Supply Chain Coordination Research under a Fuzzy Decision Environment

Transcription

1 IJCI Intenational Jounal of Comute cience Iue Vol Iue No Mach 3 IN (Pint): IN (Online): IJCIog 37 uly Chain Cooination eeach une a Fuzzy Deciion nvionment hengju ang Deatment of conomic Heze Univeity Heze hanong 745 China Abtact In a to-tage uly chain comoe of a ulie an a etaile the uly chain moel une a fuzzy envionment ae eeache The aamete of maket eman function the cot of the ulie an etaile ae teate a taezoial fuzzy numbe The eciion ocee ae analyze une the ecentalize an centalize eciion an the eciion moel ith evenue haing contact i alo built by the metho of fuzzy cut et theoy It i hon that in fuzzy eciion envionment the ouble maginalization effect i till exite in uly chain ytem; the ofit of membe can be cooinate by evenue haing contact Finally a numeical i given to illutate the moel an the olution oce Keyo: uly Chain evenue haing Fuzzy nvionment Taezoial Fuzzy Numbe Intouction Ove the lat ecae o o uly chain management ha emege a a key aea of eeach among the actitione of oeation eeach In ecent yea moe an moe eeache have alie the fuzzy et theoy an technique to evelo an olve the uly chain moel oblem Chang [] eente a fuzzy OQ moel ith imefect quality item hee the efective ate an annual eman ee coniee a the tiangula fuzzy numbe Dutta et al [] eente a ingle-eio inventoy oblem in an imecie an uncetain mixe envionment Tan an Tang [3] tuie the fuzzy afety tock moel hee the maket eman a coniee a Gau fuzzy vaiable Manal an oy [4] eveloe a multi-item ilaye inventoy moel une helf-ace containt in fuzzy envionment ecently Xu an Zhai [5 6] aume the eman to be a tiangula fuzzy numbe an ealt ith the neboy oblem in a to tage uly chain Hu et al [7] eente to PQ moel ith fuzzy efective ate hee the efective ate a coniee a the -fuzzy numbe Zheng an iu [8] contucte to moel fo neboy oblem ith fuzzy anom eman in both noncooeation an cooeation ituation Wei an Zhao [9] coniee a fuzzy cloe-loo uly chain ith etail cometition Ye an i [] eveloe a tackelbeg moel ith fuzzy eman Zhao et al [ ] analyze the icing oblem of ubtitutable ouct in a fuzzy uly chain Akinibio et al [3] eente a fuzzyontology bae infomation etieval ytem fo elevant feeback The above moel ith fuzzy uly chain oblem have focue on the cae that the acto o not make cooeation In fact in oe to imove oveall chain efomance the cooination an integation activitie ae citical facto fo an effective uly chain evenue haing contact a an imotant kin of oula contact i an intument fo uly chain cooination Giannoccao an Pontanolfo [4] hoe that evenue haing coul cooinate membe in the neboy channel ith thee tage: ulie manufactue an etaile Guta an Weeaat [5] eigne a evenue-haing contact to maximize the centalize evenue by chooing an aoiate inventoy level Cachon an aiviee [6] intenively icue a evenue haing contact beteen a ingle ulie an a ingle etaile in a ingle eio neboy oblem Yao et al [7] invetigate a evenuehaing contact fo cooinating a uly chain comiing one manufactue an to cometing etaile The above liteatue icu the evenue haing contact ith obabilitic eman in that obability itibution ae etimate fom hitoical ate Hoeve in actice eecially fo ne ouct the obabilitie ae not knon ue to lack of hitoy ata Thu the fuzzy et theoy athe than the taitional obability theoy i ell uite to the evenue haing contact oblem In thi ae the eman ae aoximately etimate by the exet an egae a fuzzy vaiable The ecentalize eciion-making moel the centalize eciion-making moel an the evenue haing contact in fuzzy linea eman envionment ill be icue an the imact of main aamete on the moel ill alo be analyze Coyight (c) 3 Intenational Jounal of Comute cience Iue All ight eeve

