Analysis of Grain Supply Chain Performance Based on Relative Impact of Channel Coordinator s Objectives on Firm Level Objectives

Transcription

1 Analy of Gran Supply Chan Performance Baed on Relatve Impact of Channel Coordnator Obectve on Frm Level Obectve Agbor-Bayee Bayee-Mb and Mchael A. Mazzocco Former Graduate Atant and Aocate Profeor Unverty of Illno at Urbana-Champagn Selected Paper prepared for preentaton at the Amercan Agrcultural Economc Aocaton Annual Meetng Provdence Rhode Iland July Copyrght 25 by Agbor-Bayee Bayee-Mb and Mchael A. Mazzocco. All rght reerved. Reader may mae verbatm cope of th document for non-commercal purpoe by any mean provded that th copyrght notce appear on uch cope.

2 Analy of Gran Supply Chan Performance Baed on Relatve Impact of Channel Coordnator Obectve on Frm Level Obectve Agbor-Bayee Bayee-Mb and Mchael A. Mazzocco Unverty of Illno at Urbana-Champagn Abtract Trend toward vertcal coordnaton preent new economc challenge n modelng and analyzng way of coordnatng value-creatng actvte n upply chan. Th tudy focue on how to model and analyze algnment of conflctng goal and to prortze goal n multobectve vertcally coordnated ytem. Specfcally th tudy analyze the optmal decon of a mult-obectve gran upply chan n whch the proft maxmzaton obectve of the producton torage and proceng level frm are conflctng wth the channel coordnator cot mnmzaton goal aocated wth qualty aurance quantty relablty and tranacton cot among frm n the upply chan. Furthermore a lnear weghtng method ued to prortze ung optmal weght the channel coordnator goal to reflect ther relatve mpact on frm level decon and the overall performance of the upply chan. Two analye are conducted ung fuzzy lnear programmng. The frt analy model the upply chan problem wth equally weghted channel coordnator goal whle the econd analy ncorporate optmal weght for the channel coordnator to reflect ther relatve mportance. The man concluon of the tudy that prortzng the channel coordnator goal n a gran the upply chan enhance the overall performance of the ytem but not by very gnfcant amount. Key Word: Mult-obectve optmzaton gran upply chan upply channel coordnaton lnear weghtng method fuzzy lnear programmng upply chan performance Introducton U.S. food and fber ytem are tranformng nto vertcally coordnated ytem mlar to upply chan of other ndutre. Trend toward vertcal coordnaton preent new economc challenge n modelng and analy of effcent way of coordnatng value-creatng actvte. Two uch challenge nvolve algnment of conflctng goal and prortzng goal n multobectve vertcally coordnated ytem. Conflct n upply chan may are from dfference n percepton about the competng prorte of the ytem. Th confounded by nterdependence between feable alternatve Bayee-Mb and Mazzocco Unverty of Illno Provdence RI July 25

3 whch could enhance the advere effect of externalte and could potentally lead to uboptmal upply chan performance. Furthermore becaue frm are maxmzer of ther utlte they may not have the ncentve to perform functon that do not drectly mpact ther outcome. Thu the role of a channel coordnator mportant to manage conflct and to perform non-frm pecfc functon n order to ynergze complementary actvte acro the upply chan. Kng 22 oberved that one ey drver of a upply chan tructure the locu and trength of channel leaderhp whch could nfluence the overall chan tructure the nature of nteracton product and nformaton flow and dtrbuton of return and cot. Th tudy focue on a mult-obectve decentralzed controlled gran upply chan problem n whch the prorty of the producton torage and proceng level frm are conflctng wth thoe of the channel coordnator. That the decon of the producton torage and proceng level frm are to maxmze proft of ther operaton whle the channel coordnator goal mnmze tranacton cot product qualty cot and upply relablty cot that are aocated wth the flow of commodte and nteracton between frm acro the ytem. Thoe channel coordnator cot have been dentfed a mportant n dentty preerved gran upply chan Maltbarger and Kalatzandonae 2. Furthermore the overall mpact of the channel coordnator goal may not equally mpact the overall performance of the ytem. Th undercore the need to examne the relatve mpact of thoe cot on the performance of the gran upply chan. The tudy adopt a fuzzy mult-obectve lnear programmng to analyze the gran upply chan problem for fve reaon: Frt the procedure capable of modelng a ytem that cont of conflctng obectve. Secondly t generate comprome oluton from multaneou optmzaton of ub-problem for frm that operate n the dfferent level of the ytem. Bayee-Mb and Mazzocco Unverty of Illno Provdence RI July 25 2

