Pricing and Service Decisions of Supply Chain in an Uncertain Environment

Transcription

1 Engineeing Lette, 4:4, EL_4_4_9 Picing and Sevice Deciion of Supply Chain in an Uncetain Envionent Shengju Sang F FAbtact In a to-echelon upply chain yte ith one anufactue and one etaile, the picing and evice deciion of thee non-coopeative gae unde an uncetain envionent ae eeached. The aket deand i aued a a function of the etail pice and evice level, and the aket bae, anufactuing cot and elling cot ae all conideed a uncetain vaiable. Thee diffeent kind of cenaio including to Stackelbeg gae and one Vetical-Nah gae ae puued by the anufactue and the etaile, and thei optial olution ae alo given. Finally, the eult of the popoed odel ae analyzed via a nueical exaple. It i hon that the anufactue ake the laget expected pofit in the anufactue-stackelbeg gae, and the allet in the Retaile-Stackelbeg gae. The etaile ake the allet expected pofit in the anufactue- Stackelbeg gae. Index Te upply chain, picing and evice, gae theoy, uncetain vaiable I I. BINTRODUCTION N cuent copetitive and uncetain envionent, anufactue and etaile often play a pice a to attact cutoe. Beide pice, evice i alo an ipotant facto that deteine the buying deciion of cutoe. Fo intance, in electonic induty, aintenance evice ha ipotant ipact on the conue deciion to buy a poduct. So, ho the pice and evice effect the deciion of the anufactue and the etaile becoe a hot iue aong pactitione and chola. Thee ae eveal tudie that deal ith the pice and evice deciion in upply chain. Iye [] tudied a upply chain ith one anufactue and to copetitive etaile ho copeted in pice and evice. Tay and Agaal [] dicued the choice of pice and evice deciion ith to non-coopeating and coopeating etaile, and found that the upply chain ebe could achieve coodination only unde vey liiting condition. Xiao and Yang [3] analyzed a pice and evice copetition odel of to upply chain and exained the ole of ik and infoation in the channel deciion. Xiao and Yang [4] alo developed a pice and evice copetition odel beteen a etaile and a anufactue ith a ik haing ule unde deand anucipt eceived ay 3, 6; evied Septebe, 6.Thi ok a uppoted by the Shandong Povincial Natual Science Foundation, China (No. ZR5GQ, and the Poject of Shandong Povincial Highe Educational Huanity and Social Science Reeach Poga (No. J5WB4. Shengju Sang i ith the Depatent of Econoic and anageent, Heze Univeity, Heze, 745, China (phone: ; e-ail: anghengju@63.co. uncetainty. Lu et al. [5] popoed a pice and evice copetition odel ith to anufactue and a coon etaile, in hich thee diffeent gae cenaio ee exained. Wu [6] focued on a pice and evice deciion odel ith to anufactue and a etaile, hee the anufactue poduced the ne and eanufactued poduct. Han et al. [7] tudied a pice and evice copetition poble ith one anufactue and to etaile hee the anufactue acted a the Stackelbeg leade and to etaile ee the folloe, and ade thei optial etail pice independently. Yan and Pei [8] analyzed picing and etail evice deciion in a dual-channel upply chain. Dan et al. [9] alo tudied the optial pice and etail evice deciion in a centalized and a decentalized dual channel upply chain. In addition, Wang and Zhao [] tudied the pice and evice deciion in a dual upply chain hee the anufactue offeed diect channel evice and etail evice. Sang [] tudied the evice and elling effot deciion a to-echelon upply chain in hich the anufactue and the etaile puue thee diffeent poe tuctue. All tudie entioned above dicued pice and evice deciion in a cip