Ying, Kuo-Ching; Pou hejazy, Pou ya; Lin, Zhi-Rong
A icle
Scheduling wi h sequence-dependen se up imes in
sho - e m p oduc ion planning: A main pa h analysis-
based e iew
Ope a ions Resea ch Pe spec i es
P o ided in Coope a ion wi h:
Else ie
Sugges ed Ci a ion: Ying, Kuo-Ching; Pou hejazy, Pou ya; Lin, Zhi-Rong (2025) : Scheduling wi h
sequence-dependen se up imes in sho - e m p oduc ion planning: A main pa h analysis-based
e iew, Ope a ions Resea ch Pe spec i es, ISSN 2214-7160, Else ie , Ams e dam, Vol. 14, pp. 1-17,
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Scheduling wi h sequence-dependen se up imes in sho - e m p oduc ion
planning: A main pa h analysis-based e iew
Kuo-Ching Ying
a
, Pou ya Pou hejazy
b,*
, Zhi-Rong Lin
a,c
a
Depa men o Indus ial Enginee ing and Managemen , Na ional Taipei Uni e si y o Technology, Taipei 10608, Taiwan
b
Depa men o Indus ial Enginee ing, UiT- The A c ic Uni e si y o No way, Lod e Langesga e 2, Na ik 8514, No way
c
CSBC Co po a ion, Zhonggang Rd., Xiaogang Dis ., Kaohsiung Ci y 81234, Taiwan
ARTICLE INFO
Keywo ds:
Scheduling
Se up ime
Main pa h analysis
Clus e analysis
Sys ema ic e iew
ABSTRACT
The ole o se up imes in p oduc ion planning and con ol was ecognised in he la e 1960s. Since hen, a
g owing numbe o scheduling p oblems ha e accoun ed o sequence-dependen se up ime a iables. This s udy
aims o p o ide a sys ema ic e iew o se up imes in he sho - e m p oduc ion planning li e a u e, using an
objec i e, algo i hm-based app oach. The Main Pa h Analysis (MPA) and Clus e Analysis (CA) me hods a e
employed o iden i y pa e ns o knowledge de elopmen and he mos signi ican ad ancemen s in he ield.
O e 2100 a icles published be ween 1986 and 2024 we e conside ed in he e iew. The seminal a icles
con ibu ing o he ad ances in se up imes o p oduc ion scheduling a e e iewed. Meanwhile, he co e op i-
misa ion echnologies, model cha ac e is ics, and eme ging issues a di e en s ages o li e a u e de elopmen
a e discussed. The key ex ensions o he main pa h a e u he explo ed o iden i y seconda y esea ch in e es s in
he ield. Twen y- wo esea ch hemes we e iden i ied o p o ide an o e all pe spec i e and shed ligh on he
echnical ea u es and challenges. Finally, u u e esea ch di ec ions a e sugges ed based on he ou comes o his
sys ema ic e iew.
1. In oduc ion
Non- alue-adding mo emen s o delays on he shop loo a e sou ces
o was e in p oduc ion, which can be minimised h ough well-in o med
p oduc ion planning decisions; se up scheduling is one p ime example
[1]. The supply chain implica ions o igno ing se up imes in p oduc ion
planning include inc eased in en o y p essu e, delays in deli e y imes,
and, in he wo s cases, p oduc ion bo lenecks, supply sho ages, and
bullwhip e ec s [2]. In some applica ion a eas, se up imes a e mo e
no able han in o he s, making i necessa y o conside hem in p o-
duc ion scheduling. In gene al, e ec i e se up planning helps educe
p oduc ion down ime and ope a ional cos s, imp o e he lexibili y o
p oduc ion ba ches, inc ease p oduc ion capaci y, and ul ima ely
enhance p oduc ion e iciency.
Se ups a e p e alen whe e esou ces mus be used o di e se pu -
poses. Scheduling wi h se up conside a ions is widely applied in bo h
se ice and manu ac u ing en i onmen s and is also employed in mod-
e n a eas such as compu e sys ems and synch onous ci cui s. In a
manu ac u ing en i onmen , a se up e e s o he ope a ions equi ed o
swi ch om one job o p oduc o ano he . This may include p epa ing
ools and ma e ials, cleaning wo ks a ions and machine y, eplacing
equipmen , adjus ing machines, and mo e. The inco po a ion o se up
ime scheduling in o cleane p oduc ion p ac ices has been shown o no
only educe ene gy consump ion [3] bu also o minimise was e [4],
he eby enhancing o e all p oduc ion e iciency. This has also been
emphasized in jus -in- ime p oduc ion, op imised p oduc ion echnol-
ogy, g oup echnology, and cellula manu ac u ing [5].
As a echnical e m in he scheduling li e a u e, he Sequence-
Dependen Se up Time (SDST) e e s o he ime equi ed o imple-
men ing p epa a o y ope a ions. In his de ini ion, he se up ime o a
ce ain job o ask depends no only on he cha ac e is ics o he ask
i sel bu also on he asks pe o med be o e i . The op imisa ion o
SDSTs consis s o (1) planning he job sequence such ha i wo adjacen
jobs can sha e ce ain p epa a o y s eps, queuing hem oge he may
educe he o al se up ime; (2) p io i ising he jobs in a way ha i an
u gen ask has o be ca ied ou immedia ely, he p epa a ion p ocess
o o he asks migh ha e o be pos poned; (3) u ilizing esou ces such
as manpowe , equipmen , and ools e ec i ely o ensu e ha se up
ope a ions can be comple ed on ime; and (4) employing coping s a-
egies o deal wi h he impac o unce ain y and changes, such as
* Co esponding au ho .
E-mail add ess: [email p o ec ed] (P. Pou hejazy).
Con en s lis s a ailable a ScienceDi ec
Ope a ions Resea ch Pe spec i es
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Recei ed 23 Sep embe 2024; Recei ed in e ised o m 8 Ap il 2025; Accep ed 8 Ap il 2025
Ope a ions Resea ch Pe spec i es 14 (2025) 100340
A ailable online 9 Ap il 2025
2214-7160/© 2025 The Au ho s. Published by Else ie L d. This is an open access a icle unde he CC BY license ( h p://c ea i ecommons.o g/licenses/by/4.0/ ).
machine ailu es, employee absences, and sudden demand su ges
a ec ing he ac ual se up ime.
