Principal-subordinate hierarchical multi-objective programming model of initial water rights allocation

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1 Water Scece ad Egeerg, 2009, 2(2): 05-6 do:0.3882/j.ss e-mal: Prcpal-subordate herarchcal mult-objectve programmg model of tal water rghts allocato Da WU, Feg-pg WU, Ya-pg CHEN Busess School, Hoha Uversty, Najg 20098, P. R. Cha Abstract: The prcpal-subordate herarchcal mult-objectve programmg model of tal water rghts allocato was developed based o the prcple of coordated ad sustaable developmet of dfferet regos ad water sectors wth a bas. Wth the precodto of strctly cotrollg maxmum emssos rghts, tal water rghts were allocated betwee the frst ad the secod levels of the herarchy order to promote far ad coordated developmet across dfferet regos of the bas ad coordated ad effcet water use across dfferet water sectors, realze the maxmum comprehesve beefts to the bas, promote the uty of quatty ad qualty of tal water rghts allocato, ad elmate water coflct across dfferet regos ad water sectors. Accordg to teractve decso-mag theory, a prcpal-subordate herarchcal teractve teratve algorthm based o the satsfacto degree was developed ad used to solve the tal water rghts allocato model. A case study verfed the valdty of the model. Key words: tal water rghts allocato; prcpal-subordate herarchy; mult-objectve programmg model; satsfacto degree Itroducto Ital bas water rghts allocato maly refers to a two-level herarchy. Ital water rghts allocato to the frst level meas that water rghts are assged to dfferet admstratve regos the bas; tal water rghts allocato to the secod level meas that water rghts obtaed from the frst level are allocated to dfferet water sectors the admstratve rego. Ital water rghts allocato s a complcated, mult-area, mult-objectve ad mult-level decso that volves ecoomc, socal, ecologcal ad poltcal factors. Ths ssue has bee researched extesvely aroud the world. Accordg to socal systems, water resources status, ad cultural tradtos of specfc coutres or regos, foreg scholars have used the allocato methods of occupacy prorty (Gopalarsha 973), rpara prorty (Goldfarb 988), ad codto prorty (Teer ad Naashma 993), ad covetoal methods (Mather 984), whch have ther respectve hstorc ratoaltes, to allocate the tal water rghts based o the legslato ad the process smulato. Howe et al. Ths wor was supported by the Publc Welfare Idustry Specal Fud Project of the Mstry of Water Resources of Cha (Grat No ) ad the Humates ad Socal Scece Foudato Program of Hoha Uversty (Grat No ). Correspodg author (e-mal: wu_dael@hhu.edu.c) Receved Dec. 5, 2008; accepted Apr. 20, 2009

2 (986) used the prcples of flexblty, safety, foreseeablty, ad poltcal ad publc acceptablty to allocate tal water rghts. Tracy (99) establshed a water rghts maagemet model of surface water ad groudwater for drought perods. She asserted that whe there was a hydraulc coecto betwee surface water ad groudwater, the effectve water dvso amout from each well the bas could be determed wth a tegrated surface water-groudwater flow model. Thur et al. (994) establshed the PROSIM model to descrbe ad smulate the Weber Rver Bas wth relevat weather, water temperature, lad applcato ad system data. The model ca cotuously calculate the total avalable water amout of a rver system ad allocate water amout based o prorty orders. Kelma ad Kelma (2002) dscussed the law of the jugle, lear ratog, the tme rule, ecoomc beefts, ad several other allocato systems, ad put forward a allocato model based o the opportuty cost of dfferet water cosumers. Domestc scholars have systematcally desged a set of tal water rghts allocato dex systems ad establshed a