A Mathematical Model for Selecting Third-Party Reverse Logistics Providers

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1 A Mathematcal Model fo Selectng Thd-Pat Revese Logstcs Povdes Reza Fazpoo Saen Depatment of Industal Management, Facult of Management and Accountng, Islamc Azad Unvest - Kaaj Banch, Kaaj, Ian, P. O. Box: Tel: 0098 (26) Fax: 0098 (26) E-mal: fazpou@ahoo.com Abstact Geneall, man optmzaton models of thd-pat evese logstcs (3PL) povde selecton assume that cadnal data, wth less emphass on odnal data, exst. Howeve, to select the best 3PL povdes, ths assumpton s not ealstc because odnal data ae vtal. Fo dealng wth ths dffcult and selectng the most effcent 3PL povde n the condtons that both odnal and cadnal data ae pesent, a methodolog s ntoduced, whch s based on mpecse data envelopment analss (IDEA). A numecal example demonstates the applcaton of the poposed method. Kewods: Thd-pat evese logstcs povde, Data envelopment analss, Cadnal and odnal data. Intoducton Logstcs plas a sgnfcant ole n ntegatng the suppl chan of ndustes. Howeve, as the maket becomes moe global, logstcs s now seen as an mpotant aea whee ndustes can cut costs and mpove the custome sevce qualt. Logstcs outsoucng s an emegng tend n the global maket. Bascall, a thd-pat evese logstcs (3PL) povde nvolves usng extenal companes to pefom logstcs functons whch have been conventonall opeatonal wthn an oganzaton. The man benefts of

2 logstcs allances ae to allow the outsoucng compan to concentate on the coe competence, ncease the effcenc, mpove the sevce, educe the tanspotaton cost, estuctue the suppl chans, and establsh the maketplace legtmac. Hence, a pope 3PL povde whch meets vaous demands s cucal fo the gowth and competence of an entepse (Lu and Wang (n pess)). On the othe hand, man manufactues have undestood that the coe competences ae not n the logstcs-feld, and have theefoe pogessvel sought to bu logstcs sevces and functons fom 3PL povde (Bottan and Rzz, (2006)). Reuse of poducts and mateals s not a new phenomenon. Metal scap bokes, waste pape ecclng, and depost sstems fo softdnk bottles ae all examples that have been aound fo a long tme. In these cases ecove of the used poducts s economcall moe attactve than dsposal. In the ecent eas, the gowth of envonmental concens has gven "euse" nceasng attenton. Waste educton effots have pomoted the dea of mateal ccles nstead of a "one wa" econom. The euse oppotuntes gve se to a new mateal flow fom the use back to the sphee of poduces. The management of ths mateal flow opposte to the conventonal suppl chan flow s the concen of the ecentl emeged feld of "evese logstcs". Revese logstcs encompasses the logstcs actvtes all the wa fom used poducts no longe equed b the use to poducts agan usable n a maket. The tpcal evese logstcs opeatons nclude the actvtes a fm, whch uses etuned mechandse due to poduct ecalls, excess nvento, salvage, unwanted o outdated poducts, etc. In addton, t ncludes the ecclng pogams, hazadous mateal pogams, and dsposton of obsolete equpment and asset ecove. The mpotance of studng evese logstcs has nceased n ecent eas fo seveal easons (Pahnsk and Kocabasoglu (2006)): The amount of poduct etuns can be ve hgh, wth some ndustes expeencng etuns at ove 50% of sales. Sales oppotuntes n seconda and global makets have nceased evenue geneaton fom pevousl dscaded poducts. 2