Since i s ecogni ion in he 1960s, conside ing SDSTs in p oduc ion
planning has emained an e ol ing esea ch opic. Se up ime was
ini ially in oduced and es ed wi hin single-machine p oduc ion en i-
onmen s and as a s a ic pa ame e [6]. SDSTs ha e mos ecen ly been
inco po a ed in o ad anced scheduling p oblems, such as he
ene gy-awa e dis ibu ed hyb id Flow Shop Scheduling P oblem (FSSP)
[7], pa allel ba ch p ocesso lo -sizing and scheduling [8], een an
hyb id FSSP [9], dual esou ce-cons ained lexible Job Shop Scheduling
P oblem (JSSP) [10], dis ibu ed wo-s age assembly FSSP [11],
dis ibu ed pe mu a ion FSSP [12], and dis ibu ed he e ogeneous
hyb id blocking FSSP wi h lexible assembly [13]. Recen s udies ha e
also in eg a ed SDST conside a ions wi h ene gy-e iciency op imisa-
ion, demons a ing ha adjus ing sequences based on se up e-
qui emen s can lead o imp o ed ene gy pe o mance in di e se
p oduc ion scena ios [7].
In he i s comp ehensi e e iews o he scheduling li e a u e,
Re . [6] showed ha mo e esea ch exis s on single-machine scheduling
p oblems wi h se up ime han in o he p oduc ion se ings. Such a
comp ehensi e e iew o he li e a u e p o ides an in-dep h unde -
s anding o he de elopmen s in he ield and equi es a subs an ial in-
es men o ime. Re . [5] co e ed scheduling s udies on andom se up
ime in a wide se o ac o y se ings. The au ho s classi ied hese
s udies based on scheduling (1) wi h and wi hou ba ching conside -
a ions; (2) wi h sequence-independen se up imes and SDSTs; and (3)
shop loo se ings, including single-machine, pa allel machines, low
shop, no-wai low shop, lexible low shop, job shop, and open shop.
The hi d comp ehensi e e iew [14] co e ed s a ic, dynamic, de e -
minis ic, and s ochas ic scheduling p oblems and classi ied hem ac-
co ding o ac o y se ings and ope a ional conside a ions o amily and
non- amily p oduc s. The h ee comp ehensi e e iews co e ed s udies
om 1960 o 2014, wi h manual e iews o 200, 300, and 500 a icles,
espec i ely. To ou knowledge, he mos ecen comp ehensi e e iew
da es back o 2016, when Re . [15] su eyed he li e a u e on JSSP ha
included se up conside a ions. This e iew ca ego ized he li e a u e
in o JSSPs wi h non-ba ch (job) se up imes and JSSPs wi h ba ch se up
imes while also p o iding an in-dep h analysis o he exac , hyb id, and
heu is ic solu ion me hods used unde each ca ego y.
The exis ing comp ehensi e e iews on scheduling wi h se up ime
ha e elied on adi ional e iew me hods, which in ol e manual da a
collec ion and analysis, subjec ing hem o he au ho s’ indi idual
judgemen . Mo eo e , a conside able amoun o ime has passed since
he mos ecen b oad e iew on scheduling wi h se up ime was las
conduc ed. I is, he e o e, app op ia e o upda e ou unde s anding o
se up imes in he scheduling li e a u e by employing ad anced da a
analysis app oaches. This s udy employs an objec i e, algo i hm-based
app oach o b oadly e iew SDSTs in he scheduling li e a u e, o e -
ing a mo e sys ema ic and da a-d i en pe spec i e compa ed o adi-
ional e iews. Th ough Main Pa h Analysis (MPA) and Clus e Analysis
(CA), his s udy explo es he his o ical ends, hemes, and dynamics o
SDSTs in he scheduling li e a u e, o e coming limi a ions in p e ious
e iews by elimina ing he biases associa ed wi h manual da a collec-
ion. This app oach also di e s om pas me hods by o e ing a mo e
p ecise and sys ema ic analysis o he li e a u e. Fo his pu pose,
MainPa h 465 so wa e was u ilized o da a p ocessing and analysis.
Subsequen ly, Pajek so wa e was employed o u he analysis o he
ci a ion ne wo k and he iden i ica ion o he Knowledge Dissemina ion
T ajec o y (KDT) and Knowledge De elopmen Clus e s (KDC). Las ly,
VOS iewe was used o isualize keywo ds wi hin di e en li e a u e
clus e s and iden i y de elopmen pa e ns in he li e a u e. This sys-
ema ic e iew app oach highligh s he co e op imisa ion echnologies,
model cha ac e is ics, and eme gen issues a a ious s ages o li e a u e
de elopmen [16].
The emainde o his e iew a icle is o ganized in Sec ions 2–6.
Sec ion 2 explains he ma e ials and me hods used in his s udy. Sec ions
3 and 4 p esen he global MPA o he de elopmen ajec o y and i s
b anches, espec i ely. Sec ion 5 analyses he esea ch clus e s o
iden i y signi ican esea ch hemes based on keywo ds and e iews he
mos ecen de elopmen s wi hin each hema ic. Finally, Sec ion 6
summa izes he key indings and o e s insigh s in o u u e esea ch
di ec ions.
2. Ma e ials and me hods
2.1. Da a collec ion and p ocessing
The Web o Science da abases we e used o da a collec ion. The
pla o m p o ided esou ces o explo ing and analyzing scien i ic
li e a u e, including academic jou nals, con e ence pape s, pa en s, and
book chap e s published be ween 1986 and he end o 2023. The
ollowing sea ch p o ocol (((TS=(se up*) OR TS=(se -up*) OR TS=
( emo al*)) AND TS=(scheduling*)) AND (TS=(sequence))) yielded a
o al o 2195 i ems. F om his se , 41 e ospec i e documen s, ea ly
access wo ks, and isola ed documen s we e excluded. Re iew a icles
ypically ha e a highe numbe o ci a ions and, he e o e, can in oduce
a subjec i e impac on he analysis o he KDTs. Ea ly access documen s
we e excluded because hey could esul in loops. Finally, 168 docu-
men s ha nei he ci ed o he documen s no we e ci ed by o he s we e
emo ed om he da ase . This da a collec ion and p ocessing p ocedu e
is illus a ed in Fig. 1.
A e inalizing he da ase , he op ion "Comple e eco ds and ci ed
e e ences" is used o expo he equi ed da a. The da a p ocessing s age
begins wi h impo ing he compiled documen s in o he so wa e o
calcula e he a e sal weigh o all links in he ci a ion ne wo k. Fi s ,
he global and key- ou e MPA a e conside ed o e iew he seminal KDTs
on SDSTs in he scheduling li e a u e and o iden i y he de elopmen o
he mos in luen ial esea ch ends and di ec ions. Nex , he clus e
analysis me hod is used o di ide he ne wo k in o se e al clus e s, each
o which ep esen s a sub- ield o scheduling wi h SDSTs, om which
addi ional insigh s can be de i ed. Conside ing he iden i ied sub- ields,
VOS iewe so wa e is ul ima ely used o comple e he keywo d analysis
and o isualize he clus e s.
