不确定需求下闭环供应链定价模型研究

1,21(1.;2.):112,2,,,:;;;:F274:A:16722884X(2009)0120045206PriceDecisionModelsforClosed-loopSupplyChainunderUncertainDemandZHANGKeyong1,2ZHOUGuohua1(1.SouthwestJiaotongUniversity,Chengdu,China;2.NorthUniversityofChina,Taiyuan,China)Abstract:Thepricedecisionmodelsofclosed2loopsupplychainthatiscomposedofonemanufac2turerandoneretailerwithproductremanufacturingunderuncertaindemandwasbuilt.Thepricemodelswereanalyzedbygametheory,andsomeconclusionswereobtained.Thecallbackproductprice,thesaleprice,theexpectedprofitofthesystemanditsmembersunderdifferentnewproductmanufacturingcostwerefurtheranalyzednumerically.Bymakingthecomparisonbetweenthetwoclosed2loopsupplychainmodels,itisfoundthatthecallbackproductpriceandthesalesincentralizedclosed2loopsupplychainismorethanthatofthedecentralizedclosed2loopsupplychain,nevertheless,itssalepriceislessthanthatofthedecentralizedclosed2loopsupplychain.Keywords:closed2loopsupplychain;uncertaindemand;game;pricing:2008204229:(2005F026),,,,,()[1][2],,,[3],[3],,[4]3,[5][4][6],,[7],,546120091ChineseJournalofManagementVol.6No.1Jan.2009©1994-2010ChinaAcademicJournalElectronicPublishingHouse.Allrightsreserved.,[8],[9][10],[11],,,[12,13],,[12],,,,[12,13],,,11(1)11:(1)Cm,Cr,CrCm(2),,2,W,P,Cs(3)Pr,Pm,,(PrPmCm-Cr),Pr=(1-r)Pm,,r,0r1(4),D=d(P)+E,,d(P),d(P)=A-BP,,AB;E,f(x),F(x)(5)Q0=bPkr([12]),(b0,k1),,b,k(6)K,(1-K)(7),S,Cb(8)()Q,c,d2,,,Q,PrP,,,0c=min(D,Q)(P-Cs)-CmQ+KbPkrõ(Cm-Cr)-bPk+1r+[Q-min(D,Q)]S-[D-min(D,Q)]Cb(1)[14,15],Q=d(P)+z,d(P)=A-BP,z,0c=[d(P)+min(E,z)](P-Cs)-[d(P)+z]Cm+KbPkr(Cm-Cr)-bPk+1r+[z-min(E,z)]S-[E-min(E,z)]Cb,(2),0c#0c=z-(P-Cs)[A-BP+x]f(x)dx-Cm[A-BP+z]+KbPkr(Cm-Cr)-bPk+1r+z-S(z-x)f(x)dx++z(P-Cs)õ[A-BP+z]f(x)dx-+zCb(x-z)f(x)dx(3):maxz,P,Pr#0c=z-(P-Cs)[A-BP+x]f(x)dx-Cm[A-BP+z]+KbPkr(Cm-Cr)-bPk+1r+646120091©1994-2010ChinaAcademicJournalElectronicPublishingHouse.Allrightsreserved.(z-x)f(x)dx++z(P-Cs)õ[A-BP+z]f(x)dx-+zCb(x-z)f(x)dx(4)zPPr,#0cz3cP3cP3cr#0czPPr,:F(z)=P-Cs+Cb-CmP-Cs+Cb-S;A+(Cm+Cs)B-2BP+z[1-F(z)]+z-xf(x)dx=0;Pr=Kk(Cm-Cr)k+1(5)(5),,Lingo8.01(4)2B(P-S-Cs+Cb)f(z)[1-F(z)]2:52#0c5P2=-2B;52#0c5P5Pr=0;52#0c5P5z=1-F(z);52#0c5z2=SF(z)-(P-Cs+Cb)f(z);52#0c5z5P=1-F(z);52#0c5z5Pr=0;52#0c5P2r=Kbk(Cm-Cr)(k-1)Pk-2r-kb(k+1)Pk-1r,Kb(Cm-Cr)kPk-1r-b(k+1)Pkr=0,:Pr=Kk(Cm-Cr)k+1,52#0c5P2r=-bkK(Cm-Cr)Pk-2r;52#0c5Pr5P=0;52#0c5Pr5z=0H=-2B1-F(z)01-F(z)Sf(z)-(P-Cs+Cb)f(z)000-bKk(Cm-Cr)Pk-2r(4),,-2B0;-2B1-F(z)1-F(z)f(z)(S-P+Cs-Cb)=2B(P-S-Cs+Cb)f(z)-[1-F(z)]2;ûHû=-bkK(Cm-Cr)Pk-2rõ{2