mult-level, sem-structural ad mult-objectve fuzzy optmzato model (Wu ad Ge 2005; Tog et al. 2007) to allocate tal water rghts to the frst level of the herarchy. Based o the prorty orders ad objectves of water sectors, domestc scholars have establshed a goal programmg model (Ge ad Wu 2005; Zhou ad J 2007) to allocate tal water rghts to the secod level of the herarchy. The teractve water rghts tal allocato method based o harmoousess judgmet was establshed by Wu ad Ge (2006) to esure harmoous allocato of tal water rghts. Water rghts qualty ad quatty requremets were dscussed by Meg et al. (2008), who argued that the total emssos rghts must be stated clearly ad specfcally durg the process of tal water rghts allocato, ad that tal water rghts allocato prcples, dex systems ad mechasms should be aalyzed comprehesvely, based o water rghts, emssos rghts ad forest rghts. Cha s payg more atteto to bas ecologcal evromets, sustaable developmet ad the costructo of harmoous socal systems. Throughout the process of tal water rghts allocato the bas, uder the premses of bas evrometal protecto ad strct cotrol of maxmum emssos rghts, far ad effcet water use dfferet regos should be esured for the sustaable developmet of the ecoomy ad socety, ad the coordated developmet of dfferet water sectors should be esured to realze the optmal comprehesve ecoomc, socal ad ecologcal beefts to the bas. Ths wll promote the costructo of a harmoous socety. Because tal water rghts allocato to the secod level of the herarchy s restrcted by tal water rghts allocato to the frst level, the tal water rghts allocato process s a prcpal-subordate herarchcal oe, formg a system wth oe leader ad multple followers. Therefore, a prcpal-subordate herarchcal mult-objectve programmg model was establshed to allocate tal water rghts to the frst ad secod levels sychroously. It was developed o the bass of total tal water rghts the bas, wth the precodtos of strctly cotrollg permtted maxmum emssos 06 Da WU et al. Water Scece ad Egeerg, Ju. 2009, Vol. 2, No. 2, 05-6

3 rghts ad restrctg each rego s water demad, ad based o prcples of far, effcet ad coordate water use. It adheres to domestc, ecologcal ad producto prorty orders of water sectors, regards the optmal comprehesve ecoomc, socal ad ecologcal beefts to the bas as plag objectves of the frst level of the herarchy, ad regards the coordated developmet of dfferet water sectors as plag objectves of the secod level. 2 Ital water rghts allocato model Ital water rghts allocato to the frst level s assocated wth socal ad ecoomc developmet ad dustral structures dfferet regos. The optmal comprehesve ecoomc, socal ad ecologcal beefts deped o the ecoomc developmet ad socal structure of each rego; meawhle, regoal tal water rghts allocated to domestc, ecologcal ad producto water sectors are restraed by tal water rghts allocato to dfferet regos, ad the far ad coordated developmet of dfferet water sectors depeds o water rghts obtaed from the frst level. The tal water rghts allocato ca realze the coordated ad sustaable developmet of the whole bas s ecoomy ad socety through the teractve fluece of tal water rghts allocato betwee the frst ad secod levels of the herarchy. Accordg to the defto of bas water rghts allocato, a prcpal-subordate herarchcal mult-objectve programmg model wth oe leader at the frst level of the herarchy ad multple followers at the secod level s descrbed below. 2. Objectve fucto of frst level of herarchy The objectve fucto of the frst level of the herarchy ca be expressed as ( ) = { ( ), 2( ), 3( )} F W F W F W F W max F( W) = max f ( W) = max ( a W3 + a2w4 + a3w5) = = W W max F2( W) max f2( W) max = = = = ( W W ) = 5 m F3( W) = m f3( W ) = m 0.0dj pjwj = = j= where F( W ) s the objectve fucto of the frst level of the herarchy, whch cludes three sub-goals: ecoomc beeft F ( W ), socal beeft F2 ( W ), ad ecologcal beeft F3 ( W ) ; f ( W ) s the ecoomc beeft of the th rego; 2 ( ) rego, whch ca be determed by the water rghts quota of the th rego; ( ) () f W s the socal beeft of the th f W s the ecologcal beeft of the th rego, whch ca be determed wth the water rghts quotas of 3 Da WU et al. Water Scece ad Egeerg, Ju. 2009, Vol. 2, No. 2,