P ecision and he Digi al Objec Iden i ie Pe cen age (DOI Pe -
cen age) indica o s a e conside ed o e alua e whe he he da ase is
ep esen a i e. P ecision de e mines whe he he numbe o nodes
cons i u es a high p opo ion o he o al numbe o a icles in he
o iginal da abase. The DOI Pe cen age measu es he da ase quali y as
he a io o he numbe o ci ed documen s in he collec ed da ase o he
o al numbe o ci a ions in he o iginal da abase. These alues e lec
he ep esen a i eness o he da ase .
Conside ing a ne wo k wi h 1973 nodes (sou ces: 198, sinks: 478,
isola es: 0, in e media es: 1297), P ecision is calcula ed as Ne wo k Size
di ided by he Numbe o A icles, yielding 1973 / 2141 =0.92. This
esul con i ms ha he da abase e ains a s ong co ela ion a e
sc eening. To calcula e he DOI Pe cen age, he ex iles o 2141 doc-
umen s we e impo ed in o he MPA so wa e o analysis o hei ci a-
ion ela ionships. The esul s showed ha he o al ci a ion eco ds
amoun ed o 61,499, while 74,856 ci a ion ela ionships we e iden i ied
in he da ase . The numbe o ci a ions accoun ed o a DOI Pe cen age
o 0.82 (DOI o al =61,499, CR o al =74,856) ela i e o he o al
numbe o ci a ions. Acco ding o Re . [17], P ecision and DOI Pe -
cen age alues exceeding 70 % con i m ha he da abase used o
analysis is ep esen a i e.
2.2. Main pa h and clus e analysis
This s udy employs MPA, a ci a ion-based me hod, o conduc a
sys ema ic and unbiased e iew o se up imes wi hin he sho - e m
p oduc ion planning li e a u e. MPA begins by cons uc ing a ci a ion
ne wo k in which a icles a e ep esen ed as nodes and ci a ion e-
la ionships a e depic ed as links. As can be seen in Fig. 2, his c ea es an
K.-C. Ying e al.
Ope a ions Resea ch Pe spec i es 14 (2025) 100340
2
acyclic di ec ed ne wo k wi h sou ces, sinks, in e media es, isola es, and
ci a ion chains. Sou ce nodes ep esen he o igin o he ci a ion
ne wo k, sink nodes indica e i s endpoin s, and in e media e nodes
cons i u e he pa hs connec ing he o igin o he endpoin s.
In his con ex , a pa h may consis o mul iple links (i.e., ci a ions),
wi h a ows di ec ed om he ci ed documen o he ci ing documen .
The MPA me hod is i s employed o iden i y all possible pa h(s) om
sou ce poin (s) o sink poin (s) in wo s eps: es ablishing a weigh ed
ne wo k and iden i ying he ‘main pa hs’. Th ee me hods can be used o
es ablish a weigh ed ne wo k cha ac e ised by he a e sal weigh o
each link: (1) Sea ch Pa h Coun (SPC), which calcula es he numbe o
imes a link is c ossed when all possible pa hs om all sou ces o all sinks
a e conside ed. (2) Sea ch Pa h Link Coun (SPLC), which calcula es he
numbe o c ossings when all possible pa hs om he ances o s o a ail
node o all sinks a e conside ed. (3) Sea ch Pa h Node Pai (SPNP),
which sums he numbe o c ossings om all possible pa hs o igina ing
om he ances o s o a ail node o he descendan s o a head node. The
SPLC scheme is conside ed he mos e ec i e me hod o ep esen ing
he KDT in he li e a u e [17] and is, he e o e, used in his s udy o
de e mine he a e sal weigh o each link in he ci a ion ne wo k.
In he weigh ed ci a ion ne wo k, he mos a e sed pa hs a e
iden i ied as he ne wo k’s ‘main pa h’ and a e selec ed o in-dep h
analysis. Se e al me hods can be used o iden i y he main pa hs in
he weigh ed ci a ion ne wo k. We employed he global and key- ou e
MPA me hods, which a e he mos commonly used in he li e a u e.
The o me iden i ies he pa h wi h he g ea es o al weigh o all links,
ep esen ing he mos impo an KDT in he ad ances o se up imes
ac oss he scheduling li e a u e. In con as , he la e conside s he mos
ci ed link(s) as he basis o explo ing all pa hs o he sou ce and sink
nodes. The key- ou e MPA me hod acili a es he explo a ion o in e -
ela ed de elopmen ajec o ies, ensu ing he inclusion o all impo an
a icles in he in-dep h analysis. This me hodology, while inno a i e
and igo ous, is complex. In e es ed eade s can consul ounda ional
wo ks on MPA [17], whe e de ailed explana ions o MPA’s compu a-
ional mechanics and applica ions a e p o ided.
Finally, CA is employed in his s udy o conduc a hema ic analysis
o he published a icles on scheduling p oblems wi h SDSTs. CA,
de eloped by [18], is a ee-based ca ego iza ion app oach ha uses he
numbe o sho es pa hs be ween all ne wo k nodes o iden i y KDCs.
CA calcula es he so-called Edge C edi = (1+∑Incoming
Edge C edi ) × Sco e o Des ina ion
Sco e o S a o each node, s a ing om he sou ce o
he sink nodes in he ci a ion ne wo k. The edge c edi sco e o a
pa icula node ep esen s he numbe o s eps om he sou ce o KDT o
he cu en node in he ci a ion ne wo k. CA emo es he edge(s) wi h
he highes o al sco e o o m clus e s.
2.3. Pa ame e selec ion
Fo bo h he MPA and CA me hods, he selec ion o algo i hm pa-
ame e s and so wa e se ings was guided by heo e ical insigh s om
he li e a u e and empi ical sensi i i y es s conduc ed on ou da ase . In
implemen ing MPA, we e alua ed se e al a e sal weigh calcula ion
me hods, namely SPC, SPLC, and SPNP. A e compa ing hese me hods,
Fig. 1. Da a collec ion and p ocessing p ocedu e.
Fig. 2. Example o a ci a ion ne wo k.
K.-C. Ying e al.
Ope a ions Resea ch Pe spec i es 14 (2025) 100340
3
we selec ed he SPLC me hod because i has been iden i ied as he mos
e ec i e app oach o ep esen ing KDT in he li e a u e [17]. In addi-
ion, his s udy es ed key- ou e alues o 10, 15, 20, 25, 30, and 35 o
de e mine he mos app op ia e key- ou e main pa h ep esen a ion.
The es esul s we e as ollows: a key- ou e alue o 10 p oduced 30
a icles, 15 p oduced 47 a icles, 20 p oduced 49 a icles, 25 p oduced
51 a icles, 30 p oduced 57 a icles, and 35 p oduced 58 a icles. Based
on hese esul s, which show a end o diminishing ma ginal e u ns,
he s udy concludes ha he mos popula a icles in his ield a e
concen a ed on he key- ou e main pa h, and u he es ing beyond
hese alues would p o ide minimal addi ional insigh s.