4 Accordngly t generate optmal oluton for each frm ub-problem and thu provde nformaton on how ncome dtrbuted n the ytem. Thrd the comprome oluton are baed on tradeoff between the memberhp functon of the ub-problem. Th mple that the comprome oluton are reached through cooperatve relatonhp thu the comprome oluton are far and equtable. Fourth the memberhp functon ncorporate uncertanty n the ub-problem through tolerance nterval. Th mplctly ugget that the optmal decon account for uncertante n the upply chan envronment and that the optmal tradeoff decon dtrbute r wthn the ytem. Fnally the procedure report global achevement level whch meaure the overall level of atfacton n the comprome oluton. Th ued a an addtonal crteron to compare the performance of the pan of control degn. The two pecfc obectve of th tudy are: to determne the cot and proft dtrbuton among frm and the channel coordnator n a decentralzed control gran upply chan and 2 to evaluate the relatve mpact of the channel coordnator goal on the performance of the gran upply chan. Two analye are conducted and compared to determne whether prortzng the channel coordnator goal enhance the performance of the gran upply chan. The frt analy aume that that channel coordnator goal are equally mportant and analyzed wth equal weght. The econd analy aume that the channel coordnator goal have unequal mportance. A lnear weghtng method to determne a prorty tructure baed on ther optmal weght. Performance of the two analye are compared n term of total frm level proft total upply chan proft channel coordnator cot net upply chan proft and the global achevement level. The ret of the paper organzed a follow: Secton Two cover the theoretcal framewor on fuzzy mult-obectve lnear programmng and the lnear weghtng method ued to Bayee-Mb and Mazzocco Unverty of Illno Provdence RI July 25 3

5 determne optmal weght. Secton Three cover the decrpton and mathematcal formulaton of the mult-obectve gran upply chan problem. Secton Four cover data ource and model parameterzaton. Secton Fve dcue the reult and the fnal ecton conclude the tudy. 2. Theoretcal Framewor Conder a three level gran upply chan problem contng of producton level frm where 2... I ; torage level frm where 2... J ; proceng level frm where 2... K and channel coordnator obectve where 2... S. The fuzzy multobectve programmng problem n whch uncertanty defned n the obectve functon defned a follow: Producton Level Obectve ~ Maxmze x ] ~ ~ ~ T [ x x 2... x I Storage Level Obectve ~ Maxmze x ~ ~ ~ [ x x... x ] T 2 J Proceng Level Obectve ~ Maxmze x ~ ~ ~ T [ x x... x ] 2 K Chnanel Coordnator' Obectve ~ Mnmze x Subect to x X ~ ~ ~ [ x x... x ] T 2 { x Ax Ax Ax Ax B x } S Where an n dmenonal vector of decon varable~ repreent fuzzy obectve x functon an operator that can tae ether gn n the contrant x X repreent Bayee-Mb and Mazzocco Unverty of Illno Provdence RI July 25 4

6 the complete et of crp upply chan contrant are m dmenonal contant vector for avalable reource and Ax are mxn matrce for technologcal coeffcent. Uncertante n the obectve functon n are ncorporated n the analy by contructng lnear non-decreang obectve memberhp functon for the frm level maxmzaton obectve and non-ncreang memberhp functon for mnmzaton obectve of the channel coordnator goal. Whle the hape of the memberhp functonal form can be ether lnear or non-lnear th tudy le mot fuzzy lnear programmng applcaton ue lnear memberhp functonal form becaue of t computatonal mplcty. Ideally the tolerance nterval of the obectve memberhp functon hould be contructed nteractvely wth experence decon-maer or expert of the ytem whch wa not accomplhed n th tudy. Followng mmermann 978 the tolerance nterval of the frm level and channel coordnator goal are determned by etmatng the upper bound or deal oluton B and the lower bound or ant-deal oluton for the maxmzaton problem and ve vera for the mnmzaton problem. The tolerance nterval of the frm level maxmzaton obectve are obtaned by olvng the followng: Ax mn x. t.. t. 2a Ax max x o B o B In the cae of the channel coordnator mnmzaton goal the tolerance nterval are obtaned by olvng the followng:. t. Ax mn x o B. t. Ax max o B x 2b Bayee-Mb and Mazzocco Unverty of Illno Provdence RI July 25 5

