A meta-heuristic approach supported by NSGA-II for the design and plan of supply chain networks considering new product development

A ouzy, Zah a Alizadeh; Payda , Mohammad Mahdi; Nasse i, Seyed Hadi; Mahda i, I aj A icle A me a-heu is ic app oach suppo ed by NSGA-II o he design and plan o supply chain ne wo ks conside ing new p oduc de elopmen Jou nal o Indus ial Enginee ing In e na ional P o ided in Coope a ion wi h: Islamic Azad Uni e si y (IAU), Teh an Sugges ed Ci a ion: A ouzy, Zah a Alizadeh; Payda , Mohammad Mahdi; Nasse i, Seyed Hadi; Mahda i, I aj (2018) : A me a-heu is ic app oach suppo ed by NSGA-II o he design and plan o supply chain ne wo ks conside ing new p oduc de elopmen , Jou nal o Indus ial Enginee ing In e na ional, ISSN 2251-712X, Sp inge , Heidelbe g, Vol. 14, Iss. 1, pp. 95-109, h ps://doi.o g/10.1007/s40092-017-0209-7 This Ve sion is a ailable a : h ps://hdl.handle.ne /10419/195594 S anda d-Nu zungsbedingungen: Die Dokumen e au EconS o dü en zu eigenen wissenscha lichen Zwecken und zum P i a geb auch gespeiche und kopie we den. 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I he documen s ha e been made a ailable unde an Open Con en Licence (especially C ea i e Commons Licences), you may exe cise u he usage igh s as speci ied in he indica ed licence. h ps://c ea i ecommons.o g/licenses/by/4.0/ ORIGINAL RESEARCH A me a-heu is ic app oach suppo ed by NSGA-II o he design and plan o supply chain ne wo ks conside ing new p oduc de elopmen Zah a Alizadeh A ouzy 1,2 •Mohammad Mahdi Payda 3 •Seyed Hadi Nasse i 2 • I aj Mahda i 4 Recei ed: 7 Ma ch 2017 / Accep ed: 29 May 2017 / Published online: 12 June 2017 The Au ho (s) 2017. This a icle is an open access publica ion Abs ac The e a e many easons o he g owing in e es in de eloping new p oduc p ojec s o any i m. The mos embossed eason is su i ing in a highly compe i- i e indus y which he cus ome as es a e changing apidly. A well-managed supply chain ne wo k can p o- ide he mos p o i o i ms due o conside ing new p oduc de elopmen . Along wi h p o i , cus ome sa is- ac ion and p oduc ion o new p oduc s a e goals which lead o a mo e e icien supply chain. As new p oduc s appea in he ma ke , he old p oduc s could become obsole e, and hen phased ou . The mos impo an pa ame e in a supply chain which conside s new and de eloped p oduc s is he ime ha de eloped and new p oduc s a e in oduced and old p oduc s a e phased ou . Wi h conside a ion o he ac o s no ed abo e, his s udy p oposes o design a i-objec i e mul i-echelon mul i- p oduc mul i-pe iod supply chain model, which inco - po a es p oduc de elopmen and new p oduc p oduc ion and hei e ec s on supply chain con igu a ion. The supply chain unde conside a ion is assumed o consis o supplie s, manu ac u e s, dis ibu o s and cus ome g oups. In e ms o o e coming NP-ha dness o he p o- posed model and in o de o sol e he complica ed p oblem, a non-domina ed so ing gene ic algo i hm is employed. As he e is no benchma k a ailable in he li e a u e, he non-domina ed anking gene ic algo i hm is de eloped o alida e he esul s ob ained and some es p oblems a e p o ided o show he applicabili y o he p oposed me hodology and e alua e he pe o mance o he algo i hms. Keywo ds Supply chain New p oduc de elopmen  NSGA-II NRGA T i-objec i e p oblem In oduc ion and li e a u e e iew In mos classical supply chain (SC) ne wo k designs, he majo goal is o p oduce and send p oduc s om one echelon o ano he echelon o sa is y he demands o he ma ke place in o de o minimize he chains’ cos s o maximize he o al bene i . Today’s compe i i e ma ke makes he supply chain managemen mo e impo an . Nowadays, o su i e in a highly compe i i e ma ke place, companies ha e o educe supply chain isk, imp o e he dis ibu ion me hods, op imize in en o y le els and imp o e cus ome se ice and cus ome sa is ac ion. In he li e a u e o supply chain ne wo k design p oblems, o make he models mo e ealis ic, se e al objec i es a e conside ed oge he (Mu illo-Al a ado e al. 2015; Pasan- dideha e al. 2015; Godichaud and Amodeo 2015; Gho- lamian e al. 2015). Besides, he solu ion o mul i-objec i e p oblems is bo h a ac i e and challenging (Kao e al. 2014; Jadidia e al. 2015; Ghod a nama e al. 2015; Validi e al. 2014). As cus ome in e es s a e apidly changing, s a egies o collabo a e wi h o compe e wi h sui able i ms wi hin a ne wo k should be conside ed in he new p oduc &Zah a Alizadeh A ouzy [email p o ec ed] 1 Depa men o Ma hema ics, Pa sa Ins i u e o Highe Educa ion, Babolsa , I an 2 Depa men o Ma hema ics, Facul y o Ma hema ical Sciences, Uni e si y o Mazanda an, Babolsa , I an 3 Depa men o Indus ial Enginee ing, Babol Noshi ani Uni e si y o Technology, Babol, I an 4 Depa men o Indus ial Enginee ing, Mazanda an Uni e si y o Science and