The e o e, conside ing he ex en o diminishing e u ns, a key- ou e
alue o 30 is deemed mos app op ia e. Fo he CA, his s udy impo ed
1937 li e a u e eco ds in o he MainPa h480 sub ou ine G oupFinde
and pe o med clus e ing using he Edge-Be weenness Clus e ing algo-
i hm. Finally, he s udy applied a key- ou e sea ch wi h a key- ou e
alue o 5 o he clus e ing esul s o iden i y he key- ou e main
pa hs, p o iding insigh s in o he ocal opics o each clus e . These
pa ame e choices and so wa e se ings ensu e ha he esul ing anal-
ysis is obus and ep oducible.
3. Resul s o he main pa h analysis
A e excluding he isola ed poin s om he o mal analysis, a o al o
22 a icles we e included o o m he global main pa h (shown in Fig. 3).
In his igu e, he size o he a ow co esponds o he SPLC alue
associa ed wi h he co esponding link. Each node ep esen s an a icle
and is labeled wi h he i s au ho ’s las name, ollowed by he ini ials o
he o he au ho s’ las names (i applicable) and he yea o publica ion.
The main pa h a icles a e discussed in ou dis inc de elopmen al
phases:
(1) 1992–2008: FSSP wi h SDSTs;
(2) 2009–2019: Hyb id/Flexible FSSP wi h SDSTs;
(3) 2020–2022: Dis ibu ed pe mu a ion FSSP wi h SDSTs; and
(4) 2022–2023: Flow shop G oup Scheduling P oblem (GSP) wi h
SDSTs.
Mos s udies on he main pa h conside ed he maximum comple ion
ime (makespan) as he op imisa ion c i e ion, bu some s udies ocus on
minimizing he o al weigh ed ea liness and a diness. These s udies
in oduced p ac ical cons ain s, such as lea ning e ec s, anspo a ion
ime, and due da es, among o he s. We p o ide a de ailed discussion o
hese a icles in he ollowing subsec ions.
3.1. 1992 o 2008
Simons1992 [19] ini ia ed he main pa h o FSSPs wi h SDSTs by
explo ing how a anging jobs while conside ing he possible se ups
could minimise he makespan. He de eloped ou heu is ic algo i hms,
among which To al and Se up, bo h based on he T a elling Salesman
P oblem (TSP), ou pe o med he minimum idle ime and minimum
comple ion ime ules in e ms o a e age pe o mance, wo s -case
scena ios, s anda d de ia ion, and he equency o bes solu ions.
Ríos-Me cadoB1998 [20] con inued Simons’s esea ch by in o-
ducing he NEHT-RB and G eedy Randomized Adap i e Sea ch P o-
cedu e (GRASP) heu is ics and compa ing hem wi h Simons’s SETUP
o sol ing FSSPs wi h SDSTs. Minimising he makespan, hey showed
ha NEHT-RB and GRASP ou pe o med SETUP when he se up ime
was sho e han he p ocessing ime. They also showed ha GRASP was
slowe han SETUP and NEHT-RB bu o e ed mo e di e se solu ions.
Ríos-Me cadoB1990 [21] p oposed an imp o ed TSP-based heu is ic
wi h a hyb id cos unc ion o balance he impac o se up ime and
i ness alue in FSSPs wi h SDSTs. They ound ha he new algo i hm
could p oduce be e solu ions in mos cases and was mo e e icien han
GRASP. The same au ho s, Ríos-Me cadoB1990 [22] p oposed a new
b anch-and-bound me hod o sol ing pe mu a ion FSSPs wi h SDSTs.
Thei app oach in oduced lowe bound calcula ion me hods, including
he gene alized lowe bound and machine-based lowe bound, o
Non-Linea P og amming (NLP). They used a new c i e ion o a oid
unnecessa y b anches and o selec he subp oblem wi h he smalles
lowe bound o b anching. The expe imen al esul s showed ha hei
algo i hm was supe io o he Linea P og amming (LP) me hods con-
ce ning e iciency and e ec i eness.
RuizMA2005 [23] sough o minimise he makespan in FSSPs wi h
SDSTs using wo ad anced Gene ic Algo i hms (GAs), one o which was
hyb idized wi h a local sea ch me hod. They compa ed hese wi h
imp o ed e sions o Simula ed Annealing (SA), Tabu Sea ch (TS),
Va iable Neighbo hood Sea ch (VNS), and I e a ed Local Sea ch (ILS).
RuizS2008 [24] add essed FSSPs wi h SDSTs, which a e commonly
encoun e ed in wa e manu ac u ing. They hyb idized he IG wi h a
local sea ch module (IG_RSLS) o minimise he makespan and o al
weigh ed a diness. Compa ing he basic and imp o ed algo i hms wi h
14 o he solu ion me hods showed ha IG was supe io o o he me hods
in e ms o solu ion quali y and e iciency and led o he disco e y o
Fig. 3. The global main pa h in he li e a u e on scheduling wi h se up ime.
K.-C. Ying e al.
Ope a ions Resea ch Pe spec i es 14 (2025) 100340
4
new bes -known solu ions.
3.2. 2009 o 2019
Nade iZR2009 [25] de eloped a hyb id SA wi h a local sea ch
module o sol e hyb id FSSPs wi h SDSTs, aiming o minimise he
makespan and maximum a diness. They in oduced se e al imp o e-
men s o he SA algo i hm, such as he mig a ion mechanism and he
gian leap. The algo i hm pe o med excep ionally well, ega dless o
he ins ance ype. Nade iRZ2009 [26] in oduced he hyb id lexible
FSSP wi h SDSTs. They de eloped he modi ied dynamic dispa ching
ule and he ILS algo i hm o minimise he makespan. MDDR alloca es
jobs o machines based on hei ea lies comple ion imes while a oiding
longe se up imes. ILS applies local sea ch and pe u ba ion ope a o s
o imp o e he explo a ion powe o he algo i hm. The au ho s
compa ed hese algo i hms wi h he s a e-o - he-a o demons a e hei
e ec i eness.
PanWMZZ2013 [27] de eloped he A i icial Bee Colony (ABC) al-
go i hm o sol e hyb id FSSPs wi h SDSTs, which a e p e alen in he
s eelmaking indus y, minimising wai ing ime and he cas ing s a ime
wi h ea ly/ a dy penal ies. The p oblem in ol es h ee consecu i e
s ages wi h pa allel machines. They in oduced a heu is ic me hod o
gene a e he ini ial solu ion and adop ed new neighbou hood sea ch
mechanisms. PanWLD2014 [28] imp o ed he ABC algo i hm h ough
hyb id ep esen a ion, enhanced sea ch s a egies, and es ed a disc e e
a ian o sol e he hyb id FSSP wi h SDSTs, conside ing he makespan.
