System Dynamics and Innovation in Food Networks 2009

Transcription

1 ytem Dynamc an Innovaton n Foo Network 2009 Proceeng of the 3 r Internatonal Eropean Form on ytem Dynamc an Innovaton n Foo Network organe by the Internatonal Center for Foo Chan an Network Reearch nverty of Bonn Germany Febrary Innbrck-Igl Atra offcally enore by EAAE(Eropean Aocaton of Agrcltral Economt) IAMA (Internatonal Foo an Agrbne Management Aocaton) AIEA2 (Aoc. Intern. Economa Almentare e Agro-Intrale) INFITA (Intern. Network for IT n Agrc. Foo an the Envronment) ete by M. Frt. Rckert G. chefer

2 Robert D. Weaver 29 pply Chan an Network Performance: Metrc for Proftablty Proctvty an Effcency Robert D. Weaver 20 E Armby Blng Pennylvana tate nverty nverty Park PA 6802 r2w@p.e Abtract The archtectre of the frm nvolve etermnaton of a bonary that encompae the fncton manage by the frm. The pat ecae ha een btantal reorganaton of frm where vertcal or horontal ntegraton ha been nbnle nto weaker form of collaboraton nclng vale chan an network. Th obervaton ha force a re-conceptalaton of the bonare of the frm to ncorporate ch collaboraton. Thee collaboraton are vrtal an hghly ynamc. They emerge an pert when two conton are met. Frt they mt enable generaton of greater vale than mght be attane throgh nepenent operaton an anonymo tranacton throgh market. econ the reltng growth mt be hare wth member n a way that retan ther partcpaton. Each of thee conton can be verfe only f performance of the collaboraton can be etablhe. Th paper recogne the nee for ch metrc of performance. Whle conceptal approache have been te n the management lteratre th paper coner from theoretc perpectve thee e an erve meare of the performance of the overall collaboraton a well a of the partcpatng enterpre. The paper preent a framework that can be apple to both vertcal an horontal collaboraton a fon n pply chan an network. The paper offer ggeton on emprcal metho for etmaton of meare erve. Keywor: Network Collaboraton metrc proctvty effcency. Introcton Three tren are wely cte a havng fnamentally change the bne envronment rng the 990. Thee change were o fnamental that they nce btantal opportnty for change n the organaton of prvate enterpre. The tren were: ) ramatc technologcal change affectng nformaton acqton analy an emnaton for control of complex ytem 2) ntttonal change that le to btantal recton n tranacton cot enablng new metho of coornaton an 3) technologcal change n ntral procee that enable flexblty of proct compoton an enhance reponvene to change n the external envronment. Weaver (2008) preent a revew of thee force of change an ther mplcaton for nnovaton n the foo ytem. Together thee tren facltate a btantal change n the organaton of enterpre. They enhance the feablty of volntary cro-enterpre coornaton allowng acce to the net beneft of vertcal ntegraton or horontal coornaton wthot ont aet ownerhp. At the ame tme by racally hftng the htorcal economc of vertcal an horontal ntegraton thee tren nce a btantal wave of nbnlng of perpheral fncton to pecalt enterpre. Fnally they enable enterpre to hft from ph pply to conmer-orente pll tratege. Competton forge thee poblte nto mperatve. By enablng rap repone to conmer eman for hghly fferentate goo thee tren pporte a btantal agmentaton of welfare.