4 dfferet water sectors the th rego; s the umber of regos the bas; W ( =,2, L, ) W W 2 W 3 W 4 W 5 s the water rghts quota of the th rego;,,,, ad are the water rghts quotas for domestc use, ecologcal eeds, agrculture, dustry, ad tertary dustry, respectvely, the th rego; a, a 2, ad a 3 are the agrcultural, dustral, ad tertary dustral added values per cubc meter of water the th rego, respectvely; W s the water demad of the th rego, whch ca be determed wth the methods of quattatve predcto ad expert cosultato based o water cosumpto of dfferet water sectors the th rego; W W s the satsfacto degree of water rghts allocato the th rego; d j s the cocetrato of major pollutats sewage dscharge from the jth water sector the th rego; ad p j s the coeffcet of sewage dscharge from the jth water sector the th rego. The costrat codtos of the frst level of the herarchy are as follows: W = W0 = W W 5 0.0dj pjwj P 0 = j= W W C 0 = ( W W ) = W W α f Z Z W0 W0 where W0 s the tal water rghts the bas, P 0 s the permtted maxmum emssos W W rghts the bas, ad C 0 meas that the far ad coordated degree = ( W W ) = of tal water rghts allocato the bas must satsfy coordato crtero C 0 to prevet a large water resources gap betwee dfferet regos based o the barrel prcple. The crtero C 0 s flueced by comprehesve socal, ecoomc ad ecologcal factors, such as the populato, cultvated area, GDP, ad gree area of dfferet regos, ad ca be determed by decso maers based o expert cosultato. Geerally, C The W W parameters W ad ' are the water rghts percetages of the th rego ad the th rego, 0 W0 respectvely. The varable α s a parameter, where 0.5 α.5. The value of α ca be determed wth the method of expert cosultato, tag to accout socal ad ecoomc codtos of dfferet regos. Geerally, α =. The parameters Z ad Z are the comprehesve domestc, ecologcal ad producto characterstc dces for the th rego (2) 08 Da WU et al. Water Scece ad Egeerg, Ju. 2009, Vol. 2, No. 2, 05-6

5 ad the th rego, respectvely, defed as 22 j= 22 j j= Z = wc j j ad Z = wc j, where s the weght of the jth dex of the th rego, ad C s the dmesoless value of. s the curret water cosumpto of the th rego; s the water resources per capta the th rego; s the water resources per ut cultvated area the th rego; s the populato of the th rego; s the domestc water productvty of the th rego; s the gree area of the th rego; s the wetlad cover of the th rego; s the stadard-reachg rate of sewage dscharge of the th rego; s the sewage treatmet rate of the th rego; s the rrgated area of the th rego; s the rato of agrcultural added value of the th rego to total agrcultural added value; value per capta the th rego; s the agrcultural added s the water cosumpto per agrcultural added value the th rego; s agrcultural water productvty of the th rego; s the rato of j C 2 w j Cj C C3 C 4 C5 C 6 C7 C 8 C 9 C0 C C 2 C 3 C4 C 5 C 6 dustral added value of the th rego to total dustral added value; added value per capta the th rego; C 7 s the dustral s the water cosumpto per dustral added value the th rego; C8 s the dustral water productvty of the th rego; C 9 s the rato of tertary dustral added value of the th rego to total tertary dustral added value; s