They u ilised 24 heu is ic ules o gene a e ini ial solu ions, es ed a new
con ol pa ame e o balance explo a ion and exploi a ion, and in o-
duced an enhanced sea ch s a egy o p e en he algo i hm om alling
in o local op ima. PanRA2017 [29] explo ed hyb id FSSP wi h SDST and
ime-window cons ain s and de eloped he ILS and IG algo i hms o
minimise weigh ed ea liness and a diness cos s. They in oduced a
no el solu ion ep esen a ion me hod ha only so s he jobs in he i s
s age and uses a dispa ch ule o de e mine he alloca ions and he job
o de s in la e s ages. PanGLG2017 [30] s udied hyb id FSSP wi h SDST
and de eloped nine heu is ics and me aheu is ics o sol e he p oblem,
conside ing he makespan. These algo i hms a e a ian s o ILS, IG,
Imp o ed F ui Fly Op imisa ion (IFFO), Imp o ed Mig a ing Bi ds
Op imisa ion (IMBO), and he disc e e ABC. They ound ha he disc e e
ABC ou pe o med he benchma ks.
Kha eA2019 [31] also sol ed hyb id FSSP wi h SDST and
ime-window cons ain s by de eloping h ee popula ion-based op i-
misa ion algo i hms, conside ing he o al weigh ed cos o he ea ly and
a dy jobs. The Hyb id Squi el Sea ch Algo i hm (HSSA),
Opposi ion-Based Whale Op imisa ion Algo i hm (OBWOA), and
Disc e e G ay Wol Op imisa ion (DGWO) we e coupled wi h VNS,
Hyb id Local Sea ch (HLS), and Opposi ion-Based Lea ning (OBL)
me hods o achie e he s udy objec i es.
3.3. 2020 o 2022
HuangPG2020 [32] s udied he dis ibu ed pe mu a ion FSSP wi h
SDSTs o minimise he makespan using an imp o ed e sion o he IG
algo i hm. The p oblem in ol ed job assignmen s o a se o pa allel
plan s, each o which consis s o mul iple machines and ope a es as a
p ocess plan . The imp o ed IG employed a es a scheme and a con ol
pa ame e o egula e solu ion di e si y and help he algo i hm escape
om local op ima.
MengP2021 [33] in oduced lo s eaming and ca yo e SDST ea-
u es in dis ibu ed pe mu a ion FSSPs wi h he e ogeneous ac o ies.
They p oposed a Mixed-In ege Linea P og amming (MILP) model and
he Enhanced ABC algo i hm o sol e he p oblem wi h he aim o
minimising he makespan in all ac o ies. The he e ogeneous a ian o
dis ibu ed pe mu a ion FSSP conside s mul iple di e en ac o ies wi h
unique p ocess ypes and mul iple machines. Ca yo e SDSTs means
ha he eede on he machine needs o be eplaced o adjus ed o
p epa e he equi ed pa s be o e p ocessing he i s sub-ba ch o a new
job sequence. This a icle was he i s o s udy he decen alized he -
e ogeneous scheduling p oblem ha combines ba ch pa i ioning and
cumula i e SDST, demons a ing high p ac icali y.
RossiN2021a [34] s udied he mixed-no-idle e sion o dis ibu ed
FSSP wi h SDSTs. They p oposed a ma hema ical o mula ion along wi h
a cons uc i e heu is ic o sol e i . The de eloped solu ion algo i hm
ou pe o med he s a e-o - he-a on a la ge new da ase de eloped by
he au ho s RossiN2021a [34]. HanHZQLLG2022 [35] in es iga ed he
dis ibu ed blocking FSSP wi h SDSTs, aiming o minimise ene gy con-
sump ion cos s while balancing esou ces ac oss ac o ies using an
imp o ed e sion o he IG algo i hm. Thei IG algo i hm was imp o ed
h ough in eg a ion wi h VNS. The algo i hm includes an e icien
ini ializa ion heu is ic, wo dis inc local sea ch s a egies, and a
lea ning-based VNS s a egy. The s udy in oduced a scheduling model
o high p ac ical signi icance.
QinHWLLP2022 [36] s udied he blocking hyb id low shop GSP,
cha ac e ised by a ac o y se ing wi hou a empo a y s o age a ea.
They p oposed a no el IG algo i hm o minimise he makespan. This
g oup o s udies demons a es ha schola s’ ocus in sol ing di e en
a ian s o he Dis ibu ed Scheduling P oblem (DSP) has g adually
shi ed owa d de eloping adap able algo i hms and away om basic
op imisa ion p oblems o mo e complex, eal-wo ld p oduc ion se ings.
3.4. 2022 o p esen
The s udy by QinHWLLP2022 [36] on blocking hyb id low shop GSP
inspi ed ou new esea ch di ec ions. SekkalB2023 [37] s udied he
low shop GSP wi h SDSTs, inco po a ing lea ning e ec s and ans-
po a ion ime. They aimed o simul aneously minimise bo h he
makespan and ene gy consump ion using an MILP model and he
Mul i-Objec i e Simula ed Annealing (MOSA) algo i hm. They consid-
e ed he p ac ical case o o ged connec ing ods o demons a e he
impac o g ouping echnology and lea ning e ec s on p oduc ion
scheduling.
WangHWLGL2023 [38] s udied he dis ibu ed low shop GSP o
minimising he makespan. They p oposed an MILP model along wi h a
wo-s age I e a i e G eedy ( IG) algo i hm o sol e i . They sugges ed
ha he dis ibu ed low shop GSP can be op imised by sol ing h ee
speci ic sub-p oblems. The IG algo i hm bene i s om wo collabo a i e
neighbou hood sea ch s a egies ac oss and wi hin ac o ies, as well as
wo enhanced sea ch s a egies ac oss and wi hin g oups. Using a
da ase o 810 es ins ances, hey demons a ed ha IG algo i hm
ou pe o med he s a e-o - he-a algo i hms.
LiHZWLG2023 [39] s udied a hyb id FSSP wi h SDSTs, inco po a ing
ba ch p ocessing machines, a iable sub-ba ches, and anspo a ion
ime, wi h he objec i e o maximising he o al e enue. The pape
p oposed an MILP o mula ion and de eloped a new collabo a i e IG
algo i hm ea u ing a no el des uc ion-cons uc ion s a egy o con ol
sub-ba ches du ing he ba ch p ocessing s age. They also in oduced a
dynamic accep ance c i e ion o balance he algo i hm’s exploi a ion
and explo a ion capabili ies.