7 Ung the tolerance nterval the lnear obectve memberhp functon expreng the degree of ndvdual optmalte for the maxmzaton and mnmzaton obectve are mathematcally expreed a follow: K and J I x f x f x x f ; 2... Obectve Maxmzaton < > µ 3a S x f x f x x f 2... Obectve Mnmzaton < > µ 3b mmermann 978 frt llutrated that the fuzzy mult-obectve lnear programmng problem n can be converted nto a tandard lnear programmng problem by frt ntroducng an auxlary varable and then applyng the Bellman and adeh 97 mn-operator. The reultng tandard lnear programmng problem pecfed a follow: [ ] µ µ µ µ x x x x X x to Subect Max x x x x 4 Bayee-Mb and Mazzocco Unverty of Illno Provdence RI July 25 6

8 Whle the mn operator wdely ued n fuzzy lnear programmng applcaton t lmted n that t may not allow tradeoff between hgh and low degree of memberhp mmermann 99. The fuzzy and operator Werner 987 a compenatory operator that addree the hortcomng of the mn operator. Lee and Shh 2 noted that the fuzzy and operator generate reaonably content reult n applcaton. Ung the fuzzy and operator 4 redefned a [ ] γ µ µ µ µ γ µ and x x x x X x to Subect w S S S K J I Max x x x x I J S K and 4 Where r µ are the memberhp functon for r defned n the nterval r µ γ the degree of compenaton defned wthn the nterval γ are the optmal weght for the channel coordnator obectve whch mut atfy the condton w w. In the frt analy n whch the channel coordnator obectve are of equal mportance the tranacton cot product qualty cot and upply relablty cot are equally weghted n the obectve Bayee-Mb and Mazzocco Unverty of Illno Provdence RI July 25 7

9 functon. That the weghted porton of the obectve functon nvolvng the channel coordnator goal defned a 3* w 3 In the econd analy the optmal weght of the channel coordnator goal are computed ung Saaty 982 egenvector method. The procedure refned to deal wth the pecfc problem addreed n th tudy. Let the vector of the channel coordnator deal 2 3. oluton be defned a S 2... T and ther correpondng optmal weght be repreented by w w 2 w... w S T. The par we comparon matrx defned a : 2 S z z2 : zs z z z S : 2 22 : 2 2 S : : : : : : : : zs zs zss S S S 4 2 : : B S A Where matrx A a recprocal matrx that ha the property 5 z / z and z z / z. Matrx B compoed of potve element reultng from the par we comparon operaton. Next we et the determnant of α I uch that matrx B now defned a follow det z α z2 : zs 2 22 : 2 z z α z S α I 6 : : : : zs zs : zss α Where α the larget Egen value of C S. The correpondng egenvector obtaned by multplyng matrx C by the vector of weght to obtan the followng equaton Bayee-Mb and Mazzocco Unverty of Illno Provdence RI July 25 8

10 w z α z2 : zs w 2 22 : z z α z2s 2 * w : : : : : zs zs : zss α ws C 7 Notce that the element of matrx C are etmated number and the vector of weght are varable. Thu equaton 7 a ytem of lnear equaton whch can be olved multaneouly to obtan the optmal weght. The multaneou equaton are explctly defned a follow z z 2 α w z α w : : : : z S w w w z 22 S 2 w w 2 2 z 2 w zs ws... z w z SS 2S S α w w S S 8 The lat contrant n 8 ncorporated to atfy the requrement that the um of the weght n the lnear weghted obectve functon hould equal to one. The optmal weght obtaned n 8 are then ncorporated n 4 uch that t oluton reflect the relatve mportance of the channel coordnator obectve. 3. Decrpton and Mathematcal Formulaton of Gran Supply Chan Problem Coordnaton of the gran upply chan wthn a maretng year tme horzon largely acheved through maret prce. Prce r are managed through contract whch pecfy term of expected future prce wth the prmary obectve to tranfer prce r from one frm to another or between the tage of the upply chan. Conderng the mportance of the temporal dmenon n gran upply chan decon-mang the gran upply chan problem modeled a a mult-perod problem uch that the optmal decon of the ytem are baed on temporal reacton to prce. Three four-month tme perod wthn the plannng horzon are ued to defne the average prce of the ytem. Bayee-Mb and Mazzocco Unverty of Illno Provdence RI July 25 9