Technology, Babol, I an 123 J Ind Eng In (2018) 14:95–109 h ps://doi.o g/10.1007/s40092-017-0209-7 de elopmen (NPD) p ocess. While in bo h ields, NPD and supply chain managemen , ha e ecei ed a conside able a en ion, hey a e ha dly conside ed oge he . Since his pape deals wi h bo h he mul i-objec i e op imiza ion and in eg a ion o NPD and SC, a b ie in oduc ion o he concep s o mul i-objec i e p oblems in supply chain and in eg a ion o NPD and SC is p esen ed below. In he nex wo subsec ions o his pape , he exis ing li e a u e on mul i-objec i e op imiza ion p oblems and in eg a ion o NPD and SC is e iewed. ‘‘Ma hema ical model and p oblem desc ip ions’’ p esen s he ma hema i- cal model and model’s assump ions. The sol ing me hod- ology is de ined in ‘‘Sol ing me hodology’’. ‘‘Applica ions and compa isons’’ p esen s he compu a ional esul s and, inally, conclusions a e epo ed in ‘‘Conclusions’’. Mul i-objec i e op imiza ion p oblem in SC Real SCs a e o be op imized simul aneously conside ing mo e han one objec i e. P oblems which y o op imize many con lic ing objec i es simul aneously a e called mul i-objec i e op imiza ion p oblems and ha e many op imal solu ions. The gene al o m o such p oblem is (Van Veldhuizen 1999): min FxðÞ¼ 1xðÞ; 2xðÞ;...; mxðÞðÞ s: : gixðÞ0i¼1;...;q hjxðÞ¼0j¼1;...;p; ( whe e x=(x 1 ,x 2 ,…,x n )2X,R n is called decision a iable and Xis n—dimensional decision space. m (x)is he m- h objec i e, g i (x) is he i- h cons ain inequali y and h j (x) is he j- h cons ain equa ion. Di e en me hodologies ound in li e a u e o ea ing mul i-objec i e op imiza ion p oblems a e he weigh ed- sum me hod, he e-cons ain me hod, goal p og amming me hod, lexicog aphy me hods, LP-me ic, maxi-min, uzzy me hod, e c. (Chen e al. 2003; Chen and Lee 2004; Guille ´na e al. 2004; Hung 2011). In all hese men ioned me hods, mul iple objec i es a e combined and o m a single objec i e p oblem and hen he op imal solu ion is ob ained. As in eal wo ld si ua ions di e en al e na i es a e willing by he decision make s, such solu ions may no sa is y he decision make . Fo his eason, due o he exponen ial g ow h o he p oblem size and complexi y, nume ous na u e-based mul i- objec i e algo i hms a e in oduced o sol ing ma hema i- cal op imiza ion models. Among a ious mul i-objec i e op imiza ion algo i hms, mul i-objec i e e olu iona y algo i hms (MOEAs), he mos signi ican ones a e mul i- objec i e gene ic algo i hms (GA) (Deb e al. 2002, Moha- pa a e al. 2015), mul i-objec i e pa icle swa m op imiza- ion algo i hms (MPSO) (Ko inis 2014; Zhang e al. 2013; Niknam e al. 2011; Tsaia e al. 2010), mul i-objec i e e olu iona y algo i hms (Shin e al. 2011; Zhu e al. 2014; Tana e al. 2014), mul i objec i e immune clone algo i hms (Shang e al. 2012), g oup sea ch op imize (Wang e al. 2012), mul i-objec i e og leaping algo i hms (Tahe e al. 2010; Sa aei A shia e al. 2014) and so on. Howe e , hyb id algo i hms ha e ecei ed conside able a en ion ecen ly. Fo ins ance, Go indan e al. (2015) combined mul i-ob- jec i e elec omagne ism mechanism algo i hm and adap ed mul i-objec i e a iable neighbo hood sea ch; Bandyopad- hyay and Bha acha ya (2013) p oposed a modi ied NSGA- II; Diaba (2014) also combined gene ic algo i hm wi h simula ed annealing algo i hm. In gene al, supply chain models na u ally lead o com- plex, la ge-scale ma hema ical models which a e ha d o sol e op imally in mos eal cases. Also, as eal SC p oblems conside mo e han one objec i e, he appea ance o con lic objec i es does no allow simul aneous op imal solu ions o all objec i es. Thus, o achie ing nea op imal solu ions in la ge size ins ances, applying MOEAs a e help ul. Sadeghi e al. (2014) p esen ed a mul i-objec i e com- bina o ial op imiza ion model o a supply chain p oblem including one- endo mul i- e aile s conside ing a endo - managed in en o y app oach. Thei p oposed model included wo objec i es, minimiza ion o in en o y cos as he i s objec i e and maximiza ion o he sys em elia- bili y o he machines ha p oduce he goods as he second. Since he de eloped model was NP-ha d, hey applied wo mul i-objec i e gene ic algo i hms, namely, NSGA-II and NRGA, o ind Pa e o on s. La ha Shanka e al. (2013) o mula ed a h ee-echelon SC ne wo k model o he op imal acili y loca ion and capaci y alloca ion decisions. While making s a egic decisions, hey conside ed ixed loca ion and a iable ma e ial cos , p oduc ion, in en o y and anspo a ion cos s. Thei p oposed model con ained wo objec i e unc ions, minimizing o al SC cos and maximizing ill a e. They applied an in elligen mul i-ob- jec i e hyb id pa icle swa m op imiza ion algo i hm op imize . As ano he s udy, Bandyopadhyay and Bha - acha ya (2014) p oposed a i-objec i e p oblem o a wo- echelon se ial supply chain. The