3 End-of-lfe take-back laws have polfeated ove the past decade n the developed countes, equng busnesses to effectvel manage the ente lfe of the poduct. Consumes have successfull pessued busnesses to take esponsblt fo the dsposal of the poducts that contan hazadous waste. Landfll capact has become lmted and expensve. Altenatves such as epackagng, emanufactung and ecclng have become moe pevalent and vable. Wth egad to the above ssues and addtonal pessues fom evolvng envonmental and electonc commece pactce ponts to stategc mplcatons of evese logstcs decsons, one of whch s the outsouce decson, whch ma nclude the selecton of 3PL povdes. In summa, thee ae numeous easons fo selectng a 3PL povde. Once the decson has been made to wok wth a 3PL povde the next decson s to detemne whch povde. Selectng evese logstcs povdes fom a lage numbe of possble 3PL povdes wth vang levels of capabltes and potental s a complcated and a tme-consumng task equng multple ctea decson makng soluton appoaches. Ths pape poposes a method fo selectng the best 3PL povdes n the pesence of both cadnal and odnal data. The objectve of ths pape s to popose a method fo selectng 3PL povdes n the condtons that both odnal and cadnal data ae pesent (wthout elng on weght assgnment b decson makes). The appoach pesented n ths pape has some dstnctve featues. The poposed model consdes cadnal and odnal data fo 3PL povde selecton. The poposed model deals wth mpecse data n a dect manne. 3PL povde selecton s a staghtfowad pocess caed out b the poposed model. The poposed model does not demand weghts fom the decson make. Ths pape poceeds as follows. In Secton 2, lteatue evew s pesented. In Secton 3, the method that selects the 3PL povdes s ntoduced. Numecal example and 3

4 manageal mplcatons ae dscussed n Sectons 4 and 5, espectvel. Secton 6 dscusses concludng emaks. 2. Lteatue evew Some mathematcal pogammng appoaches have been used fo 3PL povde selecton n the past. Meade and Saks (2002) appled analtc netwok pocess (ANP) fo 3PL povde selecton. Göl and Çata (2007) used analtc heach pocess (AHP) fo selectng 3PL povdes. The hghlghted the effots of a leadng Tuksh automotve compan to estuctue ts suppl chan fo expot pats. To select the best 3PL povdes n the pesence of vagueness, Efendgl et al. (2008) developed a two-phase model based on atfcal neual netwoks and fuzz AHP. Howeve, AHP and ANP have two man weaknesses. Fst subjectvt of AHP and ANP s a weakness. The decson make povdes the values fo the pawse compasons and, theefoe, the model s ve dependent on the weghtngs povded b the decson make. Second the tme necessa fo completon of such a model s a weakness. The numbe of pawse compasons equed could become cumbesome. Meanwhle, when the numbe of altenatves and ctea gows, the pawse compason pocess becomes dffcult, and the sk of geneatng nconsstences gows, hence jeopadzng the pactcal applcablt of AHP and ANP. Bottan and Rzz (2006) pesented a mult-attbute appoach fo the selecton and ankng of the most sutable 3PL povde. The appoach s based on the TOPSIS (Technque fo Ode Pefeence b Smlat to Ideal Soluton) technque and the fuzz set theo. To select 3PL povdes, Cao et al. (2007) poposed a two-stage method based on the socal welfae functon and TOPSIS. In the fst stage, the used the socal welfae functon theo fo selecton potental povdes fom too man 3PLs. Then, TOPSIS theo was used fo fnal selecton, avodng the subjectve estmaton of expets. Işıkla et al. (2007) pesented an ntellgent decson suppot famewok fo 3PL selecton. The poposed famewok ntegates case-based easonng, ule-based easonng and compomse pogammng technques n fuzz envonment. Lu and Wang (n pess) developed an ntegated fuzz appoach fo selecton of 3PL povdes. The method conssts of thee dffeent technques: () use fuzz Delph method to dentf mpotant 4