envionent, uch a a linea aket deand and knon poduction cot. Hoeve, in eal old, epecially fo oe ne electonic poduct, the elevant pecie date ae difficult to obtain due to lack of hitoical data. In thi ituation, the aket bae and poduction cot can uually be pedicted by oe expet. Thu, fuzzy et theoy popoed by Zadeh [], i ued to deal ith the pice deciion of upply chain by oe chola. Fo intance, Wei and Zhao [3] tudied pice deciion in a cloed-loop upply chain, in hich the deand and cot ee fuzzine. Siila iue a tudied by Wei and Zhao [4] in a evee upply chain. In addition, Zhao et al. [5] tudied pice deciion ith to copetitive etaile in fuzzy envionent. Zhao et al. [6] alo conideed a picing copetition poble ith to anufactue in fuzzy envionent. Soe eeache alo tudied pice and evice deciion in a fuzzy envionent, hee the deand a a fuzzy line function of elling pice and evice level. Fo intance, Zhao et al. [7] analyzed pice and evice copetition poble ith to copeting anufactue and one etaile in fuzzy envionent. Zhao and Wang [8] tudied the picing and etail evice deciion beteen one anufactue and to etaile ith fuzzy deand. Sang [9] popoed one expected value and to chancecontained pogaing odel ith to copetitive anufactue and a coon etaile in a fuzzy deand envionent. Hong [] tudied a Stackelbeg gae led by the etaile in a to-echelon fuzzy upply chain. Sang [] (Advance online publication: 6 Novebe 6

2 Engineeing Lette, 4:4, EL_4_4_9 analyzed a evenue haing contact in a thee-echelon upply chain hee the deand a conideed a a tapezoidal fuzzy nube. Yano et al. [] tudied ulti-objective fuzzy ando linea pogaing poble baed on coefficient of vaiation. When e ue fuzzy et theoy to olve expet pediction, thee ay be oe poble. Fo exaple, the aket bae pedicted by expet ay be about. If e eaue about by fuzzy et theoy, e ay obtain the aket bae i about ith belief degee by poibility eaue, and i not ith belief degee a ell. That i to ay, about and not have the ae belief degee in poibility eaue. It ee that nobody can accept thi concluion. Hence, thoe ipecie quantitie like about cannot be quantified by poibility eaue, and then they ae not fuzzy concept. To deal thee poble, Liu [3] popoed an uncetainty theoy. Late, Ding [4] applied the uncetainty theoy to olve the upply chain poble. To the bet of ou knoledge, thee i no tudy that deal ith the picing and evice deciion of upply chain ith uncetainty theoy in an uncetain envionent. Theefoe, in thi pape, e dicu the picing and evice deciion ith a anufactue and a etaile, in hich the aket bae, anufactuing cot and elling cot ae all uncetain vaiable. We ainly dicu the condition hee the anufactue and the etaile puue thee diffeent poe tuctue: puuing the anufactue-stackelbeg gae, playing Retaile-Stackelbeg gae and acting in Vetical- Nah gae. The et of pape i oganized a follo. In ection II, e intoduce the uncetain theoy elated to the pape. In Section III, e biefly decibe the poble and the notation in ou odel. In Section IV, e develop thee non-coopeative gae beteen the anufactue and the etaile in an uncetain envionent. In Section V, a nueical exaple i povided to illutate the eult of the popoed odel. The lat ection uaize the ok done in thi pape and futhe eeach aea. fo any eal nube x. Definition 3. [8]An uncetain vaiable L( a, b ξ i called linea if it ha a linea uncetainty ditibution, if x a Φ ( x ( x a ( b a, if a x b, if x b hee a and b ae eal nube ith a< b. Lea. [5] Let ξ be an uncetain vaiable ith uncetainty ditibution Φ. If the expected value ofξ exit, then [ ] Φ ( E ξ α dα hee Φ i