the tertary dustral added value per capta the th rego, s the water C20 C 2 cosumpto per tertary dustral added value the th rego; C 22 s the tertary dustral water productvty of the th rego; C3, C 7 ad C 2 are the cost dces, whose correspodg dmesoless values are m C j Cj = ( j = 3,7, 2) (3) C j ad other varables are beeft dces, whose correspodg dmesoless values are C j Cj = ( j =, 2, L,2,4,5,6,8,9, 20, 22) (4) max C j 2.2 Goal programmg model of secod level of herarchy After water rghts the th rego are obtaed from the frst level of the herarchy, the water rghts are allocated to dfferet water sectors the th rego wth prorty orders, order to promote the far ad coordated developmet of dfferet water sectors the th rego, prevet vcous competto for ecologcal, agrcultural ad dustral water supply, ad esure socal stablty ad gra securty. The prorty orders are as follows: domestc water demad ad ecologcal water demad are satsfed frst, followed by agrcultural water demad, ad dustral ad tertary dustral water demad. Because of the flueces of may ucerta factors the process of ecoomc developmet, the developmet objectves of dfferet water sectors caot be measured exactly. Therefore, based o the theory of mult-objectve decsos, a goal programmg model of the secod level of the herarchy s establshed. The objectve fucto ad costrat codtos of the secod level ca be Da WU et al. Water Scece ad Egeerg, Ju. 2009, Vol. 2, No. 2,

6 expressed, respectvely, as where th prorty, m f = Pd + Pd + Pd + Pd + P( d + d ) + Pd Wj = W ( =,2, L, ) j= + W + d d = L + W2 + d2 d2 = E + aw 3 + d3 d3 = P + aw d4 d4 = I aw 3 d 5 d = ε aw aw d6 d6 = S + + d, d 0, dd = 0 =,2,, ; =,2,, ( L L 6) f s the objectve fucto of the secod level of the th rego, (, 2,, 6) ad d d + the th rego, respectvely, (5) (6) P = L s the are the egatve ad postve devatos of domestc water demad of water demad of the th rego, respectvely, d ad d + are the egatve ad postve devatos of ecologcal 2 devatos of agrcultural added value of the th rego, respectvely, 2 d 3 ad d + 3 are the egatve ad postve d ad d + are the egatve ad postve devato of dustral added value of the th rego, respectvely, ad d + 5 are the egatve ad postve devatos of the rato of agrcultural added value to dustral added value the th rego, respectvely, devatos of tertary dustral added value the th rego, respectvely, water demad of the th rego, requred agrcultural added value of the th rego, the th rego, S E d 6 ad d d 5 are the egatve ad postve L s the domestc s the ecologcal water demad of the th rego, P s the I s the requred dustral added value of s the requred tertary dustral added value of the th rego, ad ε s the rato of agrcultural added value to dustral added value the th rego. The prcpal-subordate herarchcal mult-objectve programmg model of tal water rghts allocato ca be developed by couplg the objectve fuctos of the frst ad secod levels of the herarchy. 3 Prcpal-subordate herarchcal teractve decso-mag algorthm based o satsfacto degree 3. Prcpal-subordate herarchcal teractve decso mechasm The comprehesve ecoomc, socal ad ecologcal beefts to the bas are restrcted by the water rghts quotas of the frst ad secod levels of the herarchy. I order to realze the optmal comprehesve beefts, cooperatve optmzato of the two water rghts quotas s ecessary. The decso mechasm of tal water rghts allocato s as follows: 0 Da WU et al. Water Scece ad Egeerg, Ju. 2009, Vol. 2, No. 2, 05-6