5 evaluaton ctea; (2) appl fuzz nfeence method to elmnate unsutable 3PL povdes; and, (3) develop a fuzz lnea assgnment appoach fo the fnal selecton. Quesh et al. (2008) descbed TOPSIS fo selectng potental 3PL povdes n fuzz envonment. Vaous selecton ctea measued n lngustcs tem n vague and subjectve efeence wee accounted usng tangula fuzz numbes. The case poblem demonstated fuzz mult-ctea decson makng method to evaluate the potental 3PL povdes b assgnng weght to each cteon and late on sntheszng the capablt exhbted b them. Howeve, as noted befoe, all of the abovementoned efeences suffe fom subjectve judgments. A technque that can deal wth both odnal and cadnal data and not elng on weght assgnment b decson makes s needed to bette model such stuaton. Recentl, Haas et al. (2003) appled data envelopment analss (DEA) fo selectng evese logstcs channels. Howeve, the deal wth cadnal data and do not consde odnal data. To the best of autho s knowledge, n the DEA context, thee s not an efeence that deals wth 3PL povde selecton n the condtons that both odnal and cadnal data ae pesent. 3. Poposed method fo 3PL povdes selecton DEA poposed b Chanes et al. (978) (Chanes, Coope, Rhodes (CCR) model) and developed b Banke et al. (984) (Banke, Chanes, Coope (BCC) model) s an appoach fo evaluatng the effcences of decson makng unts (DMUs). Ths evaluaton s geneall assumed to be based on a set of cadnal (quanttatve) output and nput factos. In man eal wold applcatons (especall 3PL povde selecton poblems), howeve, t s essental to take nto account the exstence of odnal (qualtatve) factos when endeng a decson on the pefomance of a DMU. Ve often, t s the case that fo a facto such as 3PL povde eputaton, one can, at most, povde a ankng of the DMUs fom best to wost elatve to ths attbute. The capablt of povdng a moe pecse, quanttatve measue eflectng such a facto s geneall beond the ealm of ealt. In some stuatons, such factos can be legtmatel 5

6 quantfed, but ve often; such quantfcaton ma be supefcall foced as a modelng convenence. In stuatons such as that descbed, the data fo cetan nfluence factos (nputs and outputs) mght bette be epesented as ank postons n an odnal, athe than numecal sense. Refe agan to the 3PL povde eputaton example. In cetan ccumstances, the nfomaton avalable ma pemt one to povde a complete ank odeng of the DMUs on such a facto. Theefoe, the data ma be mpecse. To deal wth mpecse data n DEA, mpecse data envelopment analss (IDEA) models and methods have been developed. Impecse data mples that some data ae known onl to the extent that the tue values le wthn pescbed bounds whle othe data ae known onl n tems of odnal elatons. When mpecson s taken nto consdeaton, the assocated DEA model becomes nonlnea, whch makes ts soluton pocedue dffcult. Suppose thee s a set of n pee DMUs, {DMU j : j, 2,, n}, whch poduce multple outputs (, 2,, s), b utlzng multple nputs x (, 2,, m). When a DMU o s unde evaluaton b the CCR model, thee s: maxπ s. t. o s µ o s m µ w x µ, w o m, w x 0,. 0 j, () whee µ s weght of the th output and w s weght of the th nput. Coope et al. (999) and Km et al. (999) dscussed that some of the outputs and nputs ae mpecse data n the foms of bounded data, odnal data, and ato bounded data as follows. Bounded data and x x x fo BO, BI, (2) 6

7 whee and x ae the lowe bounds and and x ae the uppe bounds, and BO and BI epesent the assocated sets contanng bounded outputs and bounded nputs, espectvel. Weak odnal data k and x x k fo j k, DO, DI, o, to smplf the pesentaton, x x 2 2 x k k x n n ( DO), ( DI), (3) (4) whee DO and DI epesent the assocated sets contanng weak odnal outputs and nputs, espectvel. Stong odnal data < 2 <...< k < < n ( SO), (5) x <x 2 <...<x k < <x n ( SI), (6) whee SO and SI epesent the assocated sets contanng stong odnal outputs and nputs, espectvel. Rato bounded data L G x x o o U H ( j ( j j j o o ) ) ( RO), ( RI), (7) (8) whee L and G epesent the lowe bounds, and U and H epesent the uppe bounds. RO and RI epesent the assocated sets contanng ato bounded outputs and nputs, espectvel. If (2)-(8) ae ncopoated nto model (), thee wll be: 7

