Application of SEDEA to evaluation of degree of harmony between water resources and economic develop

Water Science and Engineering, 2011, 4(1): 110-120doi0.82j.ssn.1674-2370 2011.01.011http://www.waterjournal.cne-mail: wse2008@vip.163.comApplication of SEDEA to evaluation of degree of harmonybetween water resources and economic developmentJun MA*l,2, Chui-yong ZHENG'2I. Business School, Hohai University, Nanjing 210098. P. R. China2. Jiangsu Province Water Resources and Sustainable Development Research Centre,Hohai University, Nanjing 210098, P R. ChinaAbstract: This paper introduces the method of data envelopment analysis (DEA) for evaluationof the degree of harmony between water resources and economic development of the waterconservancy area of China's South-to-North Water Diversion Project (SNWDP). For thisevaluation, a super-efficiency DEA (SEDEA) model was developed based on the super-efficiencymethod. To verify the applicability of the SEDEA model, both the SEDEA model and anormal-efficiency DEA (NEDEA) model were used to evaluate the degree of harmony betweenwater resources and economic development of typical cities in the SNWDP water conservancyarea. The results show that the SEDEA model ranks the degree of harmony of typical cities moreefficiently than the NEDEA model, and thus can better evaluate the degree of harmony betweenwater resources and economic development of different cities than the NEDEA model.Furthermore, the SEDEA model can be applied as an operational research tool in regional waterresources management.Key words: degree of harmony; super eficiency DEA model; water conservancy area;South-to- North Water Diversion Project1 IntroductionEvaluation of the degree of harmony between water resources and economic developmentis currently a hot topic in water science research (WRFSSGCAS 2009). Zhang et al. (1999)proposed that water resources be developed in coordination with the national economy, andconstructed a system dynamics model for coordinative development between water resourcesand the national economy of China. Zuo (2007) developed an embedded system dynamicsmodel for a human water system. Wang and Ma (2006) utilized a holistic coupling model tosimulate the coordinative development between water resources and the national economy ofChina, finding that this model had a higher precision in complex system analysis than previousmodels. These studies took place mainly on the scale of China as a whole, on the scale ofThis work was supported by the Fundamental Research Fu中国煤化工ies (Grant No.2010B25814), the Philosophy and Social Science Foundation一2007402011),the Philosophy and Social Science Foundation of Jjiangsu PrYHCNMHG,andapecialproject of the Ministry of Water Resources of the People's Republic of China (Grant No.5006518023).*Corresponding author (e-mail: majun6666@gmail.com)Received Aug 20, 2010; accepted Jan. 14, 2011basins such as the Talimu River Basin, and on a regional scale such as Zhengzhou City.Although there is some literature on the degree of harmony between water resources andeconomic development of the water conservancy area of China's South-to-North WaterDiversion Project (SNWDP) (Zhou and Shi 2007; Feng et al. 2008; Sun et al. 2009; Ma2009), and on the application of DEA (data envelopment analysis) in water resourcesmanagement (Wang 2007; Liu and Li 2008; Sun and Yan 2008; Xie and Yuan 2008; Sun andLiu 2009; Ma et al. 2009; Wang 2010; Chen 2010; Yu et al.2010), to the best of our knowledgethere is no literature on ranking of cities in the SNWDP water conservancy area.In this study, to evaluate and rank the degree of harmony between water resources andeconomic development in the SNWDP water conservancy area, an SEDEA (super-efficiencyDEA) model was developed based on the super- efficiency method. To verify the applicabilityof the SEDEA model, a norrmal-efficiency DEA (NEDEA) model was also evaluated using thesame data.2 Evaluation index system2.1 Definition of degree of harmony between water resources andeconomic developmentWater resources are an important strategic resource for China's national economy. Thereshould be efficient coordination between water resources and economic development in China,in