2 IJCI Intenational Jounal of Comute cience Iue Vol Iue No Mach 3 IN (Pint): IN (Online): IJCIog 38 Peliminaie Fuzzy et theoy Definition The fuzzy et A ( a a a3 a4) hee a < a < a3 < a 4 an efine on i calle the taezoial fuzzy numbe if the membehi function of A i given by xa a< x a a a μ () x a< x a3 A () x a4 a3< x a4 a3 a4 otheie hee a a a3 an a4 ae the loe limit loe moe ue moe an ue limit eectively of the fuzzy numbe A The tiangula fuzzy numbe A i calle the oitive taezoial fuzzy numbe if a > Definition The et A { x μ } Ax hee [] i ( ) calle the -cut of A A i a non-emty boune cloe inteval containe in the et of eal numbe an it can be enote by A [ A A ] Whee A an A ae eectively the left an ight bounay of A ith A inf{ : } x μ Ax ( ) A u{ x : μ } Ax ( ) Fo [] the -cut of a taezoial numbe A ( a a a 3 a ) 4 i A a + ( a a) A a ( a a ) () Pooition (iu an iu [8] an Zhao et al [9]) et A an B be to oitive ineenent taezoial fuzzy numbe fo [] e have ( A + B) A B + ( A + B) A B + ( A B) A B ( A B) A B ( A B) A B ( A B) A B (3) Pooition et k be a oitive eal numbe then kξ ξ ( ) kξ ξ (4) ( ) k k Pooition 3 (iu an iu []) et A be a oitive taezoial numbe the execte value of A i A ( A A + ) (5) Pooition 4 (iu an iu [8]) et A an B be to ineenent fuzzy vaiable ith finite execte value Then fo any eal numbe a an b e have aa + bb a A + b B (6) Poblem ecition Conie a to-tage uly chain coniting of a ulie an a etaile The etaile ell hot life ouct uch a eonal comute conume electonic o fahion item ith high uncetain eman The ouct ae ol only in one eio A the lea time of uch goo ae much longe than thei elling eaon the acto have no chance to lace a econ oe In thi ae the linea eman function une a fuzzy eciion envionment can be itten a Q ( ) β (7) hee i the unit ice of the ouct eeent the fuzzy ize of the maket β tan fo the fuzzy enitivity of eman to the ice of the ouct offee to the maket an β ae oitive an ineenent taezoial fuzzy numbe The folloing notation ae ue fo a ouct in the moel: c : the e unit ouct fuzzy cot incue to the ulie c : the e unit fuzzy cot incue to the etaile : the holeale ice Φ : the faction evenue of the etaile in evenue haing contact an Φ () Π : the fuzzy ofit of the ulie Π : the fuzzy ofit of the etaile Π : the fuzzy ofit of the uly chain In thi ae the ulie an the etaile ae aume to be ik neutal an uue fuzzy execte value of ofit maximization We can exe the fuzzy ofit of the etaile the ulie an the uly chain a follo Π ( c )( β ) (8) Π ( c )( β ) (9) Π ( c c )( β ) () 3 uly chain moel ith fuzzy eman Coyight (c) 3 Intenational Jounal of Comute cience Iue All ight eeve