8 maxπ s. t. o s µ o s m ( x µ w x o ) Θ,, m w x 0, j,, n (9) ( µ, w ) Θ +, 0, whee ( x ) Θ and ( ) Θ epesent an o all of (2)-(8). + Obvousl, model (9) s nonlnea and non-convex, because some of the outputs and nputs become unknown decson vaables. Snce model (9) s nonlnea and non-convex, consequentl local optmum s poduced and we cannot be sue whethe ths s the global optmum o not. To convet model (9) nto the lnea pogam, Zhu (2003) developed a smple appoach b defnng X Y * o s. t. w x µ, j,, j. (0) Then model (9) can be conveted nto the followng lnea pogam: π max whee X Y + Θ and s m Y X Y 0 0, ~ X D, ~ + Y D, s o o m X,, 0, Θ ae tansfomed nto j,, n + D ~ and D ~ () wth: 8

9 . bounded data: µ Y µ, w x X w x ; 2. odnal data: Y Yk and X X k j k fo some, ; Y X 3. ato bounded data: L U and G H ( j jo ); Y X o 4. cadnal data: Y ˆ µ and X w xˆ, whee ŷ and xˆ epesent cadnal data. o In the next secton, a numecal example s pesented. 4. Numecal example The data set fo ths example s patall taken fom Fazpoo Saen (2007) and contans specfcatons on eghteen 3PL povdes. The cadnal nput consdeed s total cost of shpments (TC). 3PL povde eputaton (3R) s ncluded as a qualtatve nput whle numbe of blls eceved fom the 3PL povde wthout eos (NB) wll seve as the bounded data output. 3R s an ntangble facto that s not usuall explctl ncluded n evaluaton model fo 3PL povde. Ths qualtatve vaable s measued on an odnal scale. Table depcts the 3PL povde's attbutes. Now the tansfomaton pocess nvolved n model (), s llustated. That s, { ; x 268; x 259; ; x 26} Θ x (cadnal data) { x x } Θ (odnal data) x27 { 65; 60 70; 40 50;...; 90 50} Θ (bounded data) B usng (0), ~ D ~ D ~ D Θ Θ2, and Θ, ae, espectvel, tansfomed nto { X 253w ; X2 268w ; X3 259w ; ; X8 26w} { X 28 X 26 X 27} { 50µ Y 65µ ; 60µ Y 70µ ; 40µ Y 50µ ; ; 90µ Y 50µ } Applng model (), the effcenc scoes of 3PL povdes (DMUs) have been pesented n the last column of Table. 9

10 Model () dentfed 3PL povdes 4, 6, 8, 9,, 4, and 7 to be effcent wth a elatve effcenc scoe of. The emanng eleven 3PL povdes wth elatve effcenc scoes of less than ae consdeed neffcent. Theefoe, decson make can choose one o moe of these effcent 3PL povdes whch sut the logstcs outsoucng needs of hs/he compan. Dung the 3PL povde selecton pocess, seveal ponts should be mentoned and dscussed. Fst of all, the poposed method does not eque subjectve judgments of the decson makes n the evaluaton pocess. Secondl, the nputs and outputs selected n ths pape ae not exhaustve b an means, but ae some geneal measues that can be utlzed to evaluate 3PL povdes. In an actual applcaton of ths methodolog, decson makes must caefull dentf appopate nputs and outputs measues to be used n the decson makng pocess. Thdl, dung the ente selecton pocess, lage amount of nfomaton wee dectl offeed b the ndvdual 3PL povde. The decson makes ma use the offeed nfomaton to evaluate the pefomance of each 3PL povde. If the decson makes cannot exactl dstngush what the 3PL povdes have done wth what the plan to do, the msjudgment o bas towads a patcula 3PL povde could be occued. To avod ths stuaton, multple on-ste vsts o gatheng of elevant nfomaton ndectl ae the feasble was to obtan moe accuate decson esults. Fnall, t should be noted that the elevant evaluaton esults ae vald onl fo ths example wth ts own decson envonment and should not be genealzed fo othe companes. In addton, the applcaton of the poposed method ma eque sgnfcant tme and effots fom the decson makes. Nevetheless, t s stll wothwhle that the outsoucng compan can educe costs, focus on coe competence, and most mpotantl, educe the sk of selectng an nappopate 3PL povde. 5. Manageal mplcatons Ove the past few decades, nceased competton caused b globalzaton and apd technologcal advances has motvated fms to mpove effcenc n suppl chan management. Inceasng effcenc n evese logstcs opeatons such as the ecove of the etuned poducts s one wa n whch busnesses attempted to mantan and ncease compettveness n the global econom. 0