7 () The three objectves of the frst level clude ecoomc beeft, socal beeft, ad ecologcal beeft. The sx objectves of the secod level clude satsfacto of water demad for domestc use, ecologcal eeds, rrgato guarateeg total gra producto, agrcultural added value, dustral added value, ad tertary dustral added value. The decso process s from top to bottom; that s, a decso s frstly made the frst level to determe W, the aother decso s made the secod level to determe W j, ad the comprehesve beeft s fally determed wth the values of W ad Wj. (2) I order to obta the optmal value of the objectve fucto F( W ) of the frst level, the terrelated regos must exchage formato; that s, objectves of the secod level should be satsfed such a way that allows for the satsfacto of objectves of the frst level. I the ed, the soluto of the two-level programmg problem should atta the optmal comprehesve beeft to the frst level. Meawhle, the soluto ca promote the coordated developmet of dfferet water sectors of the secod level. (3) The objectve fucto F( W ) of the frst level s flueced by the values of W ad W j. Therefore, the optmal soluto of the two-level mult-objectve programmg problem caot be obtaed drectly, but should be determed by gradually adjustg ad correctg the values of W ad Wj wth teractve teratos betwee the frst ad secod levels. For years, may scholars have bee dedcated to loog for a effectve method of solvg the two-level mult-objectve programmg problem. The prcpal-subordate herarchcal teractve teratve algorthm based o the satsfacto degree, whch s establshed based o teractve decso theory, ca be used to solve the prcpal-subordate herarchcal mult-objectve programmg model of tal water rghts allocato. 3.2 Prcpal-subordate herarchcal teractve teratve algorthm based o satsfacto degree Prcpal-subordate herarchcal programmg s a d of herarchcal decso-mag system optmzato problem whch there are may decso maers. The decso maers of the frst level of the herarchy ca exercse the rght of cotrol ad gude the decso maers of the secod level. The prcpal-subordate herarchcal programmg model s a complcated optmzato model. Both the frst level ad the secod level programmg problems have objectve fuctos ad costrat codtos. The objectve fucto ad costrat codtos of the frst level are related to the decso varables of the frst level ad the optmal soluto of the secod level. The optmal soluto of the secod level s also flueced by the decso varables of the frst level. There are may methods of solvg such programmg problems. They ca be dvded to the followg categores (Wag et al. 2007): the polar search method, the descet method, the heurstcs algorthm, the tellget algorthm, ad the er-pot method. The teractve decso-mag method s oe of the polar search methods, ad t requres the cotuous partcpato of decso maers. The aalyst puts Da WU et al. Water Scece ad Egeerg, Ju. 2009, Vol. 2, No. 2, 05-6

8 prefereces ad treds of decso maers to the model to wor out a best decso-mag soluto. Therefore, due to the prcpal-subordate herarchcal teractve decso mechasm, the prcpal-subordate herarchcal teractve teratve algorthm based o the satsfacto degree ca be used to solve the tal water rghts allocato model through a mult-roud teractve teratve process. The steps of the prcpal-subordate herarchcal teractve teratve algorthm based o the satsfacto degree are as follows: Step : The value of s set as. Step 2: Accordg to the costrat codtos of the frst level, a tal value W s stochastcally selected for W of the frst level. Step 3: W s substtuted to the goal programmg model of the secod level, ad a tal value Wj s obtaed for Wj of the secod level. Step 4: W ad W j are substtuted to the costrat codtos of the frst level. If the costrat codtos are satsfed, the W ad W j are the tal solutos of the two-level mult-objectve programmg. They are substtuted to the objectve fucto of the frst level. The, the comprehesve ecoomc, socal ad ecologcal beefts are obtaed ad the process proceeds to Step 5. If