B(P-S-Cs+Cb)f(z)-[1-F(z)]2};,-bkK(Cm-Cr)Pk-2r0,2B(P-S-Cs+Cb)f(z)[1-F(z)]2,,11P3crkK(Cm-Cr),:Pr=Kk(Cm-Cr)k+111,,,,,3,([4]),Stackel2berg,,,WPm,,,WPm,QPPr,,:0M=(W-Cm)Q+(Cm-Cr)KbPkr-bPmPkr,(6)0R=(P-Cs)min(D,Q)+bPkr(Pm-Pr)-QW+[Q-min(D,Q)]S-[D-min(D,Q)]Cb,(7)Q=d(P)+z,d(P)=A-BP,:#0M=E(0M)=(W-Cm)(A-BP+z)+(Cm-Cr)Kb(1-r)kPkm-b(1-r)kPk+1m,(8)#0R=E(0R)=z-(P-Cs)(A-BP+x)f(x)dx+br(1-r)kPk+1m-(A-BP+z)W+z-S(z-x)f(x)dx++z(P-Cs)(A-BP+z)f(x)dx-+zCb(x-z)f(x)dx,(9):maxW,Pm#0M=(W-Cm)(A-BP+z)+(Cm-Cr)Kb(1-r)kPkm-b(1-r)kPk+1m,(10)s.t.maxp,z,r#0R=z-(P-Cs)(A-BP+x)f(x)dx+br(1-r)kPk+1m-(A-BP+z)W+z-S(z-x)f(x)dx++z(P-Cs)(A-BP+z)f(x)dx-+zCb(x-z)f(x)dx(11)74©1994-2010ChinaAcademicJournalElectronicPublishingHouse.Allrightsreserved.[16],#0RPzr,,:A-2BP+z[1-F(z)]+CsB+BW+z-xf(x)dx=0,F(z)=P-Cs+Cb-WP-Cs+Cb-S,r=1ö(1+k)(12)(12)PmW(P3d,P3dr,z3d),#0MW3P3dm,maxW,Pdm[#0M(W,Pm,P,Pr,z)],s.t.A-2BP+z[1-F(z)]+CsB+BW+z-xf(x)dx=0,F(z)=P-Cs+Cb-WP-Cs+Cb-Sr=1ö(1+k),Pm+CrWP(13)(13),2r3k,kP3m(Cm-Cr):r=11+k,50M5Pm=0,P3m=Kk(Cm-Cr)k+1,24,,,,,,,,E,,,EU(0,2)11A60Cr3k2B2Cb5K0.8EU(0.2)S5Cs1Cm9b0.5Lingo8.0,(4)(5)(13),,P3c=20.23919,P3cr=3.2,z3c=1.584182,#30c=215.1493,Q3c=A-BP3c+z3c=21.1058,Q3co=5.12P3d=25.18726,P3dr=2.133,z3d=0.8388044,#30dM=108.7353,#30dR=51.1976,Q3do=10.4643,Q3do=2.274843,74.336%,,CmCm(CrCmW),Cm4567891011121314,1,,22CmCmP3crP3drP3cP3dQ3cQ3d#30c#30dM#30dR#30dEf40.5330.35517.74923.93926.6413.119326.2226164.053778.7207242.77440.7441951.0670.71118.25024.18925.5012.586300.4264151.319872.2541223.57390.7441861.6001.06718.75024.43924.3912.053276.2054139.321366.2032205.52450.7441072.1331.42219.24724.68923.2911.522253.7717128.157960.6332188.79110.7439482.6671.77819.74424.93822.1910.990233.3463117.929355.6094173.53870.7436993.2002.13320.23925.18721.1110.465215.1493108.735351.1976159.93290.74336103.7302.48720.73425.43620.039.937199.4013100.675847.4634148.13920.74292114.2672.84521.22825.68418.959.412186.323993.850744.4728138.32350.74238124.8003.20021.72125.93217.888.887176.139088.360042.2917130.65170.74175135.3333.55522.21426.18016.828.364169.069384.303940.9861125.29000.74106145.8663.91122.70726.42715.767.840165.337681.782440.6224122.40480.74033:#30d=#30dM+#30dR,Ef=#30dö#30c846120091©1994-2010ChinaAcademicJournalElectronicPublishingHouse.Allrightsreserved.(26)26,:2Cm3Cm4Cm()5Cm6Cm3Cm,,()(),,Cm,3,Cm,(Cm-Cr),,,,,(),,,,,,,4,2:P3crP3dr,P3cP3d,Q3cQ3d,#30c#30d4,,,,,,,,,,,,94©1994-2010ChinaAcademicJournalElectronicPublishingHouse.Allrightsreserved.,,5112,,,:,,,,,2,,,,,,,,,,