Finally, WangHPLW2023 [40] s udied hyb id low shop GSP and
p oposed se e al MILP models as well as a cons ain p og amming
app oach o minimise he makespan while add essing a ious p ac ical
cons ain s. Thei expe imen s showed ha wo o he o mula ions
pe o m signi ican ly be e , highligh ing he e ec i eness o combining
sequen ial GSP wi h posi ional adjacency modelling o jobs wi hin he
g oups. O e all, he mos ecen s udies ha e ocused on g oup sched-
uling, add essing he complexi y and di e si y o GSP.
4. Resul s o he key ex ension analysis
A e iden i ying he main KDTs in he SDST li e a u e, in es iga ing
he key ex ensions om his pa h will o e an o e iew o he inno a-
i e ends. This sec ion elabo a es on he main de elopmen b anches,
K.-C. Ying e al.
Ope a ions Resea ch Pe spec i es 14 (2025) 100340
5
conside ing a o al o 57 documen s om Key ou e30 (See Sec ion 2.2);
he o e iew is exhibi ed in Fig. 4.
The key b anches a e o med along h ee de elopmen al s ages
( ep esen ed by solid blue lines), aking in o accoun he ime ac o o
he sepa a ion/in eg a ion nodes. Do ed ames a e used o delinea e
de ailed b anching pa hs wi hin each s age. Node colou s signi y he
p oblem o in e es , wi h ed, g een, and blue ep esen ing s udies on
ba ch scheduling, low shop, and GSPs, espec i ely. The ligh colou s
iden i y he subca ego ies. The pink colou e e s o he Pa allel Machine
Scheduling P oblem (PMSP), and ligh g een, b igh g een, and da k
g een co espond o pe mu a ion, hyb id, and dis ibu ed FSSPs,
espec i ely. Finally, he node’s colou a he in e sec ion poin is
de e mined based on he documen con en .
Since he a icles om he global main pa hs ha e al eady been
e iewed, his sec ion ocuses on he emaining 35 documen s ha
cons i u e he b anches in Fig. 4. The igu e shows h ee new sou ce
nodes, i.e., SinghF1987 [41], O acikU1993 [42], and
Si ikaya-se i ogluU1999 [43], in addi ion o hose on he global main
pa h. The h ee new sou ce nodes a e om he ed ca ego ies; he
esul ing b anch lines om he sou ce nodes me ge in o o he pa hs
du ing he de elopmen p ocess bu e en ually con e ge in o he global
main pa h. The da k and ligh g een pa hs b anch ou om he middle
and sides o he global main pa h and la e con e ge back in o i .
O e all, he key ex ensions ini ially e ol ed a ound FSSP and
e en ually de eloped in o low shop GSPs; his highligh s ha he mos
in luen ial p oduc ion planning s udies on SDSTs ocus p ima ily on he
low shop se ing. The de elopmen b anches in he i s s age explo e
h ee hemes: (1) The ligh g een pa h, de eloped om he sou ce poin
o Simons1992 [19] cen es a ound FSSP. (2) The pink- o-g een shi in
he le -hand-side b anch, which s a s om O acikU1993 [42] and
Si ikaya-se i ogluU1999 [43], depic s he ans o ma ion o PMSPs
in o FSSP. (3) The ed b anch line on he igh -hand side, ini ia ed by
SinghF1987 [41], b anches ou in o wo sub-b anches: he o me de-
elops om F ançaGLM1996 [44] and depic s a ans o ma ion om
PMSPs o FSSPs, while he la e ep esen s a shi om he
single-machine ba ch scheduling p oblem o he pa allel-machine ba ch
scheduling p oblems. We now del e deepe in o he de elopmen
b anches.
4.1. B anch I
The i s sou ce node, O acik1993 [42], sol ed he PMSP wi h SDSTs
o minimise he makespan and he maximum delay ime. They assumed
ha he se up ime would no exceed he p ocessing ime o he wo k
o de , inspi ed by he inal es s age in semiconduc o manu ac u ing,
whe e di e en ba ches o ci cui s need o be es ed a a ious
Fig. 4. The key b anches eme ged om he main pa h in he SDSTs li e a u e.
K.-C. Ying e al.
Ope a ions Resea ch Pe spec i es 14 (2025) 100340
6
empe a u es (i.e., empe a u e-dependen changes in SDSTs). They
de i ed he wo s -case e o bounds o a bi a y and speci ic-lis
scheduling algo i hms o scheduling wi h bounded SDSTs and p o ed
ha he e o bounds o hei p oposed algo i hms we e accu a e.
The o he sou ce node, Si ikaya-se i ogluU1999 [43], also s udied
he PMSP wi h SDSTs bu conside ed o al ea liness and delay cos s as
he op imisa ion objec i e. They de eloped a GA wi h no el c osso e
ope a o s o sol e he p oblem. By compa ing i wi h o he GAs, hey
ound ha hei de eloped me hod ou pe o med he pa ially mapped
c osso e .
Combining he di ec ions o hese wo sou ce poin s, Ku zA2001
[45] explo ed PMSP wi h SDST and elease ime, aiming o minimise he
makespan. They de eloped and es ed ou heu is ic algo i hms o
app oxima e he op imal solu ion. They also analysed he ac o s
impac ing he p oblem complexi y and es ed new echniques o
ob aining lowe bounds. Ku zA2003 [46] began o in es iga e how o
a ange a se o jobs o minimise he makespan in he lexible FSSP wi h
SDSTs. They p oposed h ee heu is ics: he Cyclic Heu is ic, he Mul iple
Inse ion Heu is ic, and Johnson’s Rule-based Heu is ic. Thei expe i-
men al analysis showed ha he algo i hm based on Johnson’s ule
pe o med bes in e ms o a e age loss, s anda d de ia ion, and
maximum loss, while he inse ion algo i hm achie ed be e solu ions
based on he equency o inding he minimum loss solu ion.
RuizM2006 [47] p oposed a no el op imisa ion me hod based on GA o
sol e hyb id FSSPs in ol ing un ela ed pa allel machines, SDSTs, and
machine adap a ion. They conduc ed an ex ensi e nume ical analysis
using da a om he ce amic ile manu ac u ing indus y, demons a ing
ha hei algo i hm ou pe o med he s a e-o - he-a .
Finally, RuizS2007 [24] in es iga ed pe mu a ion FSSP wi h SDSTs,
which a e p e alen in wa e manu ac u ing. They ex ended he IG al-
go i hm o maximise he numbe o p ocessed jobs, minimise he
makespan, and minimise he makespan o non-bo leneck machines.
They in oduced a local sea ch mechanism and an SA-inspi ed accep-
ance c i e ion o enhance he pe o mance o he IG algo i hm. The
de eloped algo i hm ou pe o med 14 solu ion me hods and iden i ied
new bes solu ions o some es ins ances.
O e all, his esea ch b anch signi ies he expansion o he esea ch
scope on SDSTs om PMSPs o mo e complex FSSPs, as well as a g adual
ad ancemen o solu ion algo i hms, om lis scheduling algo i hms o
he IG algo i hm and heu is ics.
