2_2供应链网络下生产能力和定价策略研究

1410Vol.14No.10200810ComputerIntegratedManufacturingSystemsOct.2008:1006-5911(2008)10-2036-06:2008203211;:2008206223Received11Mar.2008;accepted23June2008.:(70571049)Foundationitem:ProjectsupportedbytheNationalNaturalScienceFoundation,China(No.70571049).:(1974-),,,,,E2mail:[e-mail]222(,710071):,,:;,;,;,;,:;;;;:F253:AProductioncapacityandpricingpoliciesin222supplychainnetworkJIAJun2xiu(SchoolofEconomicsandManagement,XidianUniversity,Xipan710071,China)Abstract:Anetworkstructureofsupplychainwasfocusedincludingtwomanufacturersandtworetailers,andacompetitionmodelofexpectedprofitmaximizationwasestablishedtostudyproductioncapacitycompetitionbetweenmanufacturers,orderingandpricingcompetitionsbetweenretailers.Then,equilibriumpolicieswereanalyzed.Fol2lowingconclusionswereobtainedundertheconditionthatthedemandwaspricesensitive.Thereexisttheoptimalpricingandorderingpoliciesfortheretailers.Theoptimalpricingpolicyforaretailerwasinfluencednotonlybythewholesaleprice,butalsobythepricingofanotherretailer.Theoptimalpricewasincreasingmonotonewiththewholesalepriceandanotherretailprice.Whiletheoptimalorderquantitywasdecreasingmonotonewiththewhole2salepriceandanotherretailprice.Themanufacturersalsohaveasetofoptimalpricingpoliciesandequilibriumcom2petitiveproductionpolicies.Finally,anumericalexamplewaspresentedtoanalyzethiscompetitionmodel.Keywords:supplychainnetwork;productioncapacity;combinedordering;pricingpolicy;competitionmodel0[1],,,,,,2[2]10:222,,122,,[3][4][5],,121,,;[6][7],[7],(fulldistributionchannel),[8][14],,,[15],,,[16],122221m2n,,[6][7][2],,,,,,1111,,,,,,,,,:,,,11,(S1,S2)(R1,R2),,,,(),,,:(1),,(2),,,(3)730214,,pijvj+ui112Si,Rj(i,j=1,2)ij,iiQiiwijijci,uSiiqijji,ijpijjivjjuiiDijji,Dij=dij+j=aij-bijpij+bi,3-jpi,3-j+j,aij,bij0,bi,3-j0,bijbi,3-j,,j,Fj(),fj()2VSi,VRjij,j:VRj(w1j,w2j,p1,3-j,p2,3-j)=maxp1j,p2j,q1j,q2jE{(p1j-vj)min(q1j,D1j(p1j,p1,3-j))+(p2j-vj)min(q2j,D2j(p2j,p2,3-j))+u1[q1j-D1j(p1j,p1,3-j)]++u2[q2j-D2j(p2j,p2,3-j)]+-w1jq1j-w2jq2j}(1):12,,:jp1j,q1j,p2j,q2ja,b,min(a,b)=a-(a-b)+,:VRj(w1j,w2j,p1,3-j,p2,3-j)=maxp1j,p2j,q1j,q2j{(p1j-vj-w1j)q1j-(p1j-vj-u1)E[q1j-D1j(p1j,p1,3-j)]++(p2j-vj-w2j)q2j-(p2j-vj-u2)E[q2j-D2j(p2j,p2,3-j)]+}=maxp1j,p2j,q1j,q2j{r1j(p1j,q1j,p1,3-j,w1j)+r2j(p2j,q2j,p2,3-j,w2j)}(2),r1j(p1j,q1j,p1,3-j,w1j),r2j(p2j,q2j,p2,3-j,w2j)j12i:VSi=maxQi,wi1,wi2E{(wi1-ci)qi1+(wi2-ci)qi2+uSi(Qi-qi1-qi2)}(3):12;,Qi-qi1-qi20,,uSi(-Qi+qi1+qi2)2111,1:ij(qij,pij,p2,3-j,wij)=E[qij-Dij(pij,pi,3-j)]+=qij-dij(pij,pi,3-j)-(qij-dij(pij,pi,3-j)-s