11 A repreentatve gran upply chan analyzed that cont of a channel coordnator and fourteen frm wth ten frm that produce corn and oybean at the producton level three torage level frm that carry corn and oybean and a proceor that operate corn and oybean proceng plant. Th repreentaton of the number of frm n the gran upply chan reflect the maret tructure of the gran ndutry n whch the amount of concentraton ncreae from the producton level to the proceng level. That there are more frm at the producton level relatve to the torage level and more frm at the torage level relatve to the proceng level. The component of the fuzzy lnear programmng problem are operatonalzed wth ndce decon varable and parameter and the algebrac repreentaton of the programmng problem are formulated n the proceedng ub-ecton. Indce t : Tme ndex t 23 for three tme horzon : Producton frm ndex 2... for ten producton level frm : Storage frm ndex 23 for three torage level frm : Proceng faclty type ndex 2 for corn and oybean proceng plant n : Commodty type ndex n 2 for corn and oybean m : Proceed component part ndex m where 234 are for ethanol corn gluten meal corn gluten feed and corn ol from proceed from corn whle 567 are for oybean meal oybean ol and oybean hull from proceed oybean r : Input cah cot ndex r 234 for eed ol fertlty chemcal and hred labor Decon Varable GX n : Amount of commodty type n produced by producton frm PInt : Amount of nventory of commodty type n for producton frm n tme t X : Amount of commodty type n old by producton frm to torage frm n tme t nt SI : Amount of nventory of commodty type n for torage frm n tme t nt Q : Amount of commodty type n old by torage frm n tme t nt Y m : Amount of component part m produced by proceng plant BC : Amount of borrowed captal requred by producton frm Parameter Pc : Per unt producton cot of commodty type n for producton frm n I pnt : Per unt maret ellng prce for commodty type n for all producton frm n tme t α : Interet rate on borrowed captal for all producton frm Bayee-Mb and Mazzocco Unverty of Illno Provdence RI July 25

12 Sc nt : Per unt torage cot of commodty type n for producton frm n tme t A n : An acre of land for commodty type n for producton frm Lrn : Technologcal coeffcent of nput type r for commodty type n for frm b : Total avalable land for producton frm φ n : Yeld per acre for commodty type n for producton frm N : Maxmum amount of commodty type n that can be old by producton frm n J nt p : Per unt maret prce of commodty type for torage frm n tme n t Hc : Per unt torage cot of commodty type n for torage frm n tme t nt Pcap : Fxed torage capacty for producton frm Scap : Fxed torage capacty for torage frm τ : Throughput multpler for torage frm pm : Per unt maret prce of component part m Vcn : Per unt varable cot for proceng commodty type n for proceng plant βmn : Per unt yeld of component part m from commodty type n M m : Maxmum amount of component part m that can be old by proceng plant Cap : Proceng capacty of plant type : Per unt tranacton cot for commodty type n between torage frm and producton Tc nt frm n tme t Tc : Per unt tranacton cot for commodty type n between plant and torage frm n nt tme t : Per unt product qualty for commodty type n between torage frm and producton frm Gc nt n tme t Gc : Per unt product qualty cot for commodty type n between plant and torage frm n nt tme t Rc : Per unt upply relablty cot for commodty type n between torage frm and nt producton frm n tme t Rc : Per unt upply relablty cot for commodty type n between plant and torage frm n nt tme t a Producton Level Problem The producton level frm maxmze proft from producng corn and oybean whch can be old n the frt perod or carred n nventory over the plannng horzon. Borrowed captal ncorporated n the modelng for approprate pecfcaton of the problem but the level of borrowed captal are not reported n the reult. The et of producton level proft maxmzaton problem defned a follow: Bayee-Mb and Mazzocco Unverty of Illno Provdence RI July 25

13 N T I I Max { [ nt Pnt X nt Scnt PInt ] Pcn GX n GX n X nt PI nt BC 9 n t ω [ α n BCn ] 2... Subect to N n A n GX n b N [ Lnr GX n BCn ] n and r - φ GX X PI n and t 2 n n n n X n 2 PIn P In2 n and t 2 3 X n 3 PIn2 P In3 n and t 23 4 T t X nt Nn n and 5 N n PI nt Pcap and t 6 GX X PI BC n and t 7 n nt nt Equaton 9 defne the obectve functon for the producton level frm. It defned a the revenue from ale net the um of producton borrowed captal and nventory holdng cot for each producton level frm. Equaton the land contrant whch retrct the amount produced from exceedng amount of avalable land. Equaton the operatng captal contrant. It aumed that each producer ha zero ntal operatng captal and can borrow a much captal a needed at a % nteret rate. Equaton 2 to 4 are the nventory accumulaton contrant per producton frm over the plannng horzon. Equaton 5 the ale contrant Bayee-Mb and Mazzocco Unverty of Illno Provdence RI July 25 2