3 IJCI Intenational Jounal of Comute cience Iue Vol Iue No Mach 3 IN (Pint): IN (Online): IJCIog 39 3 Fuzzy ecentalize eciion-making moel A uual e fitly begin the analyi ith the fuzzy ecentalize uly chain The behavio of the ulie an the etaile in fuzzy ecentalize ytem can be chaacteize by the tackelbeg game In the othe o at fit the ulie et the holeale ice a the leae an then the etaile et it ice of the ouct a the folloe hich olve the folloing moel Max Π ( c )( β) tmax Π ( c )( β ) () Theoem et Π an Π be the fuzzy execte value of the ofit fo etaile an ulie then the otimal eaction function of the etaile i [ ] + c β ( ) + β Poof: The fuzzy execte ofit of the etaile i Π ( Π ) + ( Π ) (( c )( ) ) (( c )( ) ) (( c ) ( β) ( c ) ( β ) ) (( ( c ) )( ) ( ( ) )( )) β c β ( ) ( ) (( ) ( ) ) c c ( β ) ( ) (( c ) ( ) β c ) β [ ] c β β β β β + β β + β ( ) [ ] ( c c ) ( ) ( ) () Notice that the econ-oe eivative Π β < ince β i a oitive fuzzy vaiable Conequently Π i a concave function of Hence fo any given the otimal eaction function of the Π etaile can be obtaine by olving hich give [ ] + c β ( ) + β Theoem The otimal tategy of the ulie in Fuzzy ecentalize eciion-making moel i [ ] + c β cβ β Poof: The fuzzy execte ofit of the ulie i Π (( c )( )) (( )( )) β c β + [ ] (( ) ) β+ c β c + ( c) ubtituting ( ) (3) into (3) e can get the fit-oe an econ-oe eivative of Π a Π β+ ( [ ] + cβ cβ) Π β Notice that the econ-oe eivative Π β < ince β i a oitive fuzzy vaiable Conequently Π i a concave function of Hence the otimal tategy of the ulie can be obtaine by olving Π hich give [ ] + c β cβ β Theoem 3 The otimal tategy of the etaile in fuzzy ecentalize eciion-making moel i 3[ ] + c β cβ + 4 β [ ] cβ cβ Q 4 Poof: Fom Theoem an e can eaily obtain Theoem 3 Theefoe the fuzzy execte ofit of the etaile of the ulie an of the to-tage uly chain ae all given a belo: ( [ ] c β c β ) [ ] cβ Π + 6 β β (( c ) ( ) ) + c (4) ( [ ] c β c β ) [ ] cβ Π + 8 β β (( c) + ( c) ) (5) Coyight (c) 3 Intenational Jounal of Comute cience Iue All ight eeve

4 IJCI Intenational Jounal of Comute cience Iue Vol Iue No Mach 3 IN (Pint): IN (Online): IJCIog 4 3 ( [ ] c β c β) [ ]( c β+ c β) Π + 6 β β (( c ) ( ) ) ( ) ( ) c c c ( ) + + (6) 3 Fuzzy centalize eciion-making moel Conie a uly chain occuie by an integate-acto hich can alo be egae a the etaile an the ulie making cooeation The integate-acto tie to maximize it fuzzy execte value of ofit Π by chooing the otimal ice of the ouct hich olve the folloing moel Max Π ( c c )( β ) (7) Theoem 4 The otimal tategy of the uly chain in fuzzy centalize eciion-making moel i [ ] + c β cβ + β [ ] cβ cβ Q Poof: The fuzzy execte ofit of the to-tage uly chain i Π ( ( c c )( β) ) + (( c c )( β )) β + ( [ ] + c β + c β ) (( c) ( c ) ) + + (8) (( c) ( c) ) Notice that the econ-oe eivative β < ince β i a oitive fuzzy vaiable Π Conequently Π i a concave function of Hence the otimal etail ice of the uly chain can be obtaine by olving Π hich give [ ] + c β cβ + β The otimal oe quantity of the etaile in centalize eciion-making moel can be obtaine by Q β [ ] β [ ] cβ cβ Theefoe the fuzzy execte ofit of the to-tage uly chain i given a 4( [ ] cβ cβ) [ ]( cβ cβ + ) Π + 4 β β (( c ) ( ) ) + c (( c ) ( ) ) + c (9) [ ] [ ] Theoem 5 Q > Q π > π Poof: Comaing Theoem 3 an Theoem 4 q(6) an q(9) e can eaily veify that Q > Q an π > π [ ] [ ] Theoem 5 ho that the etaile otimal oe quantity in fuzzy centalize eciion-making i lage than that in fuzzy ecentalize eciion-making the total fuzzy execte ofit in fuzzy ecentalize eciion-making i le than the maximum fuzzy uly chain ofit in fuzzy centalize eciion-making That i to ay thee alo exit ouble maginalization oblem in fuzzy envionment Theefoe the ulie ha to ovie incentive mechanim uch a a evenue haing contact to encouage the etaile to oe moe to imove the efomance of the acto an the channel 33 