)dFj(s),j=1,2q11,p11M1(q11,p11,p12,w11)=511(q11,p11,p12,w11)5q11=p11-v1-w11-(p11-v1-u1)F1(q11-d11(p11,p12))=0;(4)N1(q11,p11,p12,w11)=511(q11,p11,p12,w11)5p11=q11-11(q11,p11,p12,w11)-b11p11F1(q11-d11(p11,p12))=0(5)p21,q21q11,q21,p11,p21,Hessian,,11,,,(5),55q11[q11-11(q11,p11,p12,w11)]=1-F1(q11-d11(p11,p12))0q11-11(q11,p11,p12,w11)q11,p11,p12,w11,(5)830210:222(4)q11=F-11(p11-v1-w11p11-v1-u1)+d11(p11,p12)(6),q11(p11,p12,w11),p311(p12,w11):q11(p11,p12,w11)-11(q11(p11,p12,w11),p11,p12,w11)-b11p11F1(q11(p11,p12,w11)-d11(p11,p12))=0(7),1p311(p12,w11),p321(p22,w21);2p312(p11,w12),p322(p21,w22),p311(p12,w11)p312(p11,w12),p31j(w11,w12);p321(p22,w21)p322(p21,w22),p32j(w21,w22):2,Dij=aij-bijpij+bi,3-jpi,3-j+j:,,;,wi1=wi2=wi,w3i,p3ij(w3i),,q3ij(w3i);jp3ij(wi1,wi2)q3ij(wi1,wi2),p3ij(wi1,wi2)q3ij(wi1,wi2)jii212,2,:VSi=maxQi,wi1,wi2E{(wi1-ci)q3i1(wi1,pi2)+(wi2-ci)q3i2(wi2,pi1)+uSi(Qi-q3i1(wi1,pi2)-q3i2(wi2,pi1))}(8)212113Dij=aij-bijpij+bi,3-jpi,3-j+j:(w3i1,w3i2),;p3ij(wij,pi,3-j)wij,q3ij(wij,pi,3-j)wij:i(wi1,wi2)=(wi1-ci)q3i1(wi1,pi2)+(wi2-ci)q3i2(wi2,pi1)+uSi(Qi-q3i1(wi1,pi2)-q3i2(wi2,pi1))(9)wi1,wi2,:5i(wi1,wi2)5wi1=q3i1(wi1,pi2)+(wi1-ci-uSi)5q3i1(wi1,pi2)5wi1=0(10)1,(4)(5)p11,w11,p12,q11()F1(q11-d11(p11,p12))=p11-v1-w11p11-v1-u1,b11f1(q11-d11(p11,p12))=w11-u1(p11-v1-u1)2(Jacobi)J1=5(M1(q11,p11,p12,w11),N1(q11,p11,p12,w11))5(p11,q11)=w11-u1(p11-v1-u1)3[2(w11+v1-p11)(p11-v1-u1)-p11(w11-u1)]0,J10,:5p115p12=-1J15M1(q11,p11,p12,w11)5p125M1(q11,p11,p12,w11)5q115N1(q11,p11,p12,w11)5p125N1(q11,p11,p12,w11)5q11=-b12f1(q11-d11(p11,p12))(p11-v1-u1)J105q115p120,5p115w110,5q115w11=-p11-v1-u1w11-u10,52q115w211=p11-v1-u1(w11-u1)2uici,1,521(w11,w12)5w211=-p11-v1-u1w11-u1(1+c1+uS1-u1w11-u1)0(11)521(w11,w12)5w2120,521(w11,w12)5w115w12=-b12p11-v1-u1w11-u1,Hessian,1(w311,w312),2:4Dij=aij-bijpij+bi,3-jpi,3-j+j,p3ij(wij,pi,3-j)pi,3-j,q3ij930214(wij,pi,3-j)pi,3-j,,3,,,,21212,,,wi(Qi,Q3-i)=max{0,0i-(1)iQi-(2)3-iQ3-i}(12),0i,(1)i,(2)3-i02,VSi=maxQiE{(wi(Qi,Q3-i)-ci)q3i1(wi(Qi,Q3-i))+(wi(Qi,Q3-i)-ci)q3i2(wi(Qi,Q3-i))+uSi(Qi-q3i1(wi(Qi,Q3-i))-q3i2(wi(Qi,Q3-i)))}(13)5Dij=aij-bijpij+bi,3-jpi,3-j+j,,Q3i:i=(wi(Qi,Q3-i)-ci)q3i1(wi(Qi,Q3-i))+(wi(Qi,Q3-i)-ci)q3i2(wi(Qi,Q3-i))+uSi(Qi-q3i1(wi(Qi,Q3-i))-q3i2(wi(Qi,Q3-i)))(14)1,Q1:515Q1=-(1)1[(w1(Q1,Q2)-c1-uS1)(5q3115w1+5q3125w1)+q311(w1)+q312(w1)]+uS1=0;(15)5215Q21=2(1)215q3115w1+5q3125w1+(w1(Q1,Q2)-c1-uS1)(52q3115w21+521q3125w21)(16)(16)0,5,3,34wi1=wi2[11],11a11b11b12a21b21b22a12b12b11a22b224232155642164221211856313c1c2uS1uS2v1v2u1u2A1A2b21151813135