3 292 pply Chan an Network Performance: Metrc for Proftablty Proctvty an Effcency The foo ytem ha not been exempt from thee force or ther mperatve for change. Of nteret n th paper the mearement of performance of the new vrtal organaton of enterpre that contne to emerge n th new envronment. In partclar thee tren have nce change n the nternal organaton of frm ee e.g. Brynolfon an Htt (2000) a well a btantal re-pecfcaton of the bonare enterpre. Wthn the parlance of the economc of effcency an proctvty analy the tren fnamentally change what we thnk of a a econ management nt (DM). Economt have tratonally foce on technologcal change that ha mplcaton for cot recton for operaton manage by an enterpre. Th perpectve content wth the compettve atonomo frm that ph-orente. In th cae cot-recng techncal change the frm only opton for managng proft margn over tme. In notable contrat competton mpoe an mperatve that enterpre aapt n three way to thee force of change. Frt enterpre have face an mperatve for trategc re-orentaton towar the conmer. econ enterpre have been challenge to pre trategc organatonal change to pecale an often rece the cale of ther fxe aet poton ee Powell (990). Thr thee newly pecale enterpre have by competton been rven to engage n collaboraton wth both peer enterpre an vertcally algne partner. The relt ha been the emergence of a new fabrc of hghly nterepenent relatonal enterpre that efne a new paragm for prvate enterpre relatve to the ol paragm of nepenent lo enterpre coornate throgh anonymo market tranacton. From the perpectve of tranacton co-ornaton thee trategc organatonal change have efne new mean of co-ornaton an metho of ntegratng actvte econ an economc performance acro enterpre. Together thee change have efne new organatonal approache to co-ornaton of economc tranacton throgh ntegraton of enterpre fncton n new way to reefne what known n the economc lteratre a the bonare of the frm ee Coae (937). Th paper coner from theoretc perpectve thee e an erve meare of the performance of the overall collaboraton a well a of the partcpatng DM. The paper coner both vertcal an horontal collaboraton a fon n pply chan an network. The paper offer ggeton on emprcal metho for etmaton of meare erve. To harpen foc DEA metho are gven greatet attenton. In o ong the paper clarfe the role n effcency etmaton that DM engage n collaboraton mt play. Whle tratonal metho wol chooe a grop of DM facng a common technology we examne the role that partnerng DM engage n collaboraton can play an how tratonal approache hol be mofe. 2. Obervaton an nterpretaton ner the ol commoty paragm nflexblty of technology meant that nvetment n pecfc eqpment an technologe wa reqre for procton mplyng that btantal rk wa aocate wth proct fferentaton. At the ame tme hgh nformaton an commncaton cot mple hgh earch cot that force frm to tanare proct to rece ch cot a a conton of compettvene. Wth tanare proct ale col be coornate throgh market where byer an eller are anonymo. The welfare cot of th pply-orente ph trategy that conmer are force to conme generc tanare proct rather than pecfc fferentate proct that mght prove ncreae tlty. In th paragm the procng enterpre ha lttle rect relatonhp wth the conmer. In contrat a new paragm ha been efne over the pat ecae by nformaton an commncaton technologcal change an a hft to flexble procton technologe tratonal phorente enterpre have been enable to collect analye an aapt to market ata raply. A th became feable the potental for trategc re-orentaton of the enterpre from pply-orentaton to a conmer-orentaton (from a ph orentaton to a pll orentaton) became