conside ed objec i es we e he minimiza ion o he o al cos he chain, mini- miza ion o he a iance o o de quan i y and minimiza- ion o he o al in en o y. To sol e he model, hey applied a p oposed modi ied NSGA-II. Soleimani and Kannan (2015) de eloped a de e minis ic mul i-echelon, mul i- p oduc , mul i-pe iod model o a closed-loop SC ne wo k and p esen ed a new hyb id pa icle swa m op imiza ion and gene ic algo i hm o sol e a ious kinds o p oblems. Then a comple e compu a ional analysis was unde aken o alida e hei p oposed algo i hm. In his pape , a new applica ion o me a-heu is ic based on NSGA-II is demons a ed o he p oposed i-objec i e 96 J Ind Eng In (2018) 14:95–109 123 op imiza ion o SC ne wo k conside ing NPD. The algo- i hm p o ides a se o comp omised solu ions called Pa - e o op imal solu ions which op imize all he con lic ing objec i es. Then, he solu ions sa is ying speci ic c i e ia can be chosen om he se o Pa e o op imal solu ions by he decision make . In eg a ion o NPD and SC A supply chain ne wo k e e s o a ne wo k which consis s o supplie s, manu ac u es, dis ibu es and cus ome g oups o c ea e p oduc s (see Fig. 1). Nowadays, as cus ome ’s p e e ences change apidly, o su i e in a highly com- pe i i e indus y, NPD p ocess ecei ed mo e a en ion. To o e come hese challenges, in eg a ion o he NPD p ocess and he SC can o e a sus ainable compe i i e ad an age o achie e success acco ding o he cu en compe i i e en i onmen in he ma ke place. While NPD and SC ha e d awn conside able a en ion om he esea che s, sepa- a ely, he e is li le e o in he li e a u e o co e ing SC and NPD oge he . A gene ously pe suasi e pa ame e o NPD p oblems in a SC is he s a egy o in oduc ion a new p oduc and phasing ou he old p oduc s which a e de eloped in he planning ho izon. As new p oduc s appea in he ma ke , he old p oduc s could become obsole e, and hen phased ou . Be o e launching a new p oduc , a manu ac u e mus decide he iming o he p oduc launch and he p oduc ion/ sales plan o e he planning ho izon. Acco ding o Billing on e al. (1998) he e a e wo ollo e s a egies namely single p oduc oll and dual p oduc oll o in o- duce new p oduc s o he ma ke . In he i s s a egy, single p oduc oll, he ime phasing ou he old p oduc and he ime in oducing he new p oduc a e he same which means ha as he new p oduc is in oduced he old p oduc is phased ou . As such, in dual ollo e s a egy as he new p oduc is in oduced he i m con inues p oducing he old p oduc , in o he wo ds, he coexis ence o bo h p oduc s is allowed du ing a ce ain pe iod o ime. In he p oposed model he single p oduc ollo e is assumed. SCs h ough which new p oduc s a e manu ac u ed need lexibili y and esponsi eness elemen s. Each elemen o a SC echelons may ha e op ions which a e able o sa is y a equi ed unc ion as he p ocu emen , anspo a ion and p oduc ion o a p oduc . These decisions a e a new p o- duc design a e comple ed ge mo e impo ance because i inc eases he cos s (Simchi-Le i e al. 2000). Na aha ise i and Ka imi (2010) p oposed he SC edesign and new p ocess in oduc ion in mul i-pu pose plan s. They added some p oduc ion and in en o y acili ies, dis ibu ion and cus ome cen e s o hei chain. An in eg a ed op imiza ion model o con igu ing he SC o new p oduc is de eloped by Amini and Li (2011). Thei wo k was a i s a emp o model he in e ac ion be ween new p oduc di usion and SC con igu a ion. The aim o hei esea ch is he con ig- u a ion o SC subjec o demand dynamics and o he SC pa ame e s such as lead- ime and in en o y. Also, Li and Amini (2012) de eloped an in eg a ed op imiza ion model which allowed mul iple-sou cing and sa e y s ock place- men decisions in coo dina e wi h he demand dynamics du ing he new p oduc di usion p ocess h oughou i s li e cycle. As ano he s udy, Nepal e al. (2011) ha e ex ended a mul i-objec i e op imiza ion model o SC con igu a ion du ing p oduc de elopmen . Thei p esen ed model con- sis s o wo objec i es: maximiza ion o he o al compa - ibili y index in s a egic alliance and minimiza ion o he o al SC cos s. Thei model imp o es SC e iciency and s abili y by join ly conside ing sou cing, in en o y cos s and compa ibili y decisions du ing he con igu a ion o he SC. They sol ed hei model by using gene ic algo i hm. As ano he s udy, Nage e al. (2014) de eloped a mul i- objec i e wo-s age s ochas ic p og amming supply chain model ha inco po a ed imp ecise p oduc ion a e and supplie capaci y unde scena io dependen uzzy andom demand associa ed wi h new p oduc supply chains. The objec i es which hey conside ed we e maximizing he supply chain p o i , achie ing desi ed se ice le el and minimizing he inancial isk. They used he possibili y measu e o quan i y he demand unce ain ies and sol ed he model using uzzy linea p og amming app oach. Ja