the invee function of Φ. ξ L a, b be a linea uncetain vaiable, Lea. Let ( then [ ] ( Φ Φ ( E ξ α dα α dα a b Poof: E[ ξ] Φ ( α dα ( a ( b a α dα + ( a b Φ α dα ( a ( b a( α dα + + The poof of Lea i copleted. Lea 3. [5] Let ξ, ξ, K, ξn be independent uncetain vaiable ith uncetainty ditibution Φ, Φ, K, Φn, epectively. A function f ( x, x, K, xn i tictly inceaing ith epected to x, x, K, x and tictly deceaing ith epected to x+, x+, K, xn. Then the expected value of ξ f ( ξ, ξ, K, ξn i + ( + n [ ] f Φ ( Φ ( Φ ( Φ ( K K E ξ α,, α, α,, α dα II. BPRELIINARIES Definition. [3] Let L be a σ-algeba on a nonepty,. Then i et Γ and be a et function fo L to [ ] called an uncetain eaue if it atifie the folloing thee axio: Axio. ( Γ. c Axio. ( ( Λ + Λ. Axio 3. Fo evey countable equence of event{ Λ i }, i,, K, e have U Λi Λ i i ( Definition. [3] Letξ be an uncetain vaiable, and it uncetainty ditibution Φ i defined by ( x ( ξ x Φ i III. BPROBLE DESCRIPTIONS Thi pape conide a to-echelon upply chain coniting of one anufactue and one etaile. The anufactue ell hi poduct to the etaile, and then the etaile etail it to the cutoe. The uncetain deand faced by the anufactue and the etaile i aued a a linea function of the etail pice p and the evice level, hich i given by q d p+ hee the paaete d i a poitive linea uncetain vaiable and epeent the aket potential, the paaete epeent the enitivity of deand to pice change and the paaete epeent the deand expanion effectivene coefficient of the evice level offeed by the anufactue. Futhe, let c and c denote the anufactue cot of poducing it poduct and etaile cot of elling it poduct, epectively, hich ae uncetain vaiable, the (Advance online publication: 6 Novebe 6

3 Engineeing Lette, 4:4, EL_4_4_9 holeale pice pe unit chaged to the etaile by the anufactue, and the etaile pofit agin on the poduct. A the etail pice p can be teated a the total of the pofit agin and the holeale pice, e conide etail pice a p +. Then the deand fo the poduct can be eitten a ( q d + + It i aued that the aginal cot of the anufactue i not affected by the evice level. Futhe, the cot of achieving evice level equie fixed invetent, hich i a quadatic function of evice level. It i given by λ, hee the paaete λ i the invetent coefficient. The pofit of the anufactue and the etaile can be expeed a follo ( λ ( ( ( ( ( Π c d + + ( Π c d + + ( R Theoe. The expected pofit of the anufactue and the etaile can be tanfoed a follo ( [ ] [ ] ( ( d d c ( [ ] [ ] [ ] ( ( d E Π λ + d + E c Ec + Φ α Φ α α (3 E Π R d + + E c + E c Ec Φ α Φ α α (4 d c Poof: Let c, c and d be poitive uncetain vaiable ith uncetainty ditibution Φ c, Φ c and Φ d. Fo (, e can find that E Π i onotone deceaing ith c, and onotone inceaing ith d. Then efeing to Lea, and 3, e have ( ( α ( ( α ( c d λ dα E Π Φ Φ + + E d ( + + Φ ( α Φ ( d d c α α + ( + E[ c ] E[ c ] λ ( [ ] λ + d E c + E[ c ] ( ( c d + Φ α Φ α dα In the ae ay, e can deive E Π R hoed a in (4. The poof of Theoe i copleted. IV. 3BODELS ANALYSIS In thi ection, e exaine the upply chain acto ho to et thei optial olution hen they puue diffeent poe tuctue in an uncetain envionent. We ainly dicu the condition hee the anufactue and the etaile puue thee non-coopeative gae: the anufactue doinate the channel, the etaile doinate the channel, and the anufactue and the etaile have an equal bagaining poe. A. anufactue-stackelbeg gae The S (anufactue-stackelbeg gae cenaio aie in the aket hee the ize of the etaile i alle copaed to the anufactue. In thi cae, the anufactue i the leade, and the etaile