the costrat codtos are ot satsfed, the process proceeds to Step 2. Step 5: Accordg to the values of F ( W ), F2 ( W ), ad F3 ( W ) of the frst level, ad the expected objectve value max F ( W ) ad permtted mmum objectve value m F ( W ) determed by bas sttutos, the sgle objectve satsfacto degree fucto ca be formulated as follows: F( W) m F( W) μ ( F( W) ) = (7) max F W m F W where μ ( ( )) μ ( F( W) ) max = max F W ( ) ( ) F( W) F( W) ( ) m F ( W) F W s the sgle objectve satsfacto degree fucto of the th terato. The ecoomc objectve fucto ad socal objectve fucto are the beeft-type objectve fuctos, ad ther objectve satsfacto degrees ca be calculated wth Eq. (7). The ecologcal objectve fucto s the cost-type objectve fucto, ad ts objectve satsfacto degree ca be calculated wth Eq. (8). Accordg to the sgle objectve satsfacto degree fucto, the comprehesve ecoomc, socal ad ecologcal beeft satsfacto degree fucto ca be expressed as μ F W = wμ F W + w μ F W + w μ F W (9) ( ( )) ( ( )) 2 ( 2( )) 3 ( 3( )) where ( F( W) ) μ s the comprehesve ecoomc, socal ad ecologcal beeft satsfacto degree fucto of the th terato, ad w, w2, ad w3 are the weghts of the ecoomc, socal, ad ecologcal objectve satsfacto degree fuctos, respectvely, whch fluece the (8) 2 Da WU et al. Water Scece ad Egeerg, Ju. 2009, Vol. 2, No. 2, 05-6

9 sustaable developmet of the bas s ecoomy ad socety. We ca let If the costrat codtos, are satsfed, where α, ( ( )) ( 2( )) 2 ( 3( )) w = w2 = w3 =. 3 μ F W α, μ F W α, μ F W α3 (0) α 2 ad F W α 3 are the mmum costrats of the ecoomc objectve μ F W, ad satsfacto degree μ ( ( )), socal objectve satsfacto degree ( 2 ( )) ecologcal objectve satsfacto degree μ ( F3 ( W) ), respectvely, whch ca be determed by bas sttutos wth the expert cosultato method, ad where, geerally, ( ) α 0.5 =,2,3, the the process proceeds to Step 6. If Eq. (7) s ot satsfed, the process proceeds to Step 7. Step 6: Bas sttutos evaluate the comprehesve beeft satsfacto degree ( F( W) ) μ of the th terato. If t s satsfed, the process of decso-mag s over, ad the soluto s the fal soluto of the two-level programmg model. Otherwse, s set as +, the costrat codto of μ + ( F( W) ) μ ( F( W) ) s added to the costrat codtos of the frst level, ad the process proceeds to Step 7. Step 7: The value W for W of the frst level ad the value W for W of the secod level are teratvely adjusted from bottom to top ad reallocated from top to bottom wth the expert cosultato method. That s, the sx objectve fucto values of the secod level are subdvded to the three followg objectve subsets: a objectve that ca be properly mproved, a objectve that should rema varat, ad a objectve that ca be properly decreased. The adaptablty of the sx objectve fucto values of the secod level s adjusted ad the creased or decreased amout for the value s aalyzed. The, the creased 5 ΔW j or decreased amout Δ W = Δ for the value s aalyzed. Fally, the value s W j j= W j adjusted, the value s re-determated accordg to the objectve programmg model of the secod level, ad the process returs to Step 5. 4 Aalyss of example There are fve regos the Dalghe Rver Bas of Laog Provce: Jzhou, Fux, Chaoyag, Paj ad Huludao. The total amout of water resources are m 3 through the plag year After m 3 of water have bee used for the ecologcal water supply of the er rver ad m 3 of water for govermetal reserved water, the remag water for allocato to the two levels s m 3. The soco-ecoomc developmet dces of the two levels of the herarchy the plag year 2030 are show Table. The water demad quotas for domestc use, dustry, tertary dustry ad agrculture the plag year 2030 are show Table 2. W W j j j W Da WU et al. Water Scece ad Egeerg, Ju. 2009, Vol. 2, No. 2,