a ian and Bashi i (2014) p o ided a i e echelon dynamic SC model. Thei p oposed model conside s he ime o new p oduc lunching in he SC, which is op imized wi h SC con igu a ion simul aneously. In addi ion, p o- duc ion, sales, anspo a ion planning and hei lead imes a e conside ed in he model. In hei p oposed model each Raw ma e ials P oduc s P oduc s ans e ans e Supplie s Manu ac u es Dis ibu o s Cus ome g oups o de s o de s Fig. 1 The s ages o a ou -echelon SC J Ind Eng In (2018) 14:95–109 97 123 i m indi idually decides o in oduce new p oduc s and hei model conside s de eloping a single p oduc . Aliza- deh A ouzy e al. (2016) de eloped a mul i-echelon mul i- p oduc mul i-pe iod op imiza ion model o SC con igu- a ion and NPD. Thei p oposed model inco po a es h ee kinds o p oduc s: p oduc s which a e p oduced du ing he planning ho izon, p oduc s which a e decided o be de eloped and p oduc s ha a e newly in oduced du ing he planning ho izon. Thei indica ed model was capable o de e mine he op imized lunching ime and phasing ime du ing a planning ho izon al ime in o de o maximum he o al p o i . They applied p io i y based GA o sol e he p oposed model. Gi en he limi ed numbe o s udies ela ed o he op imiza ion o SCs conside ing NPD, and in ealm con ex s in pa icula , his s udy ies o con ibu e o he li e a u e by p oposing a mul i-objec i e mul i-pe iod model o op imize he p o i o SCs conside ing NPD in acco dance o he o he wo objec i es, maximizing he cus ome sa is ac ion and maximizing he NPD p oduc ion. Unlike p e ious esea ches, he model conside s h ee ca ego izes o p oduc s; cu en p oduc s, de eloped p oduc s and comple ely new p oduc s. The ob ained model belongs o NP-Ha d class o he op imiza ion p oblems, hus, NSGA-II is de eloped o ind a nea -op i- mum solu ion. Ma hema ical model and p oblem desc ip ions Model assump ions In his pape , a i-objec i e, mul i-pe iod, mul i-p oduc and mul i-echelon ne wo k including cus ome g oups, dis ibu ion cen e s, manu ac u ing cen e s and supplie s is inqui ed. In his chain, aw ma e ials a e supplied om supplie s o manu ac u es o be ans o med in o inal p oduc s and he p oduc s a e shipped o dis ibu ion cen- e s and hen acco ding o demands o cus ome g oups hey a e esponded. NPD is assumed o espond o ma - ke place changes and cus ome s’ as es o gain o main ain compe i i e ad an age. Acco dingly, he company mus ha e he abili y o de elop and p oduce new p oduc s du ing he planning ho izon and hen lexibili y is needed o he chain pa s o espond o ma ke place changes o gain o main ain compe i i e ad an age. As he model is conside ed mul i-p oduc , he ca ego iza ion o he p od- uc s is old p oduc s, de eloping/changing p oduc s and comple ely new p oduc s. The ollo e which is conside ed in he p oposed model is a single-p oduc oll o de el- oping p oduc s. This ollo e s a egy conside s he phas- ing ou ime, he eby only one o he old o de eloped p oduc s is p oduced in a momen . Model o mula ion De ini ions o a iables and pa ame e s in he mul i-eche- lon supply chain ne wo k a e summa ized below. Then, a b ie desc ip ion abou he objec i e unc ions and con- s ain s o he model a e p esen ed. Indexing se s Index o pe iod, TNumbe o pe iods sIndex o supplie , SNumbe o supplie s Index o manu ac u e , FNumbe o manu ac u e s dIndex o dis ibu o , DNumbe o dis ibu o cen e s gIndex o cus ome g oup, GNumbe o cus ome g oups Index o aw ma e ial, RNumbe o aw ma e ials iIndex o p oduc s INumbe o p oduc s As discussed in he p e ious subsec ion, he p oduc s which he company wan s o p oduce du ing he planning ho izon con ain h ee g oups. As shown by he indices below, he i s g oup indica es he p oduc s ha a e being p oduced by he company, he second g oup ela es o he p oduc s which a e he de eloped o m o he old p oduc s and is decided o be p oduced and he hi d g oup con ains he comple ely new p oduc s ha he company decides o p oduce du ing he planning ho izon. The indices a e as he ollowing: i¼ oðoldÞo¼1;...;O jðold !newÞj¼Oþ1;...;J nðnewÞn¼Jþ1;...;I 8 < : Pa ame e s P oj 1, i p oduc ocan be de eloped o p oduc j, 0, o he wise D gi Demand o cus ome g oup g o p oduc iin pe iod PR s Pe uni p ice o aw ma e ial in he supplie sin pe iod PD i Pe uni p ice o p oduc i B i Numbe o he aw ma e ial needed o p oduce p oduc i dl i New p oduc designing du a ion o p oduc i CM Capaci y o manu ac u e in pe iod CD d Capaci y o dis ibu o d CS s Capaci y o supplie s o p o iding aw ma e ial in pe iod CP i Cos o p oducing p oduc iin manu ac u e CP i Fixed cos o p oducing p oduc iin manu ac u e TP i Hou needed o p oduce pe uni o p oduc iin manu ac u e TCS s T anspo a ion cos be ween supplie sand manu ac u e TCM d T anspo a ion cos be ween manu ac u e and dis ibu o cen e d 98 J Ind Eng In (2018) 14:95–109 123 