4 Robert D. Weaver 293 an mperatve of competton. Not only col revene be ramatcally ncreae a conmer were offere ther mot hghly vale proct attrbte bt cot of pply col alo be ramatcally rece throgh e of nformaton to enre that the rght proct wa avalable at the rght place at the rght tme an at the rght prce. Inventore col be ramatcally rece an became een a evence of error n forecatng a cot borne a a prmtve metho of copng wth ncertan market. Wth repect to trategc organatonal change th new economc playng fel ha efne gnfcant opportnte to enhance proctvty effcency proftablty an economc growth throgh trategc organatonal change of the fncton manage wthn an acro frm. In partclar th opportnty for re-organaton ha allowe frm to he bary fncton to pecale frm (ee e.g. Brch (987) Baker an Hbbar (2003)) leavng the frm telf both more pecale an n many cae maller n cale. Opportnty of thee organatonal change followe from btantal recton n tranacton cot offere by new nformaton an commncaton technologe. In partclar ner the ol paragm when tranacton cot for external acqton an management of ervce an fncton were hgh ch ervce an fncton were ntegrate nto the frm. Gven btantally rece tranacton cot aocate wth the new paragm enterpre have been enable to he (otorce) many of fncton. Th ha relte n btantal gan n proctvty an cot recton aocate wth pecalaton. Frther the heng actvte ha pawne eman for wholly new ervce organaton that throgh pecalaton can elver ervce level not poble when ch fncton were embee wthn verfe frm. Havng he fncton throgh trategc organatonal change newly pecale frm have been enable by nformaton an commncaton techncal change to procre otorce ervce throgh relatonal rather than market mechanm. Thee relatonal mechanm have taken many form from nformal to formal. They have nvolve on the one han what mght be tnghe a otorcng that coornate throgh tratonal comman-control mplemente wth contract. On other han organatonal change ha often move towar collaboraton acro enterpre nvolvng nterepenence ch a merge operaton an fncton plannng problem-olvng or trategy. Whle ch fncton mght be avalable throgh market mechanm th alternatve metho of coornaton efne here a cro-enterpre collaboraton (CEC) ha often been fon to offer ncreae pecfcty of ervce or proct qalty an rece earch cot an rk. Thee collaboraton have panne both vertcally an wthn horontal allance acro peer enterpre to effcently optme vale generate for the conmer. Throgh collaboraton management of otorce fncton ha often proven both feable an more effectve than management of mlar fncton a perpheral fncton wthn an enterpre. Acro peer enterpre new fon pecalaton ha emane new way of acceng perpheral ervce once ntegrate n the frm. Thee eman have often pawne horontal collaboraton acro peer enterpre to etablh hare ervce ch a R&D marketng or accontng. In the vertcal menon trategc re-orentaton ha been mplemente by anchorng wthn vale chan throgh vertcal collaboratve allance an relatonhp that connect the ere of frm from raw reorce to fnal goo an the conmer. Throgh thee collaboratve organatonal form the wall of the tratonal frm have been peele open leavng a new vrtal enterpre trategcally lnke to the conmer. Frm at any poton along thee vertcal chan or wthn horontal network are able to trategcally reorent towar the conmer epte ther poton. Th throgh vertcal collaboraton a metal catng enterpre olate a a lo ner the ol paragm can re-orent to be reponve to changng conmer preference for atomoble fncton. Throgh thee vertcal collaboraton frm bttte nformaton for nventore an poorly fttng or obolete proct.

5 294 pply Chan an Network Performance: Metrc for Proftablty Proctvty an Effcency Coner the procer nteret n havng proct form that atfy pecfc conmer nee. Each enterpre along the vertcal chan of proceng tranformaton an hppng that take a proct from ntal proceor to conmer ha a fferent nteret n reponng to conmer gnal concernng proct form an attrbte. The challenge to coornate thee enterpre to repon to the conmer gnal an hare the vale harvete. The recent paragm hft ha enable th coornaton. The paragm revolton of trategc re-orentaton an re-organaton of prvate enterpre contne to permeate the economy provng btantal compettve avantage to frm that partcpate n vale chan an avantagng frm an enterpre that contne to pre commoty-orente ph tratege. Whle conerable attenton ha been pa by the management lteratre to o-calle metrc of performance th lteratre ha not taken on the qeton of mearement of effcency an relate proctvty apect of the performance of the new vrtal enterpre reltng from mple otorcng to the hghly relatonal organatonal trctre I call cro-enterpre collaboraton. Of partclar nteret to ae the mplcaton of thee new type of DM for effcency an proctvty analy an to coner new meare capable of pportng a coneraton of the orce of effcency an proctvty relt they generate. More pecfcally t of nteret to etablh emprcal mean of entfyng the relatve contrbton of partclar DM engage n collaboraton a well a the overall performance of the collaboraton. Not rprngly pat lteratre offer the fonaton an tartng pont for th aement. Wthn th context conerable lteratre ha attempte to break open the black box conceptalaton of a DM mplct n early effcency an proctvty analy. Wthn the nonparametrc lteratre Fare an Whttaker (995) conere the nternal trctre of fncton wthn a DM bae on a reference et of DM. Färe an Grokopf (996a) conere the problem for a mple fxe path network where prvate goo proct allocaton along vertcal tage fxe ee Fgre. They coner a mple vertcal network of eqentally lnke noe an allow for external npt ntermeate otpt e a npt an fnal otpt. ater Färe an Grokopf ( ) allowe for allocaton between ntermeate e an fnal otpt to be enogeno. Of nteret for them wa mearement of b-dm () a well a network effcency an proctvty. In both cae they moele a aggregaton of the nptotpt proce of a partclar DM an evalate t performance agant an entcally trctre et of peer. othgren an Tambor (999) aopte the Färe an Grokopf (996a) organatonal trctre an recogne that the nterepenence mplct n a vertcal ere of mple that otpt flow mt be content wth the npt flow between tranactng. Frther they note electon of weghtng for reference DM hol be content wth the oberve flow trctre. Catell et al. (200) conere the relatve effcency of wthn a DM an efne a et of DEA-lke performance meare relatve to ) the et of homogeneo acro a et of DM 2) the et of heterogeneo pannng all operate n the et of DM ner coneraton an 3) the et of that proce otpt neceary a partclar otpt. Catell et al. (2004) how that coneraton of the nternal trctre of wthn a DM lea to fferent relatve performance etmate. ew an exton (2004) coner e of DEA to gage the relatve contrbton of to overall DM performance an ncorporate retrn-to-cale. Frther they expan the reference et for a partclar DM to ncle hypothetcal entfe from lke n other DM. Frther con of thee contrbton follow.