10 Rego Table Soco-ecoomc developmet dces of two levels of herarchy plag year 2030 Populato (0 4 ) Farmlad rrgato area (m 2 ) Tow Coutry M M 2 Cultvated area (m 2 ) Gree area (0-2 m 2 ) Agrculture Added value (0 4 yua) Idustry Tertary dustry GDP (0 4 yua) Jzhou Fux Chaoyag Paj Huludao Note: M s the effectve rrgato area, ad M 2 s the forest ad grass rrgato area. Table 2 Water demad quotas for domestc use, dustry, tertary dustry ad agrculture plag year m 3 Rego A A 2 BB BB2 C D D 2 D 3 E E 2 E 3 F F 2 F 3 Jzhou Fux Chaoyag Paj Huludao Note: A s the domestc water demad quota for tows, A 2 s the domestc water demad quota for coutres, B s the water demad quota of added value of hgh water demad dustry, B 2 s the water demad quota of added value of geeral water demad dustry, C s the water demad quota of tertary dustral added value, D, D 2, ad D 3 are, respectvely, the water demad quotas of paddy feld rrgato, rrgated lad rrgato, ad vegetable feld for agrcultural guaratee rate 50%, E, E 2, ad E 3 are, respectvely, the water demad quotas of paddy feld rrgato, rrgated lad rrgato, ad vegetable feld for agrcultural guaratee rate 75%, F, F 2, ad F 3 are, respectvely, the water demad quotas of paddy feld rrgato, rrgated lad rrgato, ad vegetable feld for agrcultural guaratee rate 90%. Table shows a sgle ecoomc structure the Paj rego that depeds o fshg, has a lesser populato desty, ad maly has a large rural populato. Accordg to the related data Table ad Table 2, ad based o water-savg ad at-foulg socal systems as well as comprehesve plag objectves for soco-ecoomc developmet, the water demad of the two levels of the herarchy the plag year 2030 s obtaed wth quattatve predcto ad expert cosultato (Table 3). Table 3 Water demad of two levels of herarchy plag year m 3 Domestc water Ecologcal Agrcultural water demad Idustral Tertary Rego demad water water dustral water Tow Coutry demad 50% 75% 90% demad demad Jzhou Fux Chaoyag Paj Huludao Note: Data wth % are the agrcultural guaratee rates. Accordg to the related data Tables through 3 ad the bas s regulato requremets for comprehesve soco-ecoomc developmet, the mmum value ad expected value of the GDP the bas are yua ad yua, respectvely. 4 Da WU et al. Water Scece ad Egeerg, Ju. 2009, Vol. 2, No. 2, 05-6

11 The mmum value ad expected value of the coordated degree of tal water rghts allocato are 0.85 ad, respectvely. Because t s dffcult to obta sewage dscharge parameters of dfferet dustres dfferet regos the bas, ad the water evrometal carryg capacty the bas ca support a sewage dscharge of dfferet dustres dfferet regos the bas wth m 3 of water resources reserved for ecologcal water supply for the er rver, the bas evrometal beeft satsfacto degree of the er rver s. Accordg to the prcpal-subordate herarchcal mult-objectve programmg model of tal water rghts allocato, ad the prcpal-subordate herarchcal teractve teratve algorthm based o the satsfacto degree, the water rghts quotas of the two levels of the herarchy the plag year 2030 are obtaed after 239 teratos (Table 4). Table 4 Water rght quotas of two levels of herarchy plag year m 3 Rego Domestc water rghts quota Ecologcal Agrcultural Idustral Tertary dustral water rghts water rghts water rghts Tow Coutry water rghts quota quota quota quota Jzhou Fux Chaoyag Paj Huludao Accordg to the results Table 4, the calculated far ad coordated degree sharg of bas water resources s 0.984, satsfyg the coordato crtero C ; the GDP the bas s yua, meag that the ecoomc beeft satsfacto degree the bas s ; the coordated degree of tal water rghts allocato s 0.984, meag that the socal beeft satsfacto degree the bas s 0.984; the ecologcal beeft satsfacto degree the bas s ; ad, therefore, the comprehesve beeft satsfacto degree the bas s These results show that the prcpal-subordate herarchcal mult-objectve programmg model of tal water rghts allocato s applcable, ad that the prcpal-subordate herarchcal teractve teratve algorthm based o the satsfacto degree s feasble. 