i the folloe. That i, fitly, the anufactue et the holeale pice and the evice level uing the etaile eaction function. Then, the etaile et the pofit agin o a to axiize hi expected pofit. Thu, the S gae odel can be given a follo ( ( ( ax E Π E c d λ, + +.t. { c } hee olve the folloing poble ax E Π R E ( c ( d ( + +.t. { c } { d ( + + } { ( } d, + + and Theoe. If ( { (, c }, then the optial epone function of the etaile in the S gae odel i ( (, [ ] E d c + (5 Poof: Fo (4, the fit-ode and econd-ode deivative of E Π R ith epect to can be obtained a d E Π R d + E[ c ] + d d E Π R d Note that the econd-ode deivative of E Π R i negative definite, ince >. Conequently, E Π R i tictly concave in. Hence, let the fit-ode condition be zeo, e can get the optial epone function of the etaile (, a hoed in (5. The poof of Theoe i copleted. Theoe 3. If { c }, { c }, { d ( + + } and 4λ >, then the optial olution of the anufactue and etaile in the S gae ae ( [ ] [ ] λ E d E c E c [ c ] (6 4λ (Advance online publication: 6 Novebe 6

4 Engineeing Lette, 4:4, EL_4_4_9 ( [ ] [ ] E d Ec Ec 4λ (7 λ E d ( Ec [ ] [ ] Ec [ c ] 4λ (8 3λ E d ( Ec [ ] [ ] Ec p [ c ] [ c ] (9 4λ Poof: Subtituting (, expected pofit of the anufactue a in (5 into (3, e can get the E Π λ + + ( [ ] [ ] E d + E c c E [ c ] ( d ( ( [ ] [ ] c E d + c Φ α Φ α dα ( c Fo (, e can get the fit-ode deivative of E Π ith epect to and a follo Π + d+ E c c Π λ + E [ c ] Thu, the Heian atix of E Π i H λ ( [ ] [ ] Note that the Heian atix of E Π i negative definite, ince >, λ > and 4λ >. Thu, E Π i tictly jointly concave in and. Let the fit-ode condition be zeo, e get and a hon in (6 and (7. Subtituting and into (5, e can eaily obtain hoed in (8. The optial etail pice p in the S gae i p + ( [ ] [ ] 3λ E d Ec Ec c + 4λ The poof of Theoe 3 i copleted. B. Retaile-Stackelbeg gae [ ] Ec [ ] The (Retaile-Stackelbeg gae cenaio aie in the aket hee the ize of the anufactue i alle copaed to the etaile. Thi cae iplie the etaile becoe the leade and the anufactue i the folloe. The etaile fit et the pofit agin uing the eaction function of the anufactue. Then the anufactue obeve the deciion ade by the etaile and ake hi epone to thi deciion by etting holeale pice and evice level. Thu, the gae odel can be given a follo ( ( ( ax E Π R E c d + +.t. { c } hee and olve the folloing poble ax E Π E ( c ( d ( λ, + +.t. { c } d ( , { } { d ( ( } { ( },and λ Theoe 4. If ( c >, then the optial epone function of the anufactue in the gae ae ( ( ( [ ] λe d + λ E c λ λ ( E d E [ c ] λ ( ( Poof: Fo (3, e can get the fit-ode deivative of E Π ith epect to and a follo Π + d + E[ c ] Π λ + E [ c ] Thu, the Heian atix of E Π i H λ Note that the Heian atix of E Π i negative definite, ince >, λ > and λ >. Thu, E Π i tictly jointly concave in and. Let the fit-ode condition be zeo, e a hon in ( and (. get ( and ( The poof of Theoe 4 i copleted. c Theoe 5. If { }, { c } { d ( + + } and λ, >, then the optial olution of the anufactue and etaile in the gae ae ( [ ] [ ] λ E d E c E c [ c ] λ (3 E d ( E[ c ] [ ] E c λ (4 E d ( Ec [ ] [ ] Ec + [ c ] (5 (Advance online publication: 6 Novebe 6