6 Robert D. Weaver The conceptal framework To coner the performance of the new vrtal enterpre pawne by otorcng an croenterpre collaboraton we frt artclate the alent featre of the organaton of thee enterpre. Next we pecfy an actvty analy form for the new nerlyng procton technology mple by thee organatonal form. Here t mportant to note that we peak of procton a procton of vale. Th we evate from conventonal vocablary an exten t to coner the technologe of procrement marketng tranacton an management. alent featre of vrtal ntegraton Tratonally the bonare of the frm have been et throgh coneraton of aet ownerhp a a ffcent conton for entfyng the fronter of the reach of comman-control management. Wthn the context of vrtally ntegrate enterpre t now clear that aet ownerhp not a reaonable ba for reolvng thee bonare. Intea we foc on the bonare of the vrtal enterpre a encompang the et of enterpre that have ont nteret that are manage. In the cae of otorcng the ont nteret n proct pecfcaton are reglate throgh explct rle an ncentve etablhe ether by a omnant agent or gamng among more eqally powerfl agent. In th ene otorcng only a hort-tep away from comman-control bae on aet ownerhp. Importantly however otorcng allow for alternatve cale a well a pecalaton econome. Cro-enterpre collaboraton (CEC) nvolve ntegraton of management fncton of coornaton (plannng problem-olvng) motvaton (ncentve egn an mplementaton throgh performance montorng an analy) a well a of procee (procton an marketng fncton). Integraton of procee can relt from rect ntegraton e.g. qalty control proct egn proce egn cro-ockng. Alternatvely procee can be ntegrate throgh ont epenence on hare aet ervce (phycal captal fnancal hman captal (knowlege know-how etc.). Throgh algnment of goal an obectve enterpre can foc ther ppler et whle recng proct verfcaton an earch cot. Whle enterpre merger wol relt n merger of all fncton procee an aet CEC only ntegrate electve element of enterpre fncton an oe not ntegrate aet ownerhp. Three type of CEC are often cte n the lteratre: ) aet ervce harng e.g. nformatonharng; 2) tactcal ntegraton e.g. ont mofcaton of tratonal procee ch a qalty control accontng proce plannng an forecatng; an 3) trategc ntegraton e.g. ont egn of econ-makng trctre an extent of ecentralaton operatonal rle an ncentve egn fnctonal pecalaton an compoton plannng problem-olvng performance montorng. A btantal management lteratre coner thee poblte. However of nteret here to entfy the mplcaton of thee charactertc of vrtal enterpre for performance mearement. From th perpectve two type of mplcaton are of nteret: ) mplcaton for the bonare of the DM an the reference et relevant for analy of performance an 2) mplcaton for the type of proct an ervce nvolve n the procee that create vale. Wth repect to the frt t clear that the natre an trctre of nteracton of contttng a vrtal DM (VDM) eerve attenton. Frther the VDM wll be compoe of DM efne by aet ownerhp o the natre an trctre of ther nteracton mt be conere. Wth repect to type of proct an ervce the perpectve mt be expane beyon mple prvate goo wth ngle attrbte.

