sum outputs.In the production process,in addition to consuming inputs to achieve the desired outputs,DMUs also produce undesirable outputs,such as wastewater and exhaust gas.In fact,in the study about undesirable output,it is very common that the sum of outputs is fixed.For example,at the national or regional level,industrial emissions are often limited.Therefore,when evaluating eco-inefficiency,it is necessary to take into account the constraint that the sum of undesirable outputs is fixed.At present,there are few studies about eco-inefficiency evaluation of DMUs with undesirable and fixed-sum outputs.In addition,there may be multiple feasible equilibrium efficient frontiers based on the GEEFDEA approach,and it has been confirmed by some researchers.The efficiency and ranking of each DMU may differ greatly under different frontiers,which makes evaluation results not objective and comprehensive enough.Based on the existing research,this article expands the GEEFDEA approach horizontally and vertically.Horizontally,this article combines the GEEFDEA method with existing eco-efficiency evaluation methods of DMUs with undesirable outputs,proposes an eco-inefficiency model to evaluating DMUs with undesirable and fixed-sum outputs and uses this model to evaluate the eco-inefficiency of carbon emissions in each province.Vertically,this article proposes a series of models to calculate the efficiency intervals,ranking intervals and dominance relations of DMUs with fixed-sum outputs under all feasible equilibrium efficient frontiers,thus solving the problem caused by the non-uniqueness of equilibrium efficient frontiers.