5 Engineeing Lette, 4:4, EL_4_4_9 p ( 4λ E d ( E[ c ] [ c ] [ ] E[ c ] λ c (6 Poof: Subtituting ( and ( in ( and ( into (4, e can get the expected pofit of the etaile a ( E d Ec [ ] c [ ] λ λ E Π R + λ λ Ec [ ] ( λ E d λec [ ] + + λ ( α c ( α dα d (7 Φ Φ Fo (7, the fit-ode and econd-ode deivative of E Π R ith epect to can be obtained a ( [ ] + [ ] d E Π λ + d λ λ d E Π R λ d λ λ E d Ec Ec R Note that the econd-ode deivative of E Π R i negative definite, ince >, λ > and λ >. Conequently, E Π R i tictly concave in. Hence, let the fit-ode condition be zeo, e can get a hoed in (5. Subtituting into ( and (, e can eaily obtain and hon in (3 and (4. The optial etail pice p in the gae i p + ( 4λ E d ( Ec [ ] c [ ] c + λ The poof of Theoe 5 i copleted. [ ] Ec [ ] C. Vetical-Nah gae The VN (Vetical-Nah gae cenaio aie in the aket hee the anufactue and etaile have equal aket poe. In thi cae the anufactue deteine the holeale pice and evice level, and the etaile ake the pofit agin iultaneouly and independently. Thu, the gae odel can be given a follo { c } { c } ( ( ( ( ( ax E Π E c d λ, + + ax E Π R E ( c d ( + +.t. { d + + } Theoe 6. If { c }, { c }, { ( } d + + and λ >, then the optial olution of the anufactue and etaile in the VN gae ae ( [ ] [ ] λ E d Ec Ec [ c ] 3λ (8 E d ( Ec [ ] [ ] Ec 3λ (9 λ E d ( Ec [ ] [ ] Ec [ c ] 3λ ( λ E d ( Ec [ ] [ ] Ec p [ c ] [ c ] ( 3λ Poof: The fit-ode deivative of E Π ith epect to and can be obtained fo (3 a follo Π + d + E[ c ] Π λ + E [ c ] The Heian atix of E Π i H λ Note that the Heian atix of E Π i negative definite, ince >, λ > and λ >. Thu, E Π i tictly jointly concave in and. The fit-ode and econd-ode deivative of E Π R ith epect to can be obtained fo (4 a d E Π R d + E[ c ] + d d E Π R d Note that the econd-ode deivative of E Π R i negative definite, ince >. Conequently, E Π R i tictly concave in. Hence, let the fit-ode condition be zeo iultaneouly, e can get, and a hoed in (9, ( and (. The optial etail pice p in the VN gae i p + λ E d ( Ec [ ] Ec [ ] c c 3λ The poof of Theoe 6 i copleted. [ ] [ ] (Advance online publication: 6 Novebe 6

6 Engineeing Lette, 4:4, EL_4_4_9 D. Analyi of the optial olution unde thee non-coopeative gae In thi ubection, e copae the optial olution naely, the holeale pice, evice level, pofit agin and etail pice. Fo convenience of analyi, upecipt S,, and VN ae ued to denote the S gae, gae and VN gae, epectively. To inue that the optial olution ae all poitive, e ipoe the condition on the paaete: λ >, that i λ >. Theoe 7. The holeale pice ae in the ode S VN > > Poof: It i eay to veify that S ( [ ] [ ] λ E d Ec Ec S > ( 4λ ( λ ( λ E d ( Ec [ ] c [ ] ( 4λ ( 3λ VN > The poof of Theoe 7 i copleted. Theoe 8. The evice level ae in the ode VN S > > Poof: It i eay to veify that VN ( [ ] [ ] λ E d Ec Ec VN > ( λ ( 3λ E d ( Ec [ ] c [ ] ( 3λ ( 4λ λ S > The poof of Theoe 8 i copleted. Theoe 9. The pofit agin atify the folloing If λ >, then If < λ <, then If λ, then Poof: It i eay to veify that VN S > > ; VN S > > ; VN S >. ( λ E d ( E[ c ] [ c ] ( 4λ λ E d ( E[ c] E[ c] ( 3λ ( 4λ ( λ E d ( Ec [ ] Ec [ ] ( 4λ S > VN S > VN VN When λ >, e obtain >. When < λ <, VN VN e obtain <. When λ, e obtain. The poof of Theoe 9 i copleted. Theoe. The etail pice atify the folloing If λ >, then If < λ <, then If λ, then Poof: It i eay to veify that p p p S VN p > p > p ; VN S p > p > p ; S VN p > p p. 4 λ( λ + Ed ( Ec [ ] c [ ] ( λ ( 4λ ( λ Ed ( Ec [ ] c [ ] ( λ ( 4λ ( λ E d ( E[ c] E[ c] ( 3λ ( 4λ S p > 4 VN p > S VN p When λ >, e have p > p. When < λ <, S VN S VN e obtain p < p. When λ, e obtain p The poof of Theoe i copleted. V. 4BNUERICAL EXAPLE p. S VN In thi ection, e tend to futhe elucidate the above popoed thee diffeent non-coopeative gae. Due to lack of the hitoical date, the cot of the anufactue and etaile, and aket bae ae pedicted by the expeience of expet hoed in Table I. We futhe aue 9 and 6. TABLE I THE UNCERTAIN VARIABLES Paaete Linguitic deciption Ditibution aket bae D About L ( 5,5 anufactuing cot c Beteen 7 and 9 L ( 7,9 Selling cot c Beteen and 3 L (, 3 Fo Table I, e have E D, 7+ 9 Ec [ ] 8, + 3 Ec [ ] ( ( c Φ α Φ α dα d 475 ( + ( + ( 3 5 α 7 α dα, ( ( c Φ α Φ α dα d (Advance online publication: 6 Novebe 6