14 whch retrct the amount old from exceedng the amount produced by each per producton frm. Equaton 6 the nventory capacty contrant per producton frm and equaton 7 the producton level non-negatvty contrant. b Storage Level Problem Each of the torage level frm maxmze proft from buyng corn and oybean from producer whch can be held n nventory and old to proceor over the plannng horzon. The et of torage level proft maxmzaton problem pecfed a follow: I J I [ pnt Qnt Hcnt SInt ] Pnt X nt T N J Maxmze X Q SI t n nt nt nt Subect to I Qn X n SIn n and t 9 I Qn 2 X n2 SIn SIn2 n and t 2 2 I Qn 3 X n3 SIn2 SIn3 n and t 23 2 T t Q nt T τ Scap n and 22 X nt Nn n and 23 T I t X nt τfcap n and 24 N SInt Fcap and t 25 n Bayee-Mb and Mazzocco Unverty of Illno Provdence RI July 25 3

15 Q X SI n and t 26 nt nt nt Equaton 8 defne the obectve functon for the torage level frm. It defned a revenue from ale net the um of the cot of buyng corn and oybean and for holdng nventory over the plannng horzon. Equaton 9 to 2 are the nventory accumulaton contrant per perod. Equaton 22 avalablty contrant that retrct total amount purchaed from each producton ource from exceedng amount avalable for ale n each perod. Equaton 23 the requrement contrant that retrct the total amount purchaed over the plannng horzon from exceedng total annual throughput for each torage frm. Equaton 24 the total upply contrant by each producer over the plannng horzon. Equaton 25 the torage capacty contrant and equaton 26 the torage level non-negatvty contrant. c Proceng Level Problem The proceng level frm maxmze t proft by buyng corn and oybean over the plannng horzon from torage level frm and proceng them nto component product whch are old. The proft maxmzaton problem of the ont corn-oybean proceng plant defned a follow: Maxmze 4243 K M K N PR J p m Ym Qnt VCn P nt J Ym Qnt m n t n t T K N J T J Q nt 27 Subect to Y Y m m T J β Q m n and 28 mn t nt M m and 29 m Bayee-Mb and Mazzocco Unverty of Illno Provdence RI July 25 4

16 Y T T Qnt τscap n and 3 t J Qnt Cap n and 3 t m Q n m t 32 nt Equaton 27 the obectve functon for the proceng level problem. It defned a the revenue from ale of proceed product net the um of the cot of purchang corn and oybean and varable proceng cot. Equaton 28 the product balance contrant equaton 29 ale contrant per component part equaton 3 the upply contrant per torage level frm equaton 3 the demand contrant per proceng plant and equaton 32 the proceng level non-negatvty contrant. d Channel Coordnator Problem The channel coordnator obectve to mnmze cot related to product qualty aurance upply relablty and tranacton acro the upply chan. The channel coordnator problem defned a follow: N I T N J T Tcnt * X nt T Mnmze 4243 Tcnt * Qnt X nt Qnt n t n J t 33 N I T N J T Gcnt * X nt G Mnmze 4243 Gcnt * Qnt 34 X nt Qnt n t n J t N I T N J T Rcnt * X nt R Mnmze 4243 Rcnt * Qnt 35 X nt Qnt n t n J t Bayee-Mb and Mazzocco Unverty of Illno Provdence RI July 25 5

17 Subect to PRODUCTION LEVEL CONSTRAINTS STORAGE LEVEL CONSTRAINTS PROCESSING LEVEL CONSTRAINTS X Q n t 37 nt nt Equaton and 35 are the tranacton product qualty and upply relablty cot mnmzaton obectve functon whch are defned a the um of tranacton cot product qualty cot and upply relablty cot between producer and torage level frm and between the torage and proceng level frm. The channel coordnator obectve are contraned by the producton torage and proceng level contrant defned n equaton 36. Fnally the nonnegatvty contrant are defned n equaton Data Source and Model Parameterzaton The fuzzy lnear programmng applcaton n th tudy doe not requre pnpont accuracy n model parameterzaton becaue of the lmtaton of detaled and comprehenve data. Ung repreentatve data from the Illno gran ndutry allow u to ncorporate extng data. The ource of the data that ued to parameterze the producton torage and proceng level problem are dcued n the proceedng paragraph. The producton level data baed on 22 farm bune record for Illno farm nvolved n ont corn-oybean producton Farm Bune Farm Management 22. A ample of ten frm elected from all regon and from all frm ze to repreent the cot tructure of ont corn-oybean operaton n the tate of Illno one fore each decle of farm ze. The onfarm torage cot are aduted to reflect the opportunty cot of carryng nventory over the plannng horzon becaue carryng nventory and delayng loan repayment an accrung cot. Bayee-Mb and Mazzocco Unverty of Illno Provdence RI July 25 6