Fuzzy evenue haing contact In a evenue haing contact the ulie hae ith the etaile a ecentage of hi evenue et Φ be the faction the etaile kee then ( Φ) i the faction the ulie ean Thu e can exe the fuzzy ofit of etaile an ulie a follo Π ( Φc )( β ) () Π (( Φ ) + c )( β ) () The etaile tie to maximize it fuzzy execte value of ofit Π in fuzzy evenue haing contact by chooing the otimal ice of the ouct hich olve the folloing moel: Max Π ( Φc )( β ) () c β Theoem 6 Fo any max Φ 5 5 c β + c β the otimal tategy in fuzzy evenue haing contact i Coyight (c) 3 Intenational Jounal of Comute cience Iue All ight eeve

5 IJCI Intenational Jounal of Comute cience Iue Vol Iue No Mach 3 IN (Pint): IN (Online): IJCIog 4 ( ) Φ c β cβ Φ β Poof: The fuzzy execte ofit of the etaile Π in fuzzy evenue haing contact i Π Φ β + ( Φ [ ] + c β + β ) ( ) [ ] ( ) ( ) c + c (3) Notice that the econ-oe eivative Π Φ β < ince β i a oitive fuzzy vaiable an Φ> Conequently Π i a concave function of Hence fo any given the otimal eaction function of Π the etaile can be obtaine by olving hich give β [ ] c β +Φ + Φ β The otimal oe quantity of the etaile in evenue haing contact can be obtaine by [ ] Q β β Φ[ ] c β β (4) Φ In oe to fully cooinate of the uly chain e make Q Q Fom Theoem 4 an q(4) e can obtain Φ c ( ) β cβ Φ β ince > e have c β Φ cβ + cβ Theefoe the fuzzy execte ofit of the etaile the ulie can be obtaine a ( [ ] ) [ ] Φ c β c β cβ Π + 4 β β + (5) (( c) ( c) ( ) [ ] ) ( ) [ ] Φ c β c β cβ Π + 4 β β (( c ) ( ) + c ) (6) To gain the in-in conition in fuzzy evenue haing contact e houl enue that the fuzzy execte ofit of each acto i lage than that in fuzzy ecentalize eciion-making moel Thu e can have Π > Π an Π > Π Fom q (4) (5) (5)an (6) e can obtain cβ max 5 <Φ< 5 cβ+ cβ 4 A numeical examle In thi ection e illutate the ooe fuzzy moel by a numeical examle The aamete ae given a follo: ( ) β ( 9 ) c ( 3 4 ) an c ( 79) Fom the Theoem 6 e can obtain the ange of contact aamete Φ atifie the conition Φ 55 ( ) Bae on the analyi hoe in the ection 3 e can get the etail ice the quantity of the etaile an the fuzzy execte ofit of the to-tage uly chain in fuzzy ecentalize eciion-making moel an in fuzzy evenue haing contact a 477 Q 46 an Π Q 48 an Π 669 The othe equilibium value in fuzzy ecentalize eciion-making moel an fuzzy evenue haing contact ae eote in Table Table : The eciion in fuzzy moel fo iffeent Φ Φ Π Π Decentalize eciion-making evenue haing contact Table ho that in fuzzy evenue haing contact the etaile otimal oe quantity i lage than that in fuzzy Coyight (c) 3 Intenational Jounal of Comute cience Iue All ight eeve

6 IJCI Intenational Jounal of Comute cience Iue Vol Iue No Mach 3 IN (Pint): IN (Online): IJCIog 4 ecentalize ytem the holeale ice i loe than that in fuzzy ecentalize eciion-making an each acto execte ofit in fuzzy evenue haing contact imove a lot comae ith that in ecentalize eciion-making In aition becaue of ominating the fuzzy execte ofit of the leae (the ulie) i geate than that of the folloe (the etaile) It alo ho that in fuzzy evenue haing contact the holeale ice an the etaile fuzzy execte ofit inceae ith Φ an the ulie fuzzy execte ofit eceae ith Φ The contact aamete Φ imove the flexibility of uly chain cooination eflect the eman ik haing beteen the ulie an etaile 5 Concluion Thi ae fomulate fuzzy uly chain moel in fuzzy linea eman envionment hee the