4.2. B anch II
This b anch illus a es he con e gence o wo pa hs in RuizS2008
[24]. One pa h ep esen s a b ie de elopmen om Ríos-Me cadoB1999
[22] o Ríos-Me cadoB2003 [48], while he o he pa h ex ends om
SinghF1987 [41] o Dobson1992 [49], which u he b anches in o
F ançaGLM1996 [44]. The KDT be ween Simons1992 [19] and
RuizS2008 [24] has al eady been explained in Sec ion 4.1. This sub-
sec ion ocuses on he pa hs om Ríos-Me cadoB1999 [22] and Dob-
son1992 [49] in wo dis inc pa s.
The i s pa (i.e., Simons1992 [19]→Ríos-Me cadoB2003 [48]) is
o med a ound FSSPs. The second pa o his b anch (i.e., F an-
çaGLM1996 [44]→Rajend anZ2003 [50]) begins wi h PMSPs and hen
ansi ions o FSSP. In he i s pa , Ríos-Me cadoB2003 [48] s udied
FSSP-SDST o minimise he makespan. They p oposed wo MILP models
based on he polyhed al s uc u e o he asymme ic TSP and he Linea
O de ing P oblem (LOP) and p o ed ha he ea u es and inequali ies o
he asymme ic TSP and he LOP can be di ec ly applied o sol ing he
scheduling issues. Nume ical expe imen s showed ha hei p oposed
me hod could imp o e he lowe bound in LP and sol e medium-sized
ins ances wi hin a easonable ime.
In he second pa , F ançaGLM1996 [44] ex ended he p oblem
de eloped by Dobson1992 [49] o he Mul ip ocesso Scheduling
P oblem (MSP), which e e s o iden ical PMSP-SDST o he makespan
minimisa ion. They de eloped a TS algo i hm ha could adap o
asymme ic se up imes and, hence, imp o e he solu ion quali y. The
de eloped solu ion me hod ou pe o med he Nea es -Neighbo Heu-
is ic algo i hm.
Radhak ishnanV2000 [51] s udied PMSP-SDST while minimising
ea liness and a diness cos s and de eloped an SA algo i hm o ind
nea -op imal solu ions o he p oblem. Th ough a se ies o compu a-
ional expe imen s, he pe o mance o he SA me hod was e alua ed
and compa ed wi h ha o a local sea ch-based heu is ic. Rajen-
d anZ2003 [50] discussed he FSSP-SDST o minimising he o al
weigh ed low ime and delays and in oduced a new heu is ic algo i hm
o app oxima ion. In hei model, ac o s such as in en o y o holding
cos s, con ac ing cos s, and cus ome sa is ac ion we e conside ed.
4.3. B anch III
The sou ce node, SinghF1987 [41], s udied he SMSP-SDST consid-
e ing mul iple p oduc s and p oposed a h ee-s age op imisa ion
amewo k. Thei me hod iden i ied a easible p oduc ion schedule wi h
a minimum sum o in en o y and main enance cos s wi hin a gi en
planning pe iod. Dobson1992 [49]’s Cyclic Lo Scheduling P oblem
(CLSP) was a con inua ion o his de elopmen pa h.
Dobson1992 [49] s udied CLSP wi h SDSTs. In his p oblem, he
p oduc ion ba ch size and p oduc ion sequence a e ixed, and he lead
ime a ies depending on he cha ac e is ics o he p oduc s. They p o-
posed a mixed-in ege p og amming model and a local-sea ch-based
heu is ic obus o di e en SDST con igu a ions. The s udy o
Haase1996 [52] is abou capaci a ed ba ch scheduling; hey p oposed a
new ma hema ical o mula ion called he capaci y-limi ed and
sequence-dependen ba ch p oduc ion p oblem. Thei me hod di e s
om ea lie models by allowing con inuous ba ch sizes, mul iple se up
imes, and idle imes. They also de eloped he Backwa d S ee ing heu-
is ic algo i hm o sol e he p oblem. KangMT1999 [53] explo ed
pa allel-machine ba ch scheduling wi h SDST in a mul i-pe iod p o-
duc ion sys em; hey de eloped a solu ion me hod based on column
gene a ion and b anch-and-bound o minimise he di e ence be ween
ope a ional cos s and sales e enue unde he condi ion ha he demand
o each p oduc in each pe iod does no exceed he p oduc ion capaci y.
They also es ed wo heu is ics o speed up he mul i-pe iod scheduling.
Mey 2002 [54] ex ended hei s udy o he gene al lo -sizing and
scheduling p oblem o pa allel p oduc ion lines o minimise p oduc-
ion, in en o y, and SDST- ela ed cos s. They de eloped a hyb id solu-
ion me hod o sol e a eal-wo ld p oblem in he consume goods
indus y. Cla k2003 [55] p oposed h ee MIP models o ba ch sched-
uling wi h capaci y cons ain s and SDSTs o op imise he Mas e P o-
duc ion Schedule (MPS) and Ma e ial Requi emen s Planning (MRP).
Conside ing he high compu a ional complexi y o hese models, wo
app oxima ion algo i hms we e de eloped o educe he numbe o bi-
na y a iables, and a heu is ic me hod called Relax-and-Fix was used o
decompose he o iginal model in o a se ies o smalle sub-p oblems.
Dea aujoAC2007 [56] p oposed an e ec i e solu ion me hodology
using MIP app oaches and heu is ics o in eg a ed lo -sizing and
scheduling p oblems, conside ing la e o de s and SDST. They employed
he Relax-and-Fix me hod and pe o med compu a ional es s wi h a
high-pe o mance MIP sol e . Addi ionally, he au ho s de eloped h ee
local sea ch me hods o imp o e he pe o mance o he Relax-and-Fix
me hod.
Fe ei aMR2009 [57] p oposed an MIP model o in eg a ed p o-
duc ion lo -sizing and scheduling decisions in he be e age indus y.
Thei s udy ocused on p oduc ion bo lenecks and in e -s age syn-
ch oniza ion equi emen s. The au ho s p oposed a Relax-and-Fix-based
solu ion me hod and explo ed di e en a iable spli ing and ixing
s a egies o sol ing he p oblem. TosoMC2009 [58] explo ed a com-
plex p oduc ion scheduling p oblem ha in ol es mul iple p oduc s and
SDSTs o a wo-s age p oduc s uc u e. They p oposed an in eg a ed
MIP o mula ion including in en o y and lo size a iables and
app oached he op imisa ion objec i e based on he T anspo a ion
K.-C. Ying e al.
Ope a ions Resea ch Pe spec i es 14 (2025) 100340
7
P oblem (TP). Cla kMT2010 [59] p oposed a new app oach o com-
bined p oduc ion lo -sizing and scheduling based on he asymme ic TSP
and es ed i s applica ion in he animal nu i ion p oduc ion indus y.