areas such as economic growth, life stability, environmental friendliness, and fullemployment; that is to say, there should be harmony between water resources and economicdevelopment. Therefore, the degree of harmony between water resources and economicdevelopment is, in fact, the degree of efficiency in the coordination between water resourcesand economic development, meaning the degree of integration and synchronization of waterresources, economic growth, life stability, environmental friendliness, and full employment. Itrepresents the extent to which water resources meet economic development needs, and is thevalue of an objective function composed of water resources inputs including water supply,water employees, and water investment, and economic development outputs including GDPper capita, water consumption per capita, the urban domestic sewage treatment rate, and theemployment rate of typical cities within China's SNWDP water conservancy area.2.2 Evaluation index system of degree of harmony between waterresources and economic developmentAccording to the definition of the degree of harmony between water resources andeconomic development given above, the combined principles of scientific, rational, objective,and advisable characteristics, related literature, and the comprehensive evaluation indexsystem framework of water resources and economic development established by an expertcounseling method (Ma 2009), we characterized typic中国煤化工WDP waterYHCNMHGJun MAet al. Water Science and Engineering, Mar. 2011, Vol. 4, No. 1, 110-120conservancy area depending on data availability. The evaluation index system of the degree ofharmony between water resources and economic development is composed of a target layer, acriterion layer, and an index layer (as shown in Table 1). The target layer is the degree ofharmony. The criterion layer comprises water resources inputs and economic developmentoutputs. The index layer comprises the water supply (x ), a resources input; employees ofwater supply departments (x ), a labor input; water investment ( ), a capital input; GDP percapita (y ), an economic output; water consumption per capita (y2 ), which represents qualityof life; the urban domestic sewage treatment rate ( y; ), which represents the quality of theenvironment; and the employment rate (y, ), which represents social stability.Table 1 Evaluation index system of degree of harmony between water resources and economic developmentTarget layerCrterion layerIndex layerWater resources inputsDegree of harmony2Economic development outputsys3 DEA models3.1 NEDEA modelTo evaluate the performance of different sections or regions based on input variables suchas investment and labor and output variables such as production and benefits, appropriateweighting should be adopted. Chamnes et al. (1978) provided the original DEA-CRS (constantreturms to scale) model, later extended to a VRS (variable returns to scale) model by Banker et al.(1984). These NEDEA models are known by the acronyms CCR (from the authors' names,Charnes, Cooper, and Rhodes) and BCC (from the authors' names, Banker, Charnes, andCooper), respectively. In NEDEA models, a decision-making unit (DMU) is considered to beefficient if its performance relative to other DMUs cannot be improved. In the absence of pricedata or preferential weightings of inputs and outputs, all efficient DMUs have equal scores of100%, and rank equally in terms of performance. Inefficient DMUs have scores of less than100% with an output orientation, and greater than 100% with an input orientation (Wei 2004).Suppose the jth DMU has. input X, and output Y, where x; =(:xp,*.",,",.".." ,Y =(y>2">",v,'.. ,x>0,y,>0,i=1,2...,m, and r=1,2,-,s. The weightvector of output Y, is u=(4+,.,,", 20, and the weight vector of input Xj isv=(v,2.,..,.... 20. Then, the eficiency index h is中国煤化工YHCNMHGJun MA et al. Water Science and Engineering. Mar. 2011, Vol.4, No. 1, 110-120uYj=.,,,.nv'X;Based on Eq. (1), to evaluate the efficiency of the j,th DMU, for the sake of convenience,withX.=X。，Yq=Y,, and 1≤ jo Sn, we can easily construct the primal programmingas follows:max.u"Y。