18 The ale prce are baed on average corn and oybean prce receved by Illno farmer Illno Agrcultural Stattc 22. Storage level data baed on the operatng cot of Topflght Aumpton and Grand Prare elevator cooperatve n Illno. The compane carry corn and oybean and operate multple faclte n dfferent locaton. The multple torage faclte of each cooperatve adopt the ame polce n term of torage rate delvery product qualty and o forth a tpulated by ther head offce. Hence a ample of three faclte repreentatve of a large number of operaton n the tate. It aumed that dfference n ther torage rate per buhel are reflecton of ther cot tructure. The torage rate per buhel were alo aduted for the opportunty cot of carryng nventory over the plannng horzon. Followng conultaton wth ndutry expert the annual throughput multpler wa fxed at.5 tme of each torage frm fxed torage capacty. The proceng level data are baed on etmate that reflect U.S. average becaue the cot tructure for corn and oybean plant are captal ntenve and competton natonal rather than local unle competton n the producton and torage level. The per unt varable cot for the oybean proceng plant are baed on 995 U.S. etmate n the Practcal Handboo of Soybean Proceng and Utlzaton Fala 995 p The per buhel oybean component oybean meal oybean ol and oybean hull yeld and per unt ale prce are baed on the average annual value n Ol Crop Stuaton and Outloo Yearboo ERS/USDA 22. Etmate on corn proceng baed on a wet corn mllng proce whch the domnant ethanol producton proce n Illno. The cot and prce of the proceed component ethanol corn gluten feed corn gluten meal and corn ol are baed on etmate from the Iowa Ethanol Plant Feablty Study Bran and Bran Inc. 2. The component yeld Bayee-Mb and Mazzocco Unverty of Illno Provdence RI July 25 7

19 from the wet corn-mllng proce collected from Soya and Oleed Blueboo Soya and Oleed Blueboo 22. Data for the channel coordnator problem baed on etmate of drect and hdden cot n dentty preerved upply chan for Mour and Illno gran elevator Maltbarger and Kalatzandonae 2. A number of aumpton are made n order to approprately apply the data to the preent tudy. Frt the cot are baed on nteracton between torage frm and producer. We aume mlar per unt cot between torage frm and the proceor. Secondly the cot are baed on an dentty preerved corn upply chan. We aume mlar per unt cot for commodty corn and oybean. Fnally the ze of gran elevator modeled are dfferent from the one condered n th tudy. We ue range to capture the ze analyzed n th tudy. 5. Dcuon of Reult The model contructed n ecton Three are analyzed for a mall gran upply chan that ha a total commodty flow capacty of one mllon buhel of corn and three hundred and eventy-fve thouand buhel of oybean. The channel ze n term of number of frm and flow capacty arbtrary and can be extended to gran upply chan of any ze. The memberhp functon are aggregated ung the fuzzy and operator. The operator lmted n that t dffcult to dentfy an optmal compenaton rate becaue the compenaton rate monotoncally ncreae wth degree of compenaton Canz 996. That a the compenaton rate ncreae from zero to one the amount of compenaton ncreae. In th tudy we aume an average compenaton rate of.5 whch the md pont of the range γ explaned n Equaton 4. Bayee-Mb and Mazzocco Unverty of Illno Provdence RI July 25 8

20 The procedure to calculate the optmal weght wa decrbed n equaton 5 to 8. Becaue the analye adopt the fuzzy lnear programmng approach n whch uncertanty ncorporated n the obectve functon the coeffcent of varaton CV ued to ncorporate uncertanty n the weght of the channel coordnator obectve. Th becaue CV a good meaure of the relatve varablty wthn a ytem and t expreed mathematcally σ acv µ where σ and µ are the tandard devaton and mean per unt of the tranacton product qualty and upply relablty cot. Snce the etmated CV are on a per unt buhel ba whle the deal oluton are total dollar etmate we multply the per unt CV by the total flow capacte to defne pread around the deal oluton. The range of the pread dfference between upper and lower bound are then ued to mplement the Egenvector method decrbed n equaton 5-8. The optmal weght from the ytem of equaton n 8 are etmated ung a mathematc olver Mathematca. The calculated optmal weght are.95 for tranacton cot.224 for product qualty cot and.58 for upply relablty cot. The detaled reult of the two analye are reported n Table 2 and 3 n the Appendx. A comparon of the two analye n term of global achevement level frm level proft total upply chan proft channel coordnator cot and net upply chan proft ummarzed n Table. The dcuon n the proceedng paragraph are baed on the ummarzed reult. Bayee-Mb and Mazzocco Unverty of Illno Provdence RI July 25 9