ulie an the etaile aot moe eaonable cooination tategy In oe to examine moel efomance in fuzzy eman e ue cut et theoy to olve thi oblem The ulie an the etaile can gain in-in conition in evenue haing contact The metho ooe in thi ae i eaie to imlement an equie le ata It i aoiate hen the envionment i comlex ambiguou o thee i lack of tatitical ata Acknolegment Thi ok a uote by National Natual cience Founation of China ( ) an the Doctoal Founation of Heze Univeity (XYB3) efeence [] H C Chang An alication of fuzzy et theoy to the OQ moel ith imefect quality item Comute an Oeation eeach vol 3 no [] P Dutta D Chakaboty an A oy A ingle-eio inventoy moel ith fuzzy anom vaiable eman Mathematical an Comute Moeling vol 4 No [3] M Y Tan an X W Tang The futhe tuy of afety tock une uncetain envionment Fuzzy Otimization an Deciion Making vol 5 No [4] N K Manal an T K oy A ilaye inventoy moel ith - fuzzy numbe Fuzzy Otimization an Deciion Making vol 5 No [5] N Xu an X Y Zhai Otimal moel fo ingle-eio uly chain oblem ith fuzzy eman Infomation cience vol 78 no [6] N Xu an X Y Zhai Analyi of uly chain cooination une fuzzy eman in a to-tage uly chain Alie Mathematical Moeling vol 34 no 9 39 [7] J Hu Xu an C Guo Fuzzy economic ouction quantity moel fo item ith imefect quality Intenational Jounal of Infomation an Management cience vol no [8] H Zheng an J C iu Fuzzy neboy oblem ith anom vaiable in a uly chain envionment Intenational Jounal of Infomation an Management cience vol no 7 4 [9] J Wei an J Zhao Picing eciion ith etail cometition in a fuzzy cloe-loo uly chain xet ytem ith Alication vol38 no9 9 6 [] F Ye an Y N i A tackelbeg ingle-eio uly chain inventoy moel ith eighte oibilitic mean value une fuzzy envionment Alie oft Comuting vol no [] J Zhao W Tang Q Zhao an J Wei Picing eciion fo ubtitutable ouct ith a common etaile in fuzzy envionment uoean Jounal of Oeational eeach vol6 no [] J Zhao W Tang an J Wei Picing eciion fo ubtitutable ouct ith etail cometition in a fuzzy envionment Intenational Jounal of Pouction conomic vol35 no [3] C T Akinibio B Afolabi B I Akhigbe an I J Uo A fuzzy-ontology bae infomation etieval ytem fo elevant feeback Intenational Jounal of Comute cience Iue vol8 no [4] I Giannoccao an P Pontanolfo uly chain cooination by evenue haing contact Intenational Jounal of Pouction conomic vol 89 no [5] D Guta an W Weeaat ulie manufactue cooination in caacitate to-tage uly chain uoean Jounal of Oeational eeach vol 75 no [6] G P Cachon tock a: Inventoy cometition in a to echelon uly chain Oeation eeach vol 49 no [7] Z Yao C H eung an K K ai Manufactue evenue haing contact an etail cometition uoean Jounal of Oeational eeach vol 86 no [8] Y iu an B iu xecte value oeato of anom fuzzy vaiable an anom fuzzy execte value moel Intenational Jounal of Uncetainty Fuzzine an Knolege-Bae ytem vol no [9] Zhao W Tang an H Yun anom fuzzy eneal oce uoean Jounal of Oeational eeach vol 69 no 89 6 [] B iu an Y iu xecte value of fuzzy vaiable an fuzzy execte value moel I Tanaction on Fuzzy ytem vol no hengju ang i a lectue at Deatment of conomic Heze Univeity He eceive hi BM Degee fom Qingao Univeity in 5 an MM Degee fom Qingao Univeity in 8 eceive hi PhD Degee fom Beijing Intitute of Technology in Hi cuent eeach inteet ae in the aea of uly chain management fuzzy eciion an it alication Coyight (c) 3 Intenational Jounal of Comute cience Iue All ight eeve