(2)v"X,.t，u"Y,≤1 j=,2,..,nv'X,u≥0，v20Then, with Charnes- Cooper transformation w =-and μ=-uthe fractionalvTXv"Xprogramming can be converted to linear programming:maxμ'Y。(3)s.t. w'X;-μ'Y,20 j=1,2,..,niw'X,=1∞o≥0, μ≥0 .The dual programming for the CCR model is as follows (Charnes et al. 1978):minθ(4)s.t.Zx,A≤θX ,h,20where n; represents the optimal solution to Eq. (4), and θ is an objective function value(here it also means the degree of harmony).With the m-dimensional vector s =(si5,;s;,",s)，where the surplus_ variables;≥0, and i=1,2,-.,m, and the s-dimensional vector S+ =(S↑,,-",s," ,,s;wherethe slack variable s; 20, and r=1,2,.",s, we obtain the NEDEA model, as follows:min θ(5)ZxA +s5 =0X。2h-S°=%λ,≥0S~≥0， S*≥0Given the time factor t, time lag k between中国煤化工ArchimedeanTHCNMHGJun MAet al. Water Science and Engineeing. Mar. 2011, Vol. 4, No. 1, 110-120113infinitesimal 8, defining X, =X,(1), and Y; =Y,(1+k), we obtain the improved NEDEAmodel, as follows:min[o-<('s +e's$)](6)s.t.Ex()i, +s~ =0X。()Zy(1+k),-S* =Y(+k)n,20S~≥0,S* 20t≥0, k20where e-=--∈R'，(=.." ∈R"，x(+=()(+)(()--.())，andY,(t+k)= (w, (+h),y21 ( +k).-.(. +k,)).3.2 SEDEA modelBanker and Gifford (1988) suggested the use of SEDEA to screen out observations withgross data errors, and obtained more reliable efficiency estimates after removing the identifiedoutliers. Andersen and Petersen (1993) improved the SEDEA model, in which thesuper-efficiency scores can be obtained using the standard CCR and BCC models. Dula andHickman (1997), Seiford (1997), and Seiford and Zhu (1999) have proved theorerms providingnecessary and sufficient conditions for infeasibility of the conventional super-efficiency model.The advantage of the conventional SEDEA model is that it permits ranking of efficient DMUs.The disadvantage is that the conventional SEDEA model does not consider time lag betweeninputs and outputs.Based on the improved NEDEA model (Eq. (6)) and the aforementioned literature,ifj≠jo, then our improved SEDEA model ismin[0-e(e"s +e's"](7).t.之X(), +S =0X()Zy,(1+k),-s* =Y。(1+k)不20S~≥0, S*≥0t≥0, k≥0The advantage of our SEDEA model (Eq. (7)) is that it not only permits ranking ofefficient DMUs, but also considers time lags between i中国煤化工YHCNMHG114Jun MA et al. Water Science and Engineering, Mar.2011, Vol. 4, No. 1, 110-1204 ApplicationTo verify the applicability of the SEDEA model, both the NEDEA and SEDEA modelswere applied to the SNWDP water conservancy area to evaluate the degree of harmonybetween water resources and economic development of typical cities in China.4.1 Study areaThe near-term target of the SNWDP general program is to supply water to cities in thewater conservancy area, including Tianjin and Jinan along the easterm route, and Beijingand Shijiazhuang along the central route. The 16 cities listed in Table 2 were selected astypical cities due to their importance and representativeness in terms of size andgeographical location.Table 2 Typical cities selected in SNWDP water conservancy areaRouteBasinProvinceCityDMUYangzhouHuaihe BasinJiangsuHuai'anXuzhouXJinanIEasterm routeYellow River BasinShandongWeifangWDezhouDZCangzhouCHaihe BasinTianjinTNanyangNYHenanZhengzhouZAnyangHandanHDCentral routeXingtaiXTHebeiShijiazhuangSJBaodingBDBeijingBejjingB4.2 Evaluation standardsIn the NEDEA model, a value of θ between 0 and 1 (excluding 1) implies disharmony; avalue of θ equal to 1when s; =s$; = 0 implies harmony.In the SEDEA model, a value of θ between 0 and 1 (excluding 1) implies disharmony; avalue of θ equal to or larger than 1 implies harmony. (the higher the value, the higher thedegree of harmony).中国煤化工MHCNMHGJun MA et al. Water Science and Engineeing, Mar. 2011, Vol. 4, No. 1, 110-1201154.3 Data collectionData came from the China City Statistical Yearbook (DUSESNBS 2008, 2009) andthe urban socio-economic survey for the selected cities. These processed data(x，x，，y，y，y, and y) are presented in Table 3 for each DMU. There is a time lag of 1year (k = 1) between input and output due to an input-output cycle of water supply andeconomic development.Table 3 Water resources and economic development data for SNWDP water conservancy area}DMU吊x(10* yuan)(yuan per(m' per(10*t)capita)YZ11 31635617 97051 36836.7657.6097HA7 50275017 86417 23427.6684.50915 699132158 63549 24737.7585.90JN30 