7 296 pply Chan an Network Performance: Metrc for Proftablty Proctvty an Effcency Tranacton Wth repect to the natre of coner frt the qeton of tranacton. A otorcng an CEC offer ramatcally fferent moe of tranacton t logcal to coner ther ntrocton nto the moel. Tratonally we have not conere tranacton n performance evalaton one wth DEA or FA. Catell et al. (2004) gget the nttve approach of pecfyng tranacton management a accomplhe by a when tranacton are proctve. Gven that clear obectve of relatonal tranacton are the recton of tranacton cot an enhancement of vale creatng procee t of nteret to ncorporate tranacton n moel that attempt to gage performance of VDM. A frther apect of tranacton the natre of epenency acro ppler. Here VDM typcally reflect mltple orcng beng replace by more foce orcng where rk manage throgh parallel proce organaton ee Fgre rather than throgh verfcaton. From the perpectve of bonare of enterpre CEC appear to hft the bonare to encompa collaboratng DM whle otorcng appear to leave the bonare of DM n place by changng the natre of tranacton operaton. Inter-enterpre effect Wthn a vertcal chan of procee perhap embee wthn a DM nter-enterpre effect can be repreente a ntermeate goo flowng acro fncton of. The motvaton for collaboraton acro DMoften follow from the extence of nter-enterpre effect that reqre management that can not be attane throgh market mechanm an for whch t may be nerable to manage throgh aet ntegraton an comman-control mechanm. Thee nter-enterpre effect can be potve or negatve erable or nerable. Thee col alo nvolve what ew an exton call revere qantte where proctvty eclne wth ther ncreae. In many cae thee nter-enterpre effect may be controllable or mtgate by the orce or recevng. In other they may be noncretonary from the perpectve of the orce an weakly poable from the perpectve of the recevng. Jont reorce An mportant tnghng charactertc of CEC the poblty of a proctve role for ont reorce. ervce flow from thee reorce col be propretary or prvate n natre forcng compettve conmpton acro DM or encompae by a VDM. Thee prvate ervce flow col be allocatable or noncretonary. In aton to prvate flow ervce flow col be qa-pblc n natre. Jont operaton Clearly an mportant apect of CEC performance the role of ont operaton an ervce. Central among ch ervce are thoe of management nclng trategy evelopment an mplementaton problem entfcaton an olton an forecatng an plannng. Qalty control often cte a a prme example. Rather than each mplementng nepenent QC procee CEC organatonal form offer the poblty of ont operaton of QC an algnment of tanar etc. Implcaton of thee alent featre of collaboratve organaton for performance evalaton can now be broaly mmare motvatng the nee to coner the performance of: ) bet of wthn a collaboraton 2) tranacton an 3) form of collaboraton.

8 Robert D. Weaver 297 Organaton of collaboraton Whle effcency an proctvty analy tratonally follow the neoclacal foc on the frm a a blackbox t of nteret here to coner the organatonal form taken on by collaboraton. Whle otorcng ha often been cte a nvolvng only market-bae tranacton to coornate acro DM t clear that otorcng mot often nvolve manage relatonhp ge by a common nertanng of core bne vale expectaton an goal a well a pre-agree plan or rle for operaton of the relatonhp management of problem an harng of retrn. Plan an rle can be formale nto contract or mple verbal agreement that emerge ether from omnant agent pecfcaton or negotaton acro agent. In the omnant agent cae the yartck competton lteratre relevant to thee form of collaboraton. To procee t efl to tngh key trctral archtectre for collaboraton to prove a ba for examnaton of how that organatonal form mght mpact effcency an proctvty. We tngh three proce type for : tranacton (procrement marketng) tranformaton an management. However whle fferng n operatonal fncton we arge they can be ecrbe n a mlar fahon at a conceptal level. In each cae we efne thee procee a beng operate by b-dm at a network noe. Whle tranacton wll be conceptale a not tranformng the phycal properte of a proct or ervce ther tranformaton of property rght wll be note a a tranformaton of qalty attrbte of the proct. 4. The Moel To procee we exten notaton e n pat lteratre e.g. Catell et al. (2004). Defne a the et of homogeno DM. We efne a DM a a econ-makng nt that a nt that coornate econ acro not necearly holng ther aet. We efne D a the et of all contane wthn an D() D a the et of n DM. To allow for pecfcaton of varo organaton of network of we efne l.. a an nex of the horontal layer to whch a belong an a an nex of the vertcal tage to whch a belong. To allow for trctly parallel chan we e r R to ncate a replcate of a partclar layer. Th each nqely confgre layer can be agne an arbtrary layer nmber. Bae on the tage nex we efne () a the et of operatng at tage an (l) a the et of operatng on layer l. To entfy each we e a percrpt to ncate poton of the an bcrpt to ncate orgn an etnaton. We note that each nqely entfe by the oble (l). To econome on th notaton where poble we e a percrpt to ncate an arbtrary. We tngh a partclar ng the notaton or k. We note the poton a ( l ) an e only the nexe n b- an per-crptng other varable. Fnally to coner performance acro we efne Dˆ a the et of all bet of homogeneo. We note ˆ Dˆ a a cla (reference) grop of homogeneo. Wth th notaton we can efne otorcng a procrement by DM from D(). We efne an m x vector y of otpt nexe wth typcal element y. We efne an n x vector x of varable npt obtane externally from the cla ˆ of nteret nexe wth typcal element x h an e a percrpt to ncate the poton. mlarly we efne two type of ntermeate proct. We e bcrpte wth otpt nexe e.g. a an ntermeate otpt. To accont for e an pply recton we efne k a a vector of ntermeate otpt e by orgnatng from k. mlarly a tle ae to ncate ntermeate pply from to k.e. ~k. To ncate pply of fnal otpt we e m to ncate otpt allocate a pply external to the cla ˆ of nteret. Note th ffer from the conventon aopte by Färe