TCD dg T anspo a ion cos be ween dis ibu o cen e dand cus ome g oup g CDN i Cos o designing new p oduc i MBig numbe Decision a iables SRM s Amoun o aw ma e ial ans e ed om supplie s o manu ac u e in pe iod SMD di Amoun o p oduc i ans e ed om manu ac u e o dis ibu o din pe iod SDG dgi Amoun o p oduc i ans e ed om dis ibu o d o cus ome g oup gin pe iod Q i P oduc ion quan i y o p oduc i o manu ac u e in pe iod ET i Bina y a iable which ep esen s he new p oduc en e ing ime o dis ibu o cen e s DP i 1, i company decide o design p oduc iin pe iod ,0, o he wise Objec i e unc ions The objec i es o he p oblem a e o mula ed as he ollowing: Maximize Z1¼X dX gX iX PDiSDGdgi X sX X X PRs SRMs X X iX CP i Q i þ CP i DPi  X X sX X SRMs TCSs X X dX gX i SDGdgi TCDdg X X X dX i SMD di TCM d X X i CDNiDPi ð1Þ Maximize Z2¼X X i min gP d SDGdgi Dgi 8 < :9 = ; ð2Þ Maximize Z3¼X i2j;nX X Q i ð3Þ The aim o he i s objec i e unc ion which consis s o se en cos ing edien s is o maximize he o al p o i a he end o he planning ho izon. The i s e m compu es he o al e enue o sales. The second e m o he objec i e unc ion ep esen s he pu chased quan i y o each aw ma e ial cos and he nex e m is he p oduc ion cos o each p oduc . The nex h ee e ms a e he anspo a ion cos s. Finally, e m se en h o mula e he cos o designing new p oduc s. The second objec i e unc ion maximizes he sa is ac- ion le el o cus ome demands. I s aim is o con ol he amoun o los sales when he chain has he same p o i in o de o sa is y mo e cus ome s. In addi ion o p o i and cus ome sa is ac ion, he hi d objec i e aims o maximize he p oduc ion o de eloped and new p oduc s. Al hough p oduc ion o de eloped and new p oduc s may no be p o i able bu he i ms ha e o in oduce hem o he ma ke in o de o su i e in he compe i i e ma ke place. Cons ain s X s SRMs ¼X i Bi Q i 8 ; ; ð4Þ Q i ¼X d SMD di 8 ;i; ð5Þ X SMD di ¼X g SDGdgi 8d;i; ð6Þ X d SDGdgi Dgi 8g;i; ð7Þ X SRMs CSs 8s; ; ð8Þ Q i TP i CM 8 ;i; ð9Þ X X i SMD di CDd8d; ð10Þ Q i METi 8 ; ;ið11Þ X T h¼ þdliþ1 EToh DPj Poj 8 ;i2o;jð12Þ X þdli h¼1 ETih DPi 8 ;i2j;nð13Þ X DPi ¼18i2j;nð14Þ SRM;SMD;SDG;Q0 and in ege DP;ET 20;1 g 8i; ; ;d;s;g; ð15Þ The Cons ain s a e p esen ed om Eqs. (4)–(15) and a e desc ibed b ie ly in he ollowing. Cons ains (4)–(6) desc ibe he amoun o low be ween he echelons o he chain. Cons ain (7) ep esen s ha he sales o each p oduc a each cus ome g oup du ing each ime pe iod should no exceed i s co esponding demand. Inequali y (8) ensu es ha he o al aw ma e ials anspo ed om each J Ind Eng In (2018) 14:95–109 99 123 a ailable supplie o he manu ac u e s canno exceed he supplie capaci y. Inequali ies (9) and (10) also s a e he same issue abou he maximum capaci y o a ailable plan s and dis ibu o s, espec i ely. Inequali y (11) desc ibes he p oduc ion allowance. Inequali y (12) is ela ed o he second ca ego y o he p oduc s, de eloping p oduc s, which desc ibes he ollo e s a egy. I s a es ha a e deciding o de elop o change a p oduc , he manu ac u e s a e able o lunch hem a e he designing du a ion ime. Inequali y (13) desc ibes he s a o he designing ime. Cons ain (14) assu es ha du ing he planning ho izon each de eloping o new p oduc s a e decided o be designed once in he planning ho izon. Cons ain (15)is he logical bina y and non-nega i i y in ege equi emen s on he decision a iables. Sol ing me hodology Mos eal-wo ld op imiza ion p oblems belong o he class o NP-ha d p oblems. In o de o sol e NP-ha d p oblems, he e a e no p o ably e icien algo i hms. F equen ly, exac me hods canno sol e his class o p oblems in no - mal and easonable ime. To op imize his class o p ob- lems me a- heu is ic algo i hms a e sui able ools. Fo expe imen a ion, his sec ion p esen s he applica- ion o he p oposed model along wi h he p oposed NSGA- II algo i hm on some andom es p oblems. Some se s o small, medium and la ge sized ins ances a e conside ed o e alua e he pe o mance o he solu ion app oach. In addi ion, since no benchma k is a ailable in he li e a u e o e i y and alida e he esul s ob ained by NSGA-II, ano he popula MOEA called NRGA is sugges ed o sol e he p oblem as well. To do his, some p elimina y concep s and p inciples o NSGA-II and NRGA a e i s e iewed. Then, he equi ed s uc u es, i.e. ch omosome encoding and decoding, c osso e and mu a ion ope a o s a e desc ibed and he NSGA-II and NRGA a e de eloped. In oduc ion o non-domina ed so ing gene ic algo i hm op imiza ion One o he i s e olu iona y algo i hms which employed he concep o Pa e o op imali y in sol ing mul i-objec i e p oblems is Non-domina ed So ing Gene ic Algo i hm (S ini as and Deb 1995). Then Deb e al. (2002) de eloped a powe ul me a-heu is ic echnique known as NSGA-II which in compa ison wi h NSGA has less compu a ional complexi y, less pa ame e s, eli is