0233 83691 31755 43053.0855.1098WF928634927 16535 72616.9284.77DZ5 01942113 57147 70535.9053.32964 38640821 26434 32329.0160.00T.68 180 .4 020109 44551 23125.9978.21NY7 63773145 43816 44717.2547.9228 073251037 42335 49940.2792.3713 16062528 76523 50925.3955.1119 60925843 98629 44127.6951.00XT698143318 16825 65826.1675.00SJZ22 7641 66642 3344031228.1270.63BI893639934 94729 26328.2565.39B142 644387159 93060 04532.1769.564.4 Result analysisThe results of the NEDEA model and SEDEA model are shown in Tables 4 and 5,respectively. The degrees of harmony between water resources and economic development oftypical cities in China's SNWDP water conservancy area are shown in the tables. From theresults shown in Table 4, Tianjin, Jinan, Bejing, Shijiazhuang, Xuzhou, Zhengzhou, Nanyang,ind Anyang cities Gjust half, i.e., 8 of the 16 cities) are categorized as being in relativedisharmony; the others are categorized as being in relative harmony by the NEDEA model.Comparing the routes, there are greater differences among the cities along the easterm route thanthose along the central route. According to the SEDEA model, the order of the degree ofharmony of the cities from low to high is as follows: Tianjin, Jinan, Beijing, Shijiazhuang,Xuzhou, Zhengzhou, Nanyang, Anyang, Baoding, Xingtai, Huai'an, Cangzhou, Yangzhou,Handan, Weifang, and Dezhou. However, the NEDEA n中国煤化工nformation.TYHCNMHG16Jun MA et al. Water Science and Engineering, Mar. 2011, Vol. 4, No. 1, 110-120Table 4 NEDEA model resultsDMU(yuan perss;θz(10*1)(10* yuan)(m' per capita) (%)(%YZ01.00XZ4.036.380.453.10318.7813 964.7928.3048.910.256.12WFDZ1.00 1.00oTJ4 455.1644.0817.2826.110.17 7.4711.944 881.7918 233.5312.0612.711.74zz7 230.98602.183 373.8228.960.562.33AY23 434.467.405.750.621.63HDXTSJZ2 427.4261.12.980.392.80BD35 283.59582.4013.5724.170.294.38Note: s; represents surplus 写; s; represents surplus 为; sj represents surplus x; s* represents y slack; s;represents 为slack; s; represents 为slack; si represents 儿slack;and θ is degree of harmony. z is retum to scale andz=点的/。air z=Iretum to scsle of他DMU wll oo cangei[ z>1.etum t scle of/h DMU wlll dese; andirz<1, retum to scale ofjth DMU will increase).Table 5 SEDEA model results(10°)5(10* yuan) Gruanperm' per capia)capita)5 167.333.184.0114.421.27 0.92HA730.83371.5311 674.011.8110.031.150.98JN0.25 6.127 354.1317.2320.36.380.90264.031.1614.3114.581.68 0.68 .CZ24.40 .12426.80 6 627.11.5.011.270.790.17 7.47，NY4881.79 18 233.530.5815 778.6037 153.7013 993.245.250.73355.269 098.902.691.12 0.902427.427.988.55.392.8010 821.2311 427.610.921.070.29 4.38The returms to scale between water resources and中国煤化工ypical citieswithin China's SNWDP water conservancy area are shoYHCNMHGrdingtotheJun MA et al. Water Science and Engineening, Mar. 2011, Vol. 4, No. 1, 110-120117SEDEA model, the retums to scale of Xuzhou, Jinan, Tianjin, Nanyang, Zhengzhou, Anyang,Shijiazhuang, Baoding, and Beijing are all greater than 1, implying that they are among thecities with decreasing returns to scale, while the other typical cities are less than I, implyingthat Yangzhou, Huai' an, Weifang, Dezhou, Cangzhou, Handan, and Xingtai are among thecities with increasing returns to scale. According to the NEDEA model, the returms to scale ofXuzhou, Jinan, Tianjin, Nanyang, Zhengzhou, Anyang, Shiiazhuang, and Beijing are allgreater than 1, implying that they are among the cities with decreasing returns to scale, whilethe other typical cities are equal to 1, implying that Yangzhou, Huai'an, Weifang, Dezhou,Cangzhou, Handan, Xingtai, and Baoding are cities with constant retums to scale. Obviously,the returns to scale calculated by the SEDEA model are more accurate than those calculated bythe NEDEA model.The values of surplus variables s, s2, ands;, and slack variables s$, s$, s, ands; forwater resources and economic development of typical cities within China's SNWDP waterconservancy area are shown in Table 4 and Table 5. Table 4 shows that Jinan, Tianjin,Nanyang, Zhengzhou, Shijiazhuang, and Beijing have redundant inputs, while Xuzhou, Jinan,Tianjin, Nanyang, Zhengzhou, Anyang, Shijiazhuang, and Beijing have deficient outputs.Tianjin, Zhengzhou, Shijiazhuang, and Bejjing have redundant water