11 Man busnesses pefe allocatng the esouces to coe competenc aeas and choose to outsouce the patal o oveall logstcs pocesses to 3PL povdes. Utlzng 3PL povdes n a closed-loop suppl chan s also effectve n ensung sustanablt snce effcent evese logstcs sevces enable busnesses wth the oppotunt to ncease the poft magns, to dffeentate the sevces fom those of the compettos, to attact new clents to these sevces, and to enhance the status n the global suppl chan netwok. On the othe hand, f etuns ae not handled effectvel, that s, when etuned assets ae not pocessed quckl o completel, consdeable value ma be lost. Hence, t s mpotant to select an effcent 3PL povde to patne wth the oganzaton n the evese logstcs pocess. Mathematcal models povde mpotant nfomaton that can be used b manages n makng stategc o opeatonal decsons. Manages can gan nfomaton about those 3PL povdes that exhbt best pactce so that the ma gan fom the expeence of the moe effcent, and ths can lead to benefts deved fom collaboaton among the 3PL povdes. Futhemoe, the pocess of defnng effcenc fo a patcula tpe of opeaton though the selecton of the mpotant nputs and outputs has sgnfcant stategc value. 6. Concludng emaks Motvated b the gowng sgnfcance of evese logstcs actvtes n an nceasngl compettve global maket, ths stud poposed a method fo selectng appopate and desable 3PL povdes. To select the most effcent 3PL povde n the condtons that both odnal and cadnal factos ae pesent, a methodolog was ntoduced. The esults of ths pape can be appled fom both a manufactue s and 3PL povde s pespectve. The manufactue can use t as a tool n selectng the "best" 3PL povde. The 3PL povde can use these esults fom a maketng pespectve. A specfc 3PL povde, who acheves a hgh mean scoe, when compaed to the othe 3PL povdes, can use these esults fo pomotng ts sevce. On the othe hand, f a patcula 3PL povde s pool pefomng, then the 3PL povde can use the analss

12 fo benchmakng puposes. Ths esult ma mean that the 3PL povde must povde bette pefomance levels at the same nput. The poblem consdeed n ths stud s at ntal stage of nvestgaton and much futhe eseaches can be done based on the esults of ths pape. Some of them ae as follows: Smla eseach can be epeated fo dealng wth odnal data and bounded data b fuzz sets. The othe eseach can be accomplshed fo 3PL povdes ankng n the pesence of qualtatve data, mpecse data, and stochastc data. Othe potental extenson to the methodolog ncludes the case that some of the 3PL povdes ae slghtl nonhomogeneous. One of the assumptons of all the classcal models of DEA s based on complete homogenet of DMUs (3PL povdes), wheeas ths assumpton n man eal applcatons cannot be genealzed. In othe wods, some nputs and/o outputs ae not common fo all the DMUs occasonall. Theefoe, thee s a need to a model that deals wth these condtons. To compae the esults of pefomance of poposed method wth fuzz DEA wll be anothe eseach topc. Acknowledgement The autho wshes to thank an anonmous evewe fo valuable suggestons and comments. Refeences Banke R. D., Chanes A. and Coope W. W. (984) Some Methods fo Estmatng Techncal and Scale Ineffcences n Data Envelopment Analss, Management Scence, Vol. 30, No. 9, pp Bottan E. and Rzz A. (2006) A Fuzz TOPSIS Methodolog to Suppot Outsoucng of Logstcs Sevces, Suppl Chan Management: An Intenatonal Jounal, Vol., No. 4, pp Cao J., Wang W. W. and Cao G. (2007) Integaton of the Socal Welfae Functon and TOPSIS Algothm fo 3PL Selecton, Fouth Intenatonal Confeence on Fuzz 2