21 Table. Comparon of Supply Chan Performance Ung Equal and Optmal Weght for the Coordnator Goal Equal Weght Optmal Weght Global Satfacton Level.67.7 Supply Chan Actvte Producton Storage Proceng Total Proft Channel Degner Cot a Qualty cot b Supply relablty cot c Tranacton cot Total Cot Net Supply Chan Proft The overall atfacton n the comprome oluton ncreaed from.67 n the analy n the analy wth equal weght to.7 n the analy wth optmal weght. Regardng the channel coordnator cot the total cot ncreaed lghtly from $ n the analy wth equal weght to $ n the analy wth optmal weght repreentng a avng of only $ to the channel coordnator. The upply relablty cot ncreaed by $8495. whle tranacton and product qualty cot dropped by $55.5 and $66.4 when comparng the oluton wth equal weght to the analy wth optmal weght. Whle the overall cot avng to the channel coordnator mnmal prortzng t goal enhanced the total producton level and total torage level proft by $ and $23.. The proceng level proft on the other hand decreaed by $35.. The total upply chan proft alo ncreaed by $ and a net upply chan proft of $ Th repreent an average gan to frm n the upply chan of about $ Concluon Th tudy analyze the optmal decon of a decentralzed controlled mult-obectve gran upply chan problem n whch the frm level proft maxmzaton obectve are conflctng wth the channel coordnator cot mnmzaton obectve. Conderng that the channel Bayee-Mb and Mazzocco Unverty of Illno Provdence RI July 25 2

22 coordnator obectve may not equal mpact the performance of the gran upply chan a lnear weghtng method ued to determne optmal weght that reflect the relatve mportance of the channel coordnator goal. Two analye were conducted to determne whether prortzng the channel coordnator goal enhance the overall performance of the gran upply chan. The frt analy model the upply chan problem wth equally weghted channel coordnator goal whle the econd analy ued the etmated optmal weght. The man fndng of the tudy that prortzng the channel coordnator obectve enhance the overall all upply chan performance of the gran upply chan n term of global atfacton of ther comprome oluton total upply chan proft channel coordnator cot net upply chan proft producton and torage level proft. However the proceor dd not beneft but not be a gnfcant amount. Two mportant queton that have mplcaton on the fndng are the followng: Frt Why hould the proceor who the domnant player of the ytem be nclned to hre a channel coordnator to manage the upply chan cot f prortzng the channel coordnator goal enhanced the producton and torage level proft and other global performance meaure but at a cot to the proceor? A upply chan compettvene not meaured by how well the domnant frm outperform the other frm of the upply chan. Rather t meaured by how well the upply chan a a whole perform relatve to a compettor upply chan. Long-run commtment of the producton and torage level frm to a proceor upply chan contngent upon the atfacton they derved on the overall upply chan outcome. Secondly doe the net gan $ to the upply chan proft utfy hrng a channel coordnator to mange the upply chan? Accordng to Illno Labor tattc 22 the average annual alary of a logtc manager about $7289. whch gnfcantly hgher than the Bayee-Mb and Mazzocco Unverty of Illno Provdence RI July 25 2

23 net gan n performng the channel coordnator functon. However the ze of the upply chan condered n th tudy relatvely mall compared to the flow capacte of maor gran upply chan n the State of Illno. For example frm uch a ADM Cargll Bunge etc. whch operate maor upply chan n the tate of Illno have annual flow capacte of tenth of mllon of buhel. Scalng the preent tudy to the ze of practcal operaton may reult n gnfcant gan to the upply chan that may utfy hrng a logtc manager. Reference Bellman E.R. and adeh A. L 97 Decon-Mang n a Fuzzy Envronment. Management Scence Bryan and Bran Inc. 22 Iowa Ethanol Pre-Feablty Study. Prepared for Iowa Ethanol Sub-commttee. Canz T. 996 Fuzzy Lnear Programmng n DDS for Energy Sytem Plannng. Internatonal Inttute for Appled Sytem Analy IISA Worng paper FBFM 22 Sze-Type Standard 2. Annual Report Unverty of Illno at Urbana-Champagn Fala J. R. 995 Cot Etmate for Soybean Proceng and Soybean Ol Refnng. n D.R. Ercon ed. Practcal Handboo of Soybean Proceng and Utlzaton Illno Department of Agrculture 22 Htorcal maret prce. Illno Agrcultural Stattcal Servce Illno Department of Labor 22 Wage Data 4 th Quarter 23. Department of Employment Securty Economc Informaton and Analy Dvon. Kng P. R. 22 Supply Chan Degn for Hgh Qualty Product: Economc Concept and Example from the Unted State. 3 th Internatonal IFMA Congre of Farm Management July 7-2 th Amhem Netherland. La Y-J. and Hwang C-L 994 Fuzzy Multple Obectve Decon Mang: Method and Applcaton Sprnger-Varleg Berln Hedelberg. Maltbarger R. and Kalatzandonae N 2 Drect and Hdden Cot n Identty Preerved Supply Chan. AgBoForum 34: Saaty T. L. 978 Explorng the Interface between Herarche Multple Obectve and Fuzzy Set. Fuzzy Set and Sytem : Shh H-S La Y-J. and Lee S. E. 996 Fuzzy Approach for Multlevel Programmng Problem. Computer and Operaton Reearch 23: Stattcal Converon 22 Soya and Oleed Blueboo USDA 22 Ol Crop Stuaton and Outloo Yearboo Agrcultural Stattc ERS/USDA. Bayee-Mb and Mazzocco Unverty of Illno Provdence RI July 25 22