They compa ed di e en MILP models and solu ion me hods, high-
ligh ing he ad an ages o he asymme ic TSP model in sol ing he
p oblem o minimising in en o y, delay, and o e ime cos s while
conside ing p ac ical cons ain s such as capaci y, demand, and mini-
mum ba ch size.
T anschelMKLE2011 [60] esea ched join lo -sizing and scheduling
o p oduc ion wi h a wo-s age p oduc s uc u e, conside ing SDSTs.
The au ho s p oposed a hyb id MIP o mula ion based on he
Quan i y-based T anspo a ion P oblem (QTP) and he
P opo ion-based T anspo a ion P oblem (PTP). Thei model add esses
p ac ical cons ain s such as minimum p oduc ion quan i ies be ween
p oduc s while minimising ope a ional cos s. Seeanne M2013 [61]
p oposed an MIP model ha akes in o accoun p oduc ion ac o s such
as capaci y, SDSTs, holding cos s, ex e nal p ocu emen , o e ime, and
s andby o minimise o al cos s in he in eg a ed p oblem o lo -sizing
and scheduling. Thei s udy p oposed a gene al ime s uc u e ha can
lexibly a oid lead ime be ween di e en p oduc ion s ages and allow
o spli ing p oduc ion ba ches and se up ime wi hin each scheduling
pe iod o imp o e e iciency. Seeanne AM2013 [62] con inued he
de elopmen pa h o in eg a ed lo -sizing and scheduling in a
mul i-le el p oduc ion sys em. They de eloped a solu ion me hod ha
combines Va iable Neighbo hood Decomposi ion Sea ch (VNDS) and
Fix & Op imise. The de eloped scheme demons a ed high lexibili y
and e ec i eness in sol ing complex scheduling p oblems, such as he
gene al lo -sizing and scheduling p oblem o mul iple p oduc ion
s ages.
O e all, he s udies unde his b anch no only ake in o accoun he
complexi y o p oduc ion schedules bu also conside a ious ac o s in
eal-li e p oduc ion en i onmen s. F om he ea ly s udies on single-
machine mul i-p oduc p oduc ion scheduling o he la e mul i-s age
ba ch scheduling, his b anch has con ibu ed o he de elopmen s in
FSSPs. Con inuing om he las node o his b anch, SioudG2018 [63]
de eloped a me aheu is ic o sol ing pe mu a ion FSSP wi h SDSTs o
minimise he makespan.
4.4. B anch IV
The li e a u e on his pa h includes publica ions be ween 2009 and
2018; his pa h b anches ou om Nade iZR2009 [25] (hyb id low
shops) in he global main pa h o Nade iZS2009 [64] ( lexible low
shops) and con inues o LiYRCS2018 [65] (no-wai low shop). This
b anch will la e me ge in o he global main pa h h ough
HuangPG2020 [32], which explo es dis ibu ed FSSPs.
Nade iZS2009 [64] adjus ed he Elec omagne ism Algo i hm (EMA)
o sol e he lexible FSSP wi h SDSTs and independen anspo a ion
imes, assuming mul iple anspo a ion ools o job deli e y. The goal
was o minimise he o al weigh ed a diness o enhance p oduc ion
e iciency and educe delays. The p oblem was ma hema ically
modelled using MILP and sol ed using EMA o la ge-scale ins ances.
JolaiRA2012 [66] s udied he no-wai e sion o he lexible FSSP
in ending o minimise he makespan; hey de eloped he
popula ion-based SA, an adap ed e sion o he Impe ialis Compe i i e
Algo i hm (ICA), and a hyb id e sion o he wo o sol e his p oblem.
Sama ghandiE2014 [67] ex ended he Pa icle Swa m Op imisa ion
(PSO) algo i hm o sol e he no-wai FSSP-SDST conside ing he
makespan. They in oduced he ma ix coding mechanism ha enables
he solu ion algo i hm o handle SDSTs mo e e ec i ely. Naga-
noDN2014 [68] s udied he no-wai a ian o FSSP-SDST using a hyb id
o he GA and E olu iona y Clus e ing Sea ch (ECS) algo i hms equip-
ped wi h a local sea ch and conside ed he makespan as he op imisa ion
goal.
Simila ly, NaganoMA2015 [69] ocused on he no-wai FSSP-SDST
and in oduced a new cons uc i e heu is ic, called QUARTS, o
minimise he o al comple ion ime o all jobs. This p oblem has appli-
ca ions in he me al, plas ics, and chemical indus ies. Thei me hod
iden i ies he bes job sequence by decomposing he p oblem in o a
combina ion o asks. LiYRCS2018 [65] s udied he no-wai FSSP-SDST
while conside ing he lea ning e ec ; hey es ablished a posi ion-based
model o he lea ning e ec and employed i in an accele a ed con-
s uc ion heu is ic me hod embedded in o he IG algo i hm o minimise
he o al p ocess ime. This esea ch p o ided new bes - ound solu ions
o his p oblem and sugges ed new ideas o u u e esea ch.
In gene al, hese s udies demons a e ad ances in sol ing he no-wai
FSSP-SDST and i s a ian s. F om ini ial cons uc i e heu is ics o
hyb id me aheu is ics, which ake in o accoun mo e complex ac o s
ha e lec eal-wo ld si ua ions, such as amily se up imes and lea ning
e ec s.
4.5. B anch V
The pa h s a ing om Gomez-gasque AL2012 [70] and inishing a
SioudG2018 [63] has b anched om Nade iRZ2009 [26] in he global
main pa h, which s udied he hyb id lexible FSSP wi h SDSTs. This
b anch la e con e ges in o he global main pa h h ough HuangPG2020
[32], which s udied he dis ibu ed pe mu a ion FSSP wi h SDSTs.
Al hough he s udies om his b anch a e ocused on FSSP wi h SDSTs,
hei ocus di e s.
Gomez-gasque AL2012 [70] s udied hyb id FSSP wi h SDSTs o
minimise he makespan; hey imp o ed he GA wi h an agen -based
me hod, which u ilises he cha ac e is ics o so wa e agen s. In hei
me hod, new indi iduals a e gene a ed based on local compe i ion
a he han global compe i ion, which enables he pa ame e s o be
dynamically adjus ed acco ding o changes in he en i onmen and a-
cili a es he applica ion o cus omized gene ic ope a o s.
S udying FSSPs wi h SDSTs, Vanchipu aSB2014 [71] in oduced new
cons uc i e heu is ics based on Va iable Neighbo hood Descen (VND)
o minimise he makespan. Thei expe imen s showed ha he VND
me hod can conside ably imp o e he solu ion quali y. Finally,
SioudG2018 [63] ocused on pe mu a ion FSