季节性商品供应商的生产库存及定价策略研究

2811200511()JOURNALOFHEFEIUNIVERSITYOFTECHNOLOGYVol.28No.11Nov.2005:2004212229:(XS04017):(1979-),,,,.(,230009):,;,:;;;;:O227:A:100325060(2005)1121413206Studyontheoptimalproduction-pricingpolicyofseasonalitemsforsuppliersZHAOJu(SchoolofManagement,HefeiUniversityofTechnology,Hefei230009,China)Abstract:Consideringtheproduction2inventoryinthesupplychainofseasonalitemsthedemandofwhichissensitivetoprice,thesupplier’soptimalproduction2pricingpolicyisstudied,theaimofwhichistoencouragetheretailersforward2buyandstablizethedemandandinventorylevels.Arecursivealgorithmandanumericalexamplearepresented,anditisillustratedthatthesupplierandtheretailercangetmoreprofitwiththestrategies.Keywords:price;discount;demand;forward2buy;stock0,,(),[1,2]Arcelus[3],;[46],2003,[7],,,,,,,,,,,;,,,,,,,,[8],,,,,,11.1,:;;P0,11p0,,i[Ti-1,Ti](i=1,2,,5)Ki()0,,pu0;[0,pu]ptD(p,t)[8],D(p,t)=a-K1(p0-p)k1t+b1-K2(p0-p)c-K3(p0-p)k2t+b2-K4(p0-p)b-K5(p0-p)T0tT1T1tT2T2tT3T3tT4T4tT5,k1=c-aT2-T1;b1=a-k1T1;k2=c-bT3-T4;b2=b-k2T4,,,ps1.2(1):Di(p)ip(i=1,3,5);fi(Qi,p)ip;Qii(i=1,3,5);fi(tij,p)ip(i=2,4);ni,tijj,qijj(,ii,j=1,2,,ni);A2;h2(0h21)();v(2):A1;Ps;cs;h1(0h11)();v;Qs,Qs=T5T0D(p,t)dt;Ts;qs2[8],,:(1),,1,3,5EOQ[9],2,4W(p,Qi,tij)=f1(p,Q1)+f2(p,t2j)+f3(p,Q3)+f4(p,t4k)+f5(p,Q5)fi(Qi,p)=(p-v)TiTi-1Di(p)dt-A2[TiTi-1Di(p)dtöQi]-h2v(Ti-Ti-1)Qiö2=(p-v-A2öQi)Di(p)(Ti-Ti-1)-h2v(Ti-Ti-1)Qiö2(i=1,3,5)f2(t2i,p)=(p-v)T2T1D(p,t)dt-n2A2-h2v6n2i=1t2(i+1)t2i(t-t2i)D(p,t)dt[10,11]4141()28f4(t4i,p)=(p-v)T42T3D(p,t)dt-n4A2-h2v6n4i=1t2(i+1)t2i(t-t4i)D(p,t)dtt21=T1t2(n2+1)=T2t41=T3t4(n4+1)=T4(2)[T1,T2],2,0(t2i,p,H,W,Q3)=(p-v0+d)[T2+HT1D(p,t)dt+K(p)c0(T3-T2-H)]+(ps-v0+d)(1-K)T2+H+WT2+HD(ps,t)dt+(ps-v0)[1-K(p)]T3T2+H+WD(ps,t)dt-(n2+1)A2-h2(v0-d){6n2i=1t2(i+1)t2i(t-t2i)[D(p,t)+Kc0(T3-T2-H)ö(T2+H-T1)]dt+12H[(c-K3(p0-p))H+Kc0H(T3-T2-H)ö(T2+H-T1)+2(1-K(p))c0W]+12c0(1-K(p))W2}-h2v0(T3-T2-H-W)Q3ö2-A2c0(T3-T2-H-W)[1-K(p)]öQ3,t21=T1;t2(n2+1)=T2;c0=D3(ps)=c-K3(p0-ps),t2i(i=1,2,,n2),,H0,W0,p3ps(ps),,2,[8]2,[T1,T2]22.1W1(v)=(v-cs)Qs-h1csH-A1,H,iHi([9]),T2TsT3T3TsT4,22.1.1T2TsT3,QsöTsPsQsöT2t3iTsT3(i+1),:ts=T1ön1,qs1=PsT1-T1tsD1(ps))dt,qs2=PsT2-T2tsD(ps,t)dt,qs=PsTs-t3(i+1)tsD(ps,t)dt,qs3=qs-(n3-i)Q3,qs4=qs3-6n4i=1q4iH1=Ps(n1Q1öD1)2ö2-(n1-1)n1Q21ö(2D1)=[(Ps-D1)T21+Q1T1]ö2H2=126n2j=1{2[qs1+Ps(t2j-t21)-6jk=1q2k]+Ps[t2(j+1)-t2j]}[t2(j+1)-t2j]H3=Q3öD3(ps){(i-1)qs2+(n3-i)qs-[i(i-1)+(n3-i+1)(n3-i)]Q3ö2+(i-1)2PsQ3ö[2D3(ps)]}+L514111:H4=6n4j=1(qs3-6jk=1q4k)(t4(j+1)-t4j)H5=(T5-T4)[2qs4-Q5-(T5-T4)D5(ps)]ö2,t3iTst3(i+1),L=12[(qs2-iQ3+(i-1)PsQ3D3(ps))+qs][Ts-T2-(i-1)Q3D3(ps)]+qs[T2+iQ3D3(ps)-Ts];Ts=t3(i+1),L=12{[qs2-iQ3+(i-1)PsQ3D3(ps)]+qs}Q3D3(ps)2.1.2T3TsT4t4iTsT4(i+1),H1,H2,qs1,qs2H3=(T3-T2)[2qs2-Q3+(Ps-D3(ps))(T3-T2)]ö2H4=126i-1j=1{2[qs3+Ps(t4j-t41)-6jl=1q4l]+Ps(t4(j+1)-t4j)}(t4(j+1)-t4j)+M+6n4j=i+1(qs-6jl=i+1q4l)(t4(j+1)-t4j),t4iTst4(i+1),M=[qs3+Ps(t4i-t41)-6il=1q4l+qs]Ts-t4i2+qs(t4(i+1)-Ts);Ts=t4(i+1),M=[qs3+Ps(t4i-t41)-6il=1q4l+qs]Ts-t4i2;qs3=PsT3-T3tsD(ps,t)dt;qs=PsTs-t4(i+1)tsD(ps,t)dt;i=1,2,,n4H5=(T5-T4)[2qs4-Q5-(T5-T4)D5(ps)]ö2;qs4=qs-6n4l=i+1q4l,:H=65i=1Hi2.2[T1,T2],3,W1d=(v-cs)[T10D(ps,t)dt+(1-K)T3T2+H+WD(po,t)dt+T5T3D(ps,t)dt]+(v-d-cs)[T2+HT1D(p3,t)dt+T2+H+WT2+HD(ps,t)dt+K(p3)co(T3-T2-H-W)]-h1cs65i=1Hi-A1,Hi22.2.1T2+H+WTsT3,[T2,T3]H3:co=D3(ps)=c-K3(po-ps)qs2=PsT2-T1tsD(ps,t)dt-T2T1[D(p3,t)+Kco(T3-T2-H)T2+H-T1]dtqd=T2+HT2(D(p3,t)+Kco(T3-T2-H)T2+H-T1)dt+(1-K)T2+H+WT2+HD(ps,t)dt=[c-K3(po-ps)+Kco(T3-T2-H)T2+H-T1]H+(1-K)coWqo=qs2-qd+Ps(H+W)6141()28[T2+H+W,T3]Q3;[(1-K(p3)]D3(ps))D3;n3,H3=[2qo-Ps(H+W)](H+W)ö2+Q3öD3{(i-1)qo+(n3-i)qs-[i(i-1)+(n3-i+1)(n3-i)]Q3ö2+(i-1)2PsQ3ö(2D3)}+Nt3iTst3(i+1),N=[q0-iQ3+(i-1)PsQ3öD3+qs][Ts-T2-(i-1)Q3öD3)]ö2+qs[T2+iQ3öD3-Ts];Ts=t3(i+1),N=[qo-iQ3+(i-1)PsQ3öD3+qs]Q3ö(2D3);n3=co(T3-T2-H-W)öQ3;qs3=qs-(n3-i)Q33,H2,q2i(i=1,2,,n32)q2i(i=1,2,,n32),2.2.2T3TsT4qs2,qo,qd,qs,Q3,D3,n3,[T2,T3]H3=[2q0-Ps(H+W)](H+W)ö2+(T3-T2-H-W)(2qo-Q3)ö2+(T3-T2-H-W)2(Ps-D3)ö2qs3=PsT3-T3tsD(p,t)dt2.3,:v(d)cs(0);cs(0)W(0),{t3ij},{q3ij}W1(W1d);v(d(v3))[cs,vu]([0,cs])(vu);W1(W1d),,v3(d3)3:A1=100,cs=0.1,h1=0.6,Ps=160,A2=35,po=10,h2=0.3,a=35,c=135,b=54;[Ki,i=1,2,,5]=[-1,-40,-50,-40,-1],[Ti,i=1,2,,5]=[0,4.0,6.0,7.0,8.5,12],,m,p3(m),H3(m),W3(m),m,p,,vc++,,:(1):v3=3.7697,W1=3694.592272;Qs=1090.368584,Ts=6.814804,H=3445.555349;H1=1084.837305,H2=1038.628023,H3=481.246708,H4=443.071183,H5=397.772129:ps=8.406995,W=4090.599496;f[T1,T3]=f2+f3=2023.559462;Q1=48.790674,n1=3,f1=463.414484;Q3=107.325131,n3=2,f3=864.709003;Q5=64.858506,n5=3,f5=668.943048;n2=3,[t2i,i=1,2,3]=[4.000000,4.737930,5.396023],f2=1158.850459;n4=2,[t4i,i=1,2]=[7.000000,7.695823],f4=934.682502;(2):d3=0.19999,W1d=4051.697737;Qs=1142.157596,Ts=7.138485,H=2968.241669;H1=1084.837305,H2=967.742221,H3=406.213527,714111:H4=342.578787,H5=166.869827:p3=7.855294,f[T1,T3]=0=2124.340244;H=0.278224,W=0.495178,Q3=45.447500,n3=1,n2=3,[t2i,i=1,,4]=[4.00,4.727620,5.387824,6.000000],p3ps,,,;H0,W0,,4,,,,,;,,,,,,,,,,,[][1]BuzzellRD,QuelchJA,SalmonWJ.Thecostlybargainoftradepromotion[J].HarvardBusinessReview,1990,68:141-149.[2]Anon.Procter’sgamble[J].TheEcono