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
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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):
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