s a egy and is an e i- cien cons ain -handling me hod. These ea u es ha e made he NSGA–II e y success ul and popula in a wide ange o enginee ing p oblems and some p ac ical wo ks in his a ea. As ea lie discussed, o imp o e NPD ac i i ies in a SC ne wo k he p oposed mul i-objec i e model has o be sol ed. Thus, a mul i-objec i e gene ic algo i hm on he basis o he NSGA-II is u ilized o p o ide Pa e o on s o he con lic ing objec i es. Since no benchma ks could be ound, he pu pose o employing he second algo i hm (NRGA) is o e i y he esul s ob ained by NSGA-II. I is no iced ha since mos eal wo ld cases a e la ge scale and NP- ha d, i jus i ies he use o me a-heu is ics; howe e hey don’ gua an ee o achie e op imal solu ions and usually ob ain nea op ima solu ions (Talbi 2009; Coello e al. 2002). The main s uc u e o he NSGA-II which has been so a applied o many complex mul i-objec i e op imiza ion p oblems success ully is p esen ed as ollows. In an e olu ion cycle o he s anda d NSGA-II, he op imiza ion begins by an ini ial popula ion ha is andomly gene a ed and hen e alua ed by all objec i e unc ions. The size o he popula ion is one o he NSGA-II pa ame e s and is o en known as pop size. Fo each and e e y p oblem, he popula ion size will depend on he complexi y o he p ob- lem. P ac ically, a popula ion size o a ound 100 indi iduals is qui e equen , bu anyway his size can be changed acco ding o he ime and he a ailable memo y on he machine compa ed o he quali y o he esul o be ob ained. Conside ing he ob ained ch omosomes, he popula ion is so ed based on he non-domina ion p inciple. Based on he ou namen selec ion he o sp ing popula ion is c ea ed and hen he c osso e and mu a ion ope a o s a e applied o he ob ained ch omosomes. Nex , he popula ion is so ed based on wo c i e ions: (i) ank and (ii) c owding dis ance. Fi s , each ch omosome is assigned a ank num- be equal o i s non-domina ion le el and hen he c owding dis ance ope a o is applied be ween wo solu ions wi h equal non-domina ion ank. Consequen ly, he equi ed popula ion is o ganized om he op elemen s o he on wi hou losing good solu ions (eli ism). Solu ions belong- ing o he bes non-domina ed on s a e di ec ly ans e ed o he ma ing pool o c ea e he nex gene a ion. These s eps a e epea ed un il a s opping condi ion is me . Rega ding he e mina ion c i e ia and i e a ing he s ages men ioned abo e, he algo i hm hope ully p esen s he bes and app oxima e Pa e o op imal solu ions. Impo an pa ame e s, such as ch omosome coding, ch omosome decoding and NSGA-II ope a o s a e desc i- bed in mo e de ails as ollows. Ch omosomes As same as GA, NSGA-II s a s wi h an ini ial se o an- dom solu ions gene ally called popula ion. Each indi idual in he popula ion is called a ch omosome. Each ch omo- some consis s o genes and as i is known, a gene in a 100 J Ind Eng In (2018) 14:95–109 123 ch omosome is cha ac e ized by wo ac o s: locus, he posi ion o he gene wi hin he s uc u e o ch omosome and allele, he alue he gene akes. In p io i y-based encoding, he posi ion o a gene is used o ep esen a node (sou ce/depo in anspo a ion ne wo k), and he alue is used o ep esen he p io i y o he co esponding node o cons uc ing a ee among candida es (Gen and Cheng 2000). The p oposed SC p oblem in ol es ou -echelons (supplie s, manu ac u e s, dis ibu o cen e s, and cus ome g oups). Each ch omosome consis s o h ee segmen s, in which he segmen s a e used o demons a e he ela ion- ship among he ou echelons. The i s pa (Segmen 1, Fig. 2) wi h a dimension o [(S?F)9R] ep esen s he ela ionship be ween supplie s and manu ac u e s in each pe iod which a e gi en as in ege numbe s belong o 1 o [(S?F)9R] as a p io i y alue. P oduc ion o he p oduc s in di e en pe iods and dis ibu ion quan i ies o he p oduc s om manu ac u e s o dis ibu o cen e s a e conside ed in he second pa (Segmen 2, Fig. 2) wi h a dimension o [(D?F)9I]. Finally, quan i ies o he dis ibu ed p oduc s om dis ibu o cen e s o cus ome g oups in each pe iod a e decisions ha should be de e - mined in he hi d pa (Segmen 3, Fig. 2) wi h a dimen- sion o [(D?G)9I]. As decisions a e made o Ip oduc s and R aw ma e ials in Tpe iods o Ssupplie s, Fmanu ac u es, Ddis ibu o cen e s, and Gcus ome g oups, he ull leng h o a ch omosome is he sum o he leng hs o hese h ee pa s mul iplied by he numbe s o pe iods [((D?G)9I)?((D?F)9I)?