5 Coclusos Ital water rghts for the two levels of the herarchy were allocated based o the developed prcpal-subordate herarchcal mult-objectve programmg model. The tal water rghts allocato strctly cotrols bas maxmum emssos rghts, promotes the uty of quatty ad qualty of tal water rghts allocato, realzes far ad coordated developmet across dfferet regos ad coordated ad effcet water use across dfferet water sectors each rego, elmates water coflct betwee regos ad water sectors, ad obtas the optmal comprehesve beeft to the ecoomy, socety ad ecology of the bas. Accordg to teractve decso theory, the prcpal-subordate herarchcal teractve Da WU et al. Water Scece ad Egeerg, Ju. 2009, Vol. 2, No. 2,

12 teratve algorthm based o the satsfacto degree was developed ad used to solve the tal water rghts allocato model through a mult-roud teractve teratve process. The results of a case study show that the prcpal-subordate herarchcal mult-objectve programmg model s effectve ad applcable to tal water rghts allocato, ad that the prcpal-subordate herarchcal teractve teratve algorthm based o the satsfacto degree ca be used to solve the prcpal-subordate herarchcal mult-objectve programmg model. Refereces Ge, M., ad Wu, F. P Ital allocato model for water rghts of the secod herarchy. Joural of Hoha Uversty (Natural Sceces), 33(5), ( Chese) Goldfard, W Water Law (2d edto). Chelsea: Lews Publshers, Ic. Gopalarsha, C The doctre of pror approprato ad ts mpact o water developmet: A crtcal survey. Amerca Joural of Ecoomcs ad Socology, 32(), [do:0./j tb0280.x] Howe, C. W., Schurmeer, D. R., ad Shaw, W. D Iovatve approaches to water allocato: The potetal for water marets. Water Resources Research, 22(4), Kelma, J., ad Kelma, R Water allocato for ecoomc producto a sem-ard rego. Water Resources Developmet, 8(3), [do:0.080/ ] Mather, J. R Water Resources: Dstrbuto, Use, ad Maagemet. New Yor: Joh Wley ad Sos, Ic. Meg, Q., Y, Y. S., ad Meg, L. J Research o the tal water rght allocato a bas. Resources ad Evromet the Yagtze Bas, 7(5), ( Chese) Teer, J. R., ad Naashma, M Water Allocato, Rghts, ad Prcg: Examples from Japa ad the Uted States. Washgto, D. C.: World Ba. Thur, S. M., Summers, P. C., ad Carpeter, P. K PROSIM: A water rghts-based operatoal smulato model of the Provo Rver. Fotae, D. G., ad Tuvel, H. N. eds., Proceedgs of the 2st Aual Coferece o Water Polcy ad Maagemet: Solvg the Problems, Dever: Amerca Socety of Cvl Egeers. Tog, J. P., Wag, H. M., ad Nu, W. J Ital allocato system modellg of water rghts bas. Systems Egeerg, 25(3), ( Chese) Tracy, J. C. 99. A model for the maagemet of groudwater ad surface water rghts durg droughts. Aderso, J. L., ed., Proceedgs of the 8th Aual Coferece ad Symposum o Water Resources Plag ad Maagemet ad Urba Water Resources, New Yor: Amerca Socety of Cvl Egeers. Wag, G. M., Wa, Z. P., ad Wag, X. J Bblography o blevel programmg. Advaces Mathematcs, 36(5), ( Chese) Wu, F. P., ad Ge, M Ital allocato model for water rght of the frst herarchy. Joural of Hoha Uversty (Natural Sceces), 33(2), ( Chese) Wu, F. P., ad Ge, M Method for teractve water rght tal allocato based o harmoousess judgmet. Joural of Hoha Uversty (Natural Sceces), 34(), ( Chese) Zhou, N. L., ad J, C. M Research o tal allocato model for regoal water rght. Water Resources ad Power, 25(3), 6-8. ( Chese) 6 Da WU et al. Water Scece ad Egeerg, Ju. 2009, Vol. 2, No. 2, 05-6