7 Engineeing Lette, 4:4, EL_4_4_9 5 ( + ( + ( 3 5 α α dα. Baed on the analyi hoed in the Section IV, e peent the optial olution in the S, and VN gae in Table II. TABLE II THE OPTIAL SOLUTIONS WITH DIFFERENT λ λ p E Π E Π R S VN Baed on the eult hoed in Table II, e find: ( The optial olution and fo the anufactue deceae in the thee gae cae, a the paaete λ inceae. The holeale pice unde the cae i the highet, folloed by S and then VN cae. The optial evice level i the highet in the cae hen the etaile ha oe bagaining poe. The S cae povide the loet evice level thi i becaue unde thi cae the full cot of evice ae affoded by the anufactue. ( When the paaete λ inceae, the etail pice p fo the etaile deceae in the thee gae cae, the pofit agin deceae in the S and VN cae, hile doe not vay in the cae. When λ < 4, the pofit agin in the cae of VN i the highet, folloed by and then S cae, and the etail pice p in the cae of i the highet, folloed by VN and then S cae. When λ 4, the pofit agin in the cae of S i the loet, and the pofit agin in the cae i equal to that in the VN cae. The etail pice p in the cae of i the highet, and the etail pice p in the S cae i equal to that in the VN cae. When λ > 4, the etaile ake the laget pofit agin in the cae, and the allet in the S cae. The etail pice p unde the cae i the highet, folloed by S and then VN cae. (3 The anufactue expected pofit deceae in the S and VN cae, and doe not vay in the cae, a the paaete λ inceae. The etaile expected pofit inceae in the S cae, and deceae in the and VN cae. The anufactue ake the laget expected pofit in the S cae, and the allet in the cae. The etaile ake the allet expected pofit in the S cae. When λ < 4, the expected pofit of the etaile in the cae i highe than that in the VN cae. When λ 4, the etaile ake the ae expected pofit in the and VN cae. When λ < 4, the expected pofit of the etaile in the cae i alle than that in the VN cae. VI. 5BCONCLUSION Thi pape popoe a to-echelon upply chain anageent in an uncetain envionent, hee the anufactue and etaile puue thee diffeent kind of cenaio: anufactue-stackelbeg, Retaile-Stackelbeg and Vetical-Nah gae. The odel in ou cae contain to tategic vaiable, pice and evice level, thee uncetain vaiable, aket bae, anufactuing cot and elling cot, hich i tuly epeentative of the electonic induty. The ain contibution of the pape i that e conide the picing and evice deciion of upply chain in an uncetain envionent. One liitation of thi pape i that e only conide one anufactue and one etaile. Theefoe, one poible extenion ok i to tudy the picing and evice deciion ith ultiple copeting anufactue o etaile in an uncetain envionent. The othe liitation i that the uncetain vaiable ae only conideed a linea uncetain vaiable, the othe type of the uncetain vaiable can be conideed in the futue. REFERENCES [] G. Iye, Coodinating channel unde pice and non-pice copetition, aketing Science, vol.7, no 4, pp , 999. [] A. A. Tay and N. Agaal, Channel dynaic unde pice and evice copetition, anufactuing & Sevice Opeation anageent, vol., no 4, pp ,. [3] T. J. Xiao and D.Q. Yang, Pice and evice copetition of upply chain ith ik-avee etaile unde deand uncetainty, Intenational Jounal of Poduction Econoic, vol.4, no, pp. 87, 8. [4] T. J. Xiao