((S?F) 9R)] 9T. As an example, he s uc u e o a ch omosome o one pe iod wi h wo aw ma e ials, i e supplie s, wo manu ac u e s, ou dis ibu e s, wo cus ome g oups, h ee p oduc s is shown in Fig. (2). Since he p oposed model imp o es NPD, as he com- pany decides o p oduce new p oduc s and also de elop cu en p oduc s in some pe iods, his has o be shown in he ch omosome. This is done by andomly gene a ing a pe iod and depending on he new p oduc designing du a- ion o each p oduc pa ame e , he ollowing con e sion s a emen s a e going o be done: 1. Fo p oduc s which a e decided o be p oduced comple ely new and o he i s ime du ing he planning ho izon, depending on he pe iod ob ained by andomly gene a ed pe iod plus he designing du a ion pa ame e , he genes alue o his p oduc is upda ed in a way ha he p io i y o he ela ed p oduc o he pe iods up o he de e mined pe iod is conside ed ze o and he es emain unchanged. 2. Fo p oduc s which a e decided o be de eloped o ano he p oduc , depending on he pe iod ob ained by sum o andomly gene a ed pe iod and he designing du a ion pa ame e , he alue o he genes o hese p oduc s a e upda ed in a way ha he p io i y o he old p oduc om he de e mined pe iod up o he end o he planning ho izon is conside ed ze o and on con a y, he p io i y o he de eloped p oduc o he pe iods up o he de e mined pe iod is conside ed ze o and he es emain unchanged. Segmen 3: Dis ibu o cen e s (d) → P oduc s (i) → Cus ome g oups (g) P oduc 1 P oduc 2 P oduc 3 Dis ibu o s cus ome s Dis ibu o s cus ome s Dis ibu o s cus ome s 1234 12 1234 1 2 1234 12 [4 8 2 10 7 12 ] [ 17 1 15 5 14 18 ] [ 16 6 9 13 3 11 ] Segmen 2: Manu ac u es ( ) → P oduc s (i) → Dis ibu o cen e s (d) P oduc 1 P oduc 2 P oduc 3 Manu ac u es Dis ibu o s Manu ac u es Dis ibu o s Manu ac u es Dis ibu o s 1 2 12 3 4 1 2 1 2 34 1 2 12 3 4 [ 2 11 6 13 15 5 ] [ 3 7 14 10 4 16 ] [ 18 1 9 12 17 8 ] Segmen 1: Supplie s (s) → Raw ma e ials ( ) → Manu ac u es ( ) Raw ma e ial 1 Raw ma e ial 2 Supplie s Manu ac u es Supplie s Manu ac u es 12 345 12 12345 12 [6 12 10 2 9 5 14 ] [ 11 1 8 13 3 7 4 ] Fig. 2 An example o ep esen a ion o mul i-p oduc mul i-echelon SC o one pe iod J Ind Eng In (2018) 14:95–109 101 123 A ch omosome gene a ed by he abo e p ocedu e is easible, and he popula ion will no lose di e si y. Decoding p ocedu e o he SC p oblem T anspo a ion ee be ween cus ome g oups and dis ib- u o cen e s, dis ibu ion cen e s and manu ac u e s, man- u ac u e s and supplie s which a e ob ained wi h decoding o he hi d, second and i s segmen o a ch omosome, espec i ely, is gene a ed by sequen ial a c appending be ween sou ces and depo s. A each s ep o he decoding p ocedu e, he highes p io i y in he ch omosome is de e mined. Al hough i s posi ion gi es he p oduc ype, i gi es a sou ce (depo ) o ealize a shipmen o he p oduc ype, oo. Depending on he selec ed sou ce (depo ), a depo (sou ce) is de e mined conside ing minimum ans- po a ion cos and an a c be ween hem is added o he co esponding ee (Al ipa mak e al. 2009). The ch omosome o SC is decoded on he backwa d di ec ion. Mo e speci ically, he ollowing s a egy is aken: •Fi s , a anspo a ion ee be ween cus ome g oups and dis ibu ion cen e s is ob ained. •In he second s ep, by he ou pu s o he hi d segmen and he pe iods ob ained o in oducing new and de eloped p oduc s om he hi d segmen , he ans- po a ion ee be ween dis ibu ion cen e s and manu- ac u e s is de i ed o he second segmen . •Las ly, he anspo a ion ee be ween manu ac u e s and supplie s is ob ained o he i s segmen by he ou pu s o he second segmen . The di e ence o decoding he i s segmen om he p e ious segmen s is ha he ob ained pe iods do no a ec his segmen and i emains unchanged and he gene al decoding p ocedu e is applied. C osso e and mu a ion ope a o s In an NSGA-II, simila o GA, he o sp ing popula ion is de e mined by a se o ope a o s ha ecombine and mu a e selec ed membe s o he cu en popula ion. To pe o m he c osso e , wo pa en s a e selec ed based on ou namen selec ion. Then, hei pe iods o de eloping and in oducing new p oduc s a e exchanged. In o he wo ds, when wo pa en s a e selec ed by ou namen selec ion, hei p io i y based ch omosomes a e upda ed by he exchanged pe iods and hen is decoded and he i ness unc ion is ob ained. The swap mu a ion is conside ed as he mu a ion ope a- o . The p ocedu e o mu a ion is summa ized as ollows: Fi s ly, a ch omosome is andomly ex ac ed. Then, he swap mu a ion is done. Since he second segmen s p io i y based ch omosome is ela ed o he hi d segmen , mu a ion is done only on he hi d and i s segmen which a e inde- penden . A pe iod is andomly selec ed o each segmen . The ope a o selec s wo gens om he co esponding seg- men s and exchanges hei places. Since he p oposed ch omosome conside s NPD, no e ha o he hi d segmen he gens wi h nonze o alue mus be swapped. In oduc ion o non-domina ed anking gene ic algo i hm op imiza ion Acco ding o Al Jadaan e al. (2008) in NRGA, oule e wheel selec ion s a egy is conside ed ins ead o ou na- men selec ion in NSGA-II. In he selec ion s a egy o NRGA, hey conside ed wo anked- based oule e wheel i es; he i s ie is o selec ing he on , and he second ie is o selec ing solu ion om he on . The indi iduals in a on a e anked based on hei c owding dis ance, and he on s anked based on he non-domina ed ank. Ini- ially, a andom pa en popula ion is c ea ed. The p oce- du e is di e en a e he ini ial gene a ion. Now, wo ie s anked based oule e wheel selec ion is applied and he solu ions belonging o he bes non-domina ed se o he less p obabili y a e chosen. Then he same c osso e and mu a ion ope a o s conside ed in NSGA-II a e used. In addi ion, o s op he NRGA algo i hm, a simila p ocedu e is conside ed as he one o NSGA-II. Applica ions and compa isons In his sec ion, he applica ion o he wo MOGA’s, NSGA-II and NRGA, is p esen ed on some andom es p oblems. Then, hey a e compa ed based on some compa ison me ics and s a is ical app oaches. To do so, he pa ame e s o he algo- i hms a e uned ia Taguchi me hod. I should be men ioned ha , bo h algo i hms a e coded by Ma lab 8.2.0.701 (R2013b) so wa e o comple e he p ocess o compa ison. All compu- a ions a e un on an In el(R) Co e(TM) i7-4501U CPU@ 2.60 GHz p ocesso lap op. Mul i-objec i e pe o mance measu es In o de o e alua e he pe o mance o mul i-objec i e algo i hms, he algo i hms a e assessed acco ding o mul i- objec i e measu es. The me ics which a e used o e alua e he pe o mance o he wo me a-heu is ic algo i hms p oposed a e as ollows: 1. Numbe o Pa e o solu ions (NPS) which coun s he Pa e o solu ions in he Pa e o op imal on . 2. Mean Ideal Dis ance (MID) which measu es he con e gence o he Pa e o on s is p o ided in exp ession (16) bellow (Deb 2001): 102 J Ind Eng In (2018) 14:95–109 123 Niknam T, Meymand Hamed Z, Moja ad Hasan DA (2011) P ac ical mul i objec i e PSO algo i hm o op imal ope a ion manage- men o dis ibu ion ne wo k wi h ega d o uel cell powe plan s. Renew Ene gy 36(5):1529–1544 Pasandideha SHR, Akha an Niakib ST, Asadi K (2015) Op imizing a bi-objec i e mul i-p oduc mul i-pe iod h ee echelon supply chain ne wo k wi h wa ehouse eliabili y. Expe Sys Appl 42(5):2615–2623 Sadeghi J, Sadeghi S, Akha anNiaki ST (2014) A hyb id endo managed in en o y and edundancy alloca ion op imiza ion p oblem in supply chain managemen : an NSGA-II wi h uned pa ame e s. Compu Op Res 41:53–64 Sa aei A shia S, Zol agha ib A, Mi akili SM (2014) A mul i- objec i e shu led og leaping algo i hm o in-co e uel managemen op imiza ion. Compu Phys Commun 185(10):2622–2628 Shang RH, Jiao LC, Liu F, Ma WP (2012) A no el immune clonal algo i hm o MO p oblems. IEEE T ans E ol Compu 16(1):35–50 Shin KS, Pa k J-O, Kim YK (2011) Mul i-objec i e FMS p ocess planning wi h a ious lexibili ies using a symbio ic e olu iona y algo i hm. Compu Op Res 38(3):702–712 Simchi-Le i D, Kaminsky P, Simchi-Le i E (2000) Designing and managing he supply chain: concep s, s a egies, and case s udies. McG aw-Hill, New Yo k Soleimani H, Kannan G (2015) A hyb id pa icle swa m op imiza ion and gene ic algo i hm o closed-loop supply chain ne wo k design in la ge-scale ne wo ks. Appl Ma h Model 39(14):3990–4012 S ini as N, Deb K (1995) Mul i objec i e op imiza ion using non domina ed so ing in gene ic algo i hm. E ol Compu 2:221–248 Taguchi G (1986) In oduc ion o quali y enginee ing. Asian P oduc i i y O ganisa ion/UNIPUB, Whi e Plains Tahe N, Ehsan AF, Majid N (2010) An e icien mul i-objec i e modi ied shu led og leaping algo i hm o dis ibu ion eede con igu a ion p oblem. Eu T ans Elec Powe 21(1):721–739 Talbi E-G (2009) Me aheu is ics: om design o implemen a ion. Wiley, NewYo k Tana CJ, Limb CP, Cheaha Y-N (2014) A mul i-objec i e e olu ion- a y algo i hm-based ensemble op imize o ea u e selec ion and classi ica ion wi h neu al ne wo k models. Neu ocompu ing 125:217–228 T ian aphyllou E (2000) Mul i-c i e ia decision making me hods: a compa a i e s udy. Kluwe Academic Publishe s, Do d ech Tsaia S-J, Suna T-Y, Liub C-C, Hsiehc S-T, Wua W-C, Chiua S-Y (2010) An imp o ed mul i-objec i e pa icle swa m op imize o mul i-objec i e p oblems. Expe Sys Appl 37(8):5872–5886 Validi S, Bha acha ya A, By ne PJ (2014) A case analysis o a sus ainable ood supply chain dis ibu ion sys em—a mul i- objec i e app oach. In J P od Econ 152:71–87 Van Veldhuizen DA (1999) Mul iobjec i e e olu iona y algo i hms: classi ica ions, analyses, and new inno a ions. Ai Fo ce Ins i u e o Technology, W igh Pa e son AFB, OH Wang L, Zhong X, Liu M (2012) A no el g oup sea ch op imize o mul i-objec i e op imiza ion. Expe Sys Appl 39(3):2939–2946 Zhang Y, Gong DW, Gong N (2013) Mul i-objec i e op imiza ion p oblems using coope a i e e ol emen pa icle swa m op i- mize . J Compu Theo Nanosci 10(3):655–663 Zhu YS, Wang J, Qu BY (2014) Mul i-objec i e economic emission dispa ch conside ing wind powe using e olu iona y algo i hm based on decomposi ion. In J Elec Powe Ene gy Sys 63:434–445 J Ind Eng In (2018) 14:95–109 109 123