9 298 pply Chan an Network Performance: Metrc for Proftablty Proctvty an Effcency an Grokopff who note both orgn an etnaton. mmarng the (n+2m) x vector of npt e by (l) [ x ] the m x otpt vector y an the m x vector of ntermeate otpt pple to other ~. Wthn th notaton for prvate goo that are allocatable to external peer or forwar tage e we ame that the allocaton exhat avalable pply notng of core that nventore col be ae to th notaton wth poble nteretng complcaton. Th the followng phycal balance conton are ame to hol for each : y m + ~ ˆ () ~ (2) D () clarfe that each otpt from layer l tage can be allocate externally wth repect to the cla ˆ an acro at all forwar tage an all layer. (2) reqre that at noe e oe not excee avalable pply of ntermeate goo. ng th notaton Fgre preent a et of poble network confgraton that wll erve a a ba for coneraton. We tngh the followng type: ) Vertcally algne ere 2) Parallel ere 3) Cro-layer orce 4) Peer orce 5) hare ervce collaboraton By comparon we note partclar confgraton conere n pat lteratre. We note that organaton ) - 3) col be coornate throgh anonymo market aet ntegrate DM or collaboratve DM. To ecrbe thee network graphcally we enote a network noe ncate wth an open amon an external lnkage an flow are ncate wth an arrow. We are now prepare to ntroce a metho to compte the effcency performance of network. Before ong o we note pat approache n part to motvate or approach. Färe an Grokopf foce on each or noe comptng ntenty for each at that noe n each DM ner coneraton an a raal recton meare of techncal effcency of the each bae on the reltng reference fronter. nerlyng th approach the noton that n the ame tage are homogeneo an face a common fronter. Färe an Grokopf alo coner network effcency a a raal recton of exogeno npt to the two noe n ther network contonal on ntermeate an fnal otpt lyng on the vrtal fronter. ew an exton (2004) extene exton an ew (2003) to coner effcency at each noe of a network. They recrvely olve for effcency at each tage an for the network a a whole by olvng a DEA raal recton at the mot ptream an progrevely movng owntream. Wth each move the ntermeate otpt flow that are on the fronter are e a npt n the next owntream level. Th enre that at ntermeate level compte effcency content wth the fronter at frther ptream level. They vew the network a a DM an network effcency compte a the effcent level of fnal otpt at the lat owntream pont relatve to oberve fnal otpt at that pont. Both the Färe an Grokopf an ew an exton approache procee wth fferent reference grop an fronter at each noe. Th the fnal network effcency bae on the reference grop or fronter of the prevo ptream not on a ont coneraton of the actvte throghot the network. In th ene thee approache fal to comprehenvely ae network performance.