and D.Q. Yang, Rik haing and infoation evelation echani of a one-anufactue and one-etaile upply chain facing an integated copetito, Euopean Jounal of Opeational Reeach, vol.96, no 3, pp , 9. [5] J.C. Lu, Y. Tao and C. Chaoeniiath, Copetition unde anufactue evice and etail pice, Econoic odeling, vol.8,no 3, pp ,. [6] C.H. Wu, Pice and evice copetition beteen ne and eanufactued poduct in a to-echelon upply chain, Intenational Jounal of Poduction Econoic, vol.4, no, pp ,. [7] X. Han, X. Chen and Y. Zhou, The equilibiu deciion in a to-echelon upply chain unde pice and evice copetition, Sutainability, vol.6, no 7, pp , 4. [8] R. L. Yan and Z. Pei, Retail evice and fi pofit in a dual-channel aket, Jounal of Retailing and Conue Sevice, vol.6, no 4, pp , 9. [9] B. Dan, G. Xu and C. Liu, Picing policie in a dual-channel upply chain ith etail evice, Intenational Jounal of Poduction Econoic, vol.39, no, pp. 3 3,. [] L. Wang and J. Zhao, Picing and evice deciion in a dual-channel upply chain ith anufactue diect channel evice and etail evice, WSEAS Tanaction on Buine and Econoic, vol., pp. 93 3, 4. [] S. Sang, Sevice and elling effot deciion in a to-echelon decentalized upply chain, Engineeing Lette, vol.4, no, pp. 5 3, 6. (Advance online publication: 6 Novebe 6

8 Engineeing Lette, 4:4, EL_4_4_9 [] L.A. Zadeh, Fuzzy et, Infoation and Contol, vol.8, no 3, pp , 965. [3] J. Wei, and J. Zhao, Picing deciion ith etail copetition in a fuzzy cloed-loop upply chain, Expet Syte ith Application, vol.38, no 9, pp. 9 6,. [4] J. Wei and J. Zhao, Revee channel deciion fo a fuzzy cloed-loop upply chain, Applied atheatical odelling, vol.37, no 3, pp. 5 53, 3. [5] J. Zhao, W. Tang and J. Wei, Picing deciion fo ubtitutable poduct ith etail copetition in a fuzzy envionent, Intenational Jounal of Poduction Econoic, vol.35, no, pp ,. [6] J. Zhao, W. Tang, R. Zhao and J. Wei, Picing deciion fo ubtitutable poduct ith a coon etaile in fuzzy envionent, Euopean Jounal of Opeational Reeach, vol.6, no, pp ,. [7] J. Zhao, W. Liu and J. Wei, Copetition unde anufactue evice and pice in fuzzy envionent, Knoledge-Baed Syte, vol.5, pp. 33,. [8] J. Zhao and L. Wang, Picing and etail evice deciion in fuzzy uncetainty envionent, Applied atheatic and Coputation, vol.5, pp , 5. [9] S. Sang, Pice copetition of anufactue in upply chain unde a fuzzy deciion envionent, Fuzzy Optiization and Deciion aking, vol.4, no 3, pp , 5. []. Hong. Stackelbeg gae in a upply chain led by etaile in a fuzzy envionent, Engineeing Lette, vol.4, no, pp. 45 5, 6. [] S. Sang, Coodinating a thee tage upply chain ith fuzzy deand Engineeing Lette, vol., no 3, pp. 9 7, 4. [] H. Yano, K. atui and. Fuuhahi, ulti-objective fuzzy ando linea pogaing poble baed on coefficient of vaiation, IAENG Intenational Jounal of Applied atheatic, vol.44, no 3, pp , 4. [3] B. Liu, Uncetainty theoy, nd edn, Spinge, Belin, 7, ch.. [4] S.B. Ding, Uncetain ando neboy poble, Jounal of Intelligent & Syte, vol.6, no, pp , 4. [5] B. Liu, Uncetainty theoy, 4nd edn, Spinge, Belin,, ch.. Shengju Sang i an aociate pofeo at Depatent of Econoic and anageent, Heze Univeity, Heze, China. He eceived hi Ph.D. degee in at the School of anageent and Econoic, Beijing Intitute of Technology, China. Hi eeach inteet include upply chain anageent, fuzzy deciion and it application. He i an autho of eveal publication in thee field uch a Fuzzy Optiization and Deciion aking, Jounal of Intelligent & Fuzzy Syte, atheatical Poble in Engineeing and othe jounal. (Advance online publication: 6 Novebe 6