24 Warner B. 987 An Interactve Fuzzy Programmng Sytem. Fuzzy Set and Sytem 23: mmermann H-J. 978 Fuzzy Programmng and Lnear Programmng wth Several Obectve Functon. Fuzzy Set and Sytem : mmermann H.-J. 99 Fuzzy Set Theory and t Applcaton Kluwer Nhoff Publhng Boton MA. Bayee-Mb and Mazzocco Unverty of Illno Provdence RI July 25 23

25 APPENDIX Table 2. Comprome Soluton for Gran Supply Chan Problem Analyzed Ung Equal Weght for the Channel Coordnator Goal SUPPLY CHAIN FIRMS AND ACTIVITIES PRODUCTION LEVEL FIRMS FIRM FIRM2 FIRM3 FIRM4 FIRM5 FIRM6 FIRM7 FIRM8 FIRM9 FIRM STORAGE LEVEL FIRMS FIRM FIRM2 FIRM3 PROCESSING LEVEL FIRM PROCESSED PRODUCTS a Ethanol b Corn gluten meal c Corn gluten feed d Corn Ol e Soybean meal f Soybean ol g Soybean Hull PROPORTION OF LAND Acre GLBAL SATISFACTION LEVEL.67 DECISION VARIABLES COMMODITY FLOW & INVENTORY PER PERIOD buhel PERIOD PERIOD2 PERIOD PROCESSED PRODUCTS Ltter a and Pound for b to g PROFIT/COST Dollar TOTAL SUPPLY CHAIN PROFIT Tranacton Cot Product Qualty Cot Supply Relablty Cot TOTAL SUPPLY CHAIN COST * Inventory value are n bracet Bayee-Mb and Mazzocco Unverty of Illno Provdence RI July 25 24

26 Table 3. Comprome Soluton for the Gran Supply Chan Problem Analyzed Ung Optmal Weght for the Channel Coordnator Coal SUPPLY CHAIN FIRMS AND ACTIVITIES PRODUCTION LEVEL FIRMS FIRM FIRM2 FIRM3 FIRM4 FIRM5 FIRM6 FIRM7 FIRM8 FIRM9 FIRM STORAGE LEVEL FIRMS FIRM FIRM2 FIRM3 PROCESSING LEVEL FIRM a Ethanol b Corn gluten meal c Corn gluten feed d Corn Ol e Soybean meal f Soybean ol g Soybean Hull PROPORTION OF LAND Acre GLBAL SATISFACTION LEVEL.7 DECISION VARIABLES COMMODITY FLOW & INVENTORY PER PERIOD buhel PERIOD PERIOD2 PERIOD PROCESSED PRODUCTS Ltter a and Pound for b to g PROFIT/COST Dollar TOTAL SUPPLY CHAIN PROFIT Tranacton cot Qualty cot 39.9 Supply relablty Cot TOTAL SUPPLY CHAIN COST * Inventory value are n bracet Bayee-Mb and Mazzocco Unverty of Illno Provdence RI July 25 25

27 SHORT SUMMARY A fuzzy mult-obectve programmng model ued to analyze the optmal decon n a mult-obectve gran upply chan n whch the frm-level frm goal are conflctng wth the channel coordnator goal. The relatve mpact of the channel coordnator goal on performance of the upply chan determned through a lnear weghtng method. The tudy fnd that prortzng the channel coordnator goal enhance the overall performance of the ytem. Bayee-Mb and Mazzocco Unverty of Illno Provdence RI July 25 26