supply. Jinan, Tianjin,Nanyang, Zhengzhou, Shijiazhuang, and Beiing have redundant employees of water supplydepartments. Nanyang has redundant water investment. Jinan, Nanyang, Zhengzhou, andAnyang are among the cities with deficient GDP per capita. Xuzhou, Tianjin, Nanyang,Anyang, Shijiazhuang, and Beijing are among the cities with deficient water consumption percapita. Jinan, Nanyang, and Anyang are among the cities with deficient urban domesticsewage treatment rates. Xuzhou, Jinan, Tianjin, Zhengzhou, Shijiazhuang, and Beijing areamong the cities with deficient employment rates. Adding water supply to Yangzhou, Huai'an,Weifang, Dezhou, Cangzhou, Handan, Xingtai, and Baoding could improve their socialeconomic development. However, adding water supply to Xuzhou, Jinan, Tianjin, Nanyang,Zhengzhou, Anyang, Shjjiazhuang, and Beijing would not improve their social economicdevelopment. Table 5 shows that all typical cities except Xuzhou and Anyang have redundantinputs, and all typical cities have deficient outputs. In detail, Yangzhou, Huai'an, Tianjin,Zhengzhou, Handan, Xingtai, Shijiazhuang, and Beijing have redundant water supplies.Huai' an, Jinan, Dezhou, Cangzhou, Tianjin, Nanyang, Zhengzhou, Shijiazhuang, and Beijinghave redundant employees of water supply departments. Weifang, Cangzhou, Nanyang,Handan, and Baoding have redundant water investment. Huai'an, Jinan, Cangzhou, Nanyang,Zhengzhou, Anyang, Handan, Xingtai, and Baoding are among the cities with deficient GDPper capita. Yangzhou, Huai' an, Xuzhou, Weifang, Dezhou, Cangzhou, Tianjin, Nanyang,Anyang, Shjjazhuang, and Beijing are among the cities with deficient water consumption percapita. Yangzhou, Jinan, Dezhou, Nanyang, Anyang, and Handan are among the cities withdeficient urban domestic sewage treatment rates. Yangzhou, Huai'an, Xuzhou, Jinan, Weifang,Dezhou, Tianjin, Zhengzhou, Xingtai, Shijiazhuang,中国煤化Ile cities withdeficient employment rates. Actually, almost all the t:MYHCN MH Gundant inputs118Jun MA et al. Water Science and Engineering, Mar. 2011, Vol. 4, No. 1, 110-120or deficient outputs.Hence, the results of the SEDEA model are more precise than those of the NEDEA model.In the SEDEA model, the different characteristics of different cities are more obvious than inthe NEDEA model. The SEDEA model has better evaluation results than the NEDEA model inthis study area due to an important extension of super-efficiency models developed during thepast decade. In comparison to the SEDEA model, the NEDEA model is only a traditionalconceptual DEA model; it does not take into consideration the order of the objective functionvalue. This indicates that the SEDEA model is superior to the NEDEA model.5 ConclusionsWe developed the SEDEA model based on the NEDEA model and the super-fficiencymethod, used the SEDEA model to evaluate the degree of harmony between water resourcesand economic development of the SNWDP water conservancy area, and compared theevaluation results with those of the NEDEA model. The main conclusions are as follows:(l) Both the SEDEA and NEDEA models can be used to evaluate the degree of harmonybetween water resources and economic development in different cities in China's SNWDP waterconservancy area. However, the SEDEA model additionally allows ranking of fficient DMUs.(2) The SEDEA model describes the objective function values and returns to scale ofDMUs by the super efficiency method. Therefore, the SEDEA model can be used for relativeefficiency sorting.(3) The SEDEA model provides a reasonable description of the harmony of the study area.The SEDEA model is superior to the NEDEA model in evaluating the degree of harmonybetween water resources and economic development of different cities in China because it cantake into consideration the order of the objective function values.The research presented in this paper on the degree of harmony between water resourcesand economic development covers only a limited number of cities in China's SNWDP waterconservancy area. The applicability of the SEDEA model needs further verification in morecities, and even other countries.ReferencesAndersen, P., and Petersen, N. C. 1993. 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