13 Sstems and Knowledge Dscove (FSKD 2007), IEEE Compute Socet, Vol. 3, pp Chanes A., Coope W. W. and Rhodes E. (978) Measung the Effcenc of Decson Makng Unts, Euopean Jounal of Opeatonal Reseach, Vol. 2, No. 6, pp Coope W. W., Pak K.S. and Yu G. (999) IDEA and AR-IDEA: Models fo Dealng wth Impecse Data n DEA, Management Scence, Vol. 45, No. 4, pp Efendgl T., Önüt S. and Konga E. (2008) A Holstc Appoach fo Selectng a Thd- Pat Revese Logstcs Povde n the Pesence of Vagueness, Computes & Industal Engneeng, Vol. 54, No. 2, pp Fazpoo Saen R. (2007) Supples selecton n the pesence of both cadnal and odnal data, Euopean Jounal of Opeatonal Reseach, Vol. 83, No. 2, pp Göl H. and Çata B. (2007) Thd-Pat Logstcs Povde Selecton: Insghts fom a Tuksh Automotve Compan, Suppl Chan Management: An Intenatonal Jounal, Vol. 2, No. 6, pp Haas D. A., Muph F. H. and Lancon R. A. (2003) Managng Revese Logstcs Channels wth Data Envelopment Analss, Tanspotaton Jounal, Vol. 42, No. 3, pp Işıkla G., Alptekn E. and Büüközkan G. (2007) Applcaton of a Hbd Intellgent Decson Suppot Model n Logstcs Outsoucng, Computes & Opeatons Reseach, Vol. 34, No. 2, pp Km S. H., Pak C. G. and Pak K. S. (999) An Applcaton of Data Envelopment Analss n Telephone Offces Evaluaton wth Patal data, Computes & Opeatons Reseach, Vol. 26, No., pp

14 Lu H. T. and Wang W. K. 'An Integated Fuzz Appoach fo Povde Evaluaton and Selecton n Thd-Pat Logstcs', Expet Sstems wth Applcaton, n pess. Meade L. and Saks J. (2002) A Conceptual Model fo Selectng and Evaluatng Thd- Pat Revese Logstcs Povdes, Suppl Chan Management: An Intenatonal Jounal, Vol. 7, No. 5, pp Pahnsk C. and Kocabasoglu C. (2006) Empcal Reseach Oppotuntes n Revese Suppl Chans, Omega, Vol. 34, No. 6, pp Quesh M. N., Kuma D. and Kuma P. (2008) 'Decson suppot model fo evaluaton and selecton of Thd Pat Logstcs sevce povdes', Intenatonal Jounal of Logstcs Sstems and Management, Vol. 4, No.3, pp Zhu J. (2003) Impecse Data Envelopment Analss (IDEA): A Revew and Impovement wth an Applcaton, Euopean Jounal of Opeatonal Reseach, Vol. 44, No. 3, pp

15 Table. Related attbutes fo eghteen 3PL povdes and effcenc scoes 3PL povde No. (DMU) Inputs Output TC 3R * NB x j x 2j j Effcenc [50, 65] [60, 70] [40, 50] [00, 60] [45, 55] [85, 5] [70, 95] [00, 80] [90, 20] [50, 80] [250, 300] [00, 50] [80, 20] [200, 350] [40, 55] [75, 85] [90, 80] [90, 50].892 * Rankng such that 8 hghest ank,, lowest ank (x 2,8 > x 2,6 > x 2,7 ) A local optmum of a poblem s a soluton optmal wthn a neghbong set of solutons. Ths s n contast to a global optmum, whch s the optmal soluton among all possble solutons. 5