10 Robert D. Weaver 299 To procee we frt note that the tncton between an DM or network mportant. From the perpectve of a network the et of are heterogeneo acro tage thogh homogeneo acro layer for any partclar tage. For example the cla of efne by ˆ( ) contan all at tage acro all layer n the network an for all DM. By contrat ˆ( l ) the cla of at layer l acro all tage. Whle ˆ( ) contan a homogeneo et of ˆ( l ) oe not. ew an exton compte fronter for each ˆ( ) progrevely from back to ng ntenty weght from each tage to compte the effcent level of ntermeate otpt that carre nto the next tage. Färe an Grokopf pool all nto a cla ˆ ( l) nvolvng heterogenety thogh they recogne th heterogenety by allowng for fferent ntenty weght an fronter for each cla ˆ( ). To procee coner the followng problem (3) for comptaton of the otpt-orente effcency for 0 n the cla ˆ( ) recallng 0 ( 0 l 0 ) for all n ˆ ( ). (3) max 0 φ() l l x h x 0 h 0 h... n... m l y φ( ) 0 y 0... m l 0 where a vector menone by (l) an RT can be re-pecfe approprately for partclar ettng. Th problem col be agmente followng Färe an Grokopf(2000) wth contrant to accommoate allocatable exogeno npt. Whle t clear that (3) coner only a bet of nvolve n the network t oe coner a bet of homogeneo. However t of nteret to reconer the appropratene of ong o nepenently of other D n the network. In partclar the above technology not necearly network feable. pecfcally network feablty mt be enre for the effcent level of proct flow between. Th phycal balance between nteractng mt be preerve by the choce of actvty weght. Th reqrement rae the nee to enre that flow nvolve n contranng phycal balance eqlbrm hol be effcent flow bae on etmate fronter at correponng noe poton n the network. Whle ew an exton (2004) note that the external an ntermeate otpt level e a npt by a at any tage mt be content wth effcent ntermeate otpt from pplyng tage they not exten ther concern to phycal balance contrant. In partclar we nee to enre the followng phycal balance contrant are met for the effcent level of ntermeate proct flow throghot the network:

11 300 pply Chan an Network Performance: Metrc for Proftablty Proctvty an Effcency (4) ~ l *... m... (5) k ~ * y m ~ *... m k l D where the aterk ncate the ntermeate proct pply to each content wth phycal balance n the network. (4) reqre that the e of ntermeate proct by each effcent pple by the m of pple of the ntermeate proct from effcent ˆ( ). Frther for each of thee effcent pply allocate to ntermeate pply contrane by (5). (5) reqre that the pply that allocate to any k mt be feable gven avalable pply from. The mplcaton of ang (4) an (5) a contrant to problem (3) that the ntenty weght n (3) mt be choen contonal on thoe choen for effcent n all tage not mply tage. Propoton follow rectly. Propoton. Effcency of a relatve to a reference et e.g. ˆ( ) that a bet of the et of contane n a network e.g. ˆ( ) D mt be etermne contonal on effcent allocaton of ntermeate proct by not contane n the bet. Operatonally Propoton. mple problem (3) an all other ch problem that examne effcency of a bet of mt be olve a a econ tep after the effcent ntermeate proct flow are etermne for the entre et of contane n the DM ner ty. To procee we efne problem (6) below for comptaton of the otpt-orente tage effcence for DM 0 n the cla ˆ the et of all operatng n the network an acro all DM contane n D. To o o we nee to expan or notaton lghtly by ang a percrpt to ncate the DM wth whch the flow aocate. (6) max φ 0 (7) (8) (9) (0) l l l l x h y x φ 0 h 0 0 y h... n m m......

