Research On Malmquist-DEA Method Based On Fixed-sum Output

The traditional Data Envelopment Analysis(DEA)approach mainly aims at the horizontal comparison of different Decision Making Units(DMUs)in the same period to calculate the static efficiency.The application of DEA also uses cross-section data to evaluate the efficiency statically.Malmquist Productivity Index is a time series analysis approach,which is used to measure the productivity of DMUs over time.How to use Malmquist-DEA method to analyze the productivity of DMUs in time series is a very important research,which has sufficient practical application value.In addition,in the actual production process,we often encounter the situation that the total amount of one or some outputs of DMUs is fixed-sum.In the traditional DEA research,it is usually assumed that outputs are independent,that is,outputs are scalable,so it is not suitable for efficiency evaluation with fixed-sum output DMUs.In recent years,how to use DEA method to evaluate the efficiency of DMUs with fixed-sum output is a hot issue in DEA field.However,the current Malmquist-DEA method rarely considers the fixed-sum output,so this paper makes an extended study on the dynamic efficiency evaluation of fixed-sum output DMUs.Fixed-sum output can also be divided into desirable output and undesirable output.For the dynamic efficiency evaluation of fixed-sum desirable output,this paper proposes a Malmquist-DEA approach considering fixed-sum undesirable output DMUs based on the general equilibrium efficient frontier data envelopment analysis(GEEFDEA)approach,and applies the approach to the dynamic efficiency evaluation of the participating countries in the Winter Olympic Games.For the fixed-sum undesirable output,this paper extends the GEEFDEA approach to the efficiency evaluation of fixed-sum undesirable output DMUs,proposes a Malmquist-DEA approach considering the fixed-sum undesirable output DMUs,and applies it to the dynamic carbon emission environmental efficiency evaluation of 30 provinces in China.