12 Robert D. Weaver 30 () (2) Th problem can be vewe a a tackng of tage actvte that efne tage pecfc fronter an meare effcency throgh raal otpt expanon at each tage. Th actvty analytc moel agmente however by phycal balance contrant () - (2) that reqre that effcent level of ntermeate proct e efne by the ntenty weght are content throgh ot the network. Defne the olton for to th problem a. Gven thee olton problem ch a (3) that coner effcency of a bet of can now be olve ) bect to contrant ch a (4) an (5) an ) contonal on network effcent flow of ntermeate otpt bae on. Next coner network effcency. everal approache are poble for th tak. ew an exton (2004) e a eqental ptream metho. tartng wth the mot owntream at tage they etermne effcency T () of ( 0 ) an compte the aocate effcent e of ntermeate goo. Next they etermne effcency T (-) of (- 0 ) an compte the aocate effcent e of ntermeate goo -.contonal on. They contne th protocol throgh the vertcal chan ntl the mot ptream evalate. Fnal network effcency evalate by comparon of fnal otpt bae on effcent npt e wth oberve fnal otpt for the mot owntream. However th approach oe not reqre phycal flow balance throghot the network. Th n th paper the followng otpt-orente meare of network effcency ntroce. Two e are of nteret to reolve n the pecfcaton. Frt we wol lke phycal balance to be enre for effcent vrtal DM. econ we wol lke to each tage technology to be homogeneo acro DM thogh allow for heterogenety acro n the ame layer. (3) max (4) (5) (6) (7) (8) m l ~ D m m y l k k... ~ ~ * * N 0 φ n h x x l h h m l m y y l N φ l... 0 m l ~

13 302 pply Chan an Network Performance: Metrc for Proftablty Proctvty an Effcency (9) where the npt level of exogeno an for ntermeate otpt are retrcte to ther effcent level by (8) an (9). 5. Conclon The goal of th paper wa to coner the general problem of gagng effcency of network of nter-relate or collaboratng econ-makng nt that are bary to more centrale econ-makng. Th the concept of b-dm or wa ntroce an alternatve organaton of were entfe. A etale notaton wa ntroce that elcate two fnamental reqrement of network effcency analy overlooke by prevo work. Frt network effcency mt allow for n the ame tage to face a common technology whle not reqrng ch a retrcton for n the ame layer. econ ntenty weght mt be electe bect to phycal flow contrant that pan acro all n a DM. Th reqre that a network-we problem be efne even when effcency of a bet of wthn the DM of nteret. 6. Reference ~ k y m l ~ k... m D Catell C Peent R kovch W.. DEA-lke moel for the e.cency evalaton of herarchcally trctre nt. Eropean Jornal of Operatonal Reearch 54 (2004) Catell C Peent R kovch W. DEA-lke moel for e(cency evalaton of pecale an nterepenent nt. Eropean Jornal of Operatonal Reearch 200;32: Färe R. (99). Mearng Farrell Effcency for Frm wth Intermeate Inpt Acaema Economc Paper 9 (2) Färe R. an. Grokopf. (996a). Proctvty an Intermeate Proct: A Fronter Approach. Economc etter 50 () Färe R Grokopf. Intertemporal Procton Fronter; Wth Dynamc DEA. Norwell: Klwer Acaemc Pblher 996. Färe R Grokopf. Network DEA. oco-economc Plannng cence 2000;34: Färe R Whttaker G. An ntermeate npt moel of ary procton ng complex rvey ata. Jornal of Agrcltral Economc 995;46(2): ew HF exton TR. Network DEA: effcency analy of organaton wth complex nternal trctre. 2004;3: öthgren M. an M. Tambor. (999). Proctvty an Conmer atfacton n weh Pharmace: A DEA Network Moel. Eropean Jornal of Operatonal Reearch 3 (3) exton TR ew HF. Two-tage DEA: An applcaton to maor leage baeball. Jornal of Proctvty Analy 2003;9:

14 Robert D. Weaver Fgre Fgre. Network Confgraton Each noe ame to tle external npt x ncate by a agonal otte tem arrow only n the frt confgraton. Fnal otpt y are note by oble temme arrow only n the frt confgraton an are ame feable at each noe for all other confgraton. ngle chan (3lr0) External npt are ame at each noe one fnal otpt (mlar to Färe & Grokopf (995996) Parallel chan (3l r2) Cro-layer orcng (3lr2) mlar to Färe & Grokopf ( ) Catell et al. (2004) Peer orcng (3R2) Peer orcng wth heterogeneo layer (32 R2) hare ervce (33R2)

15 304 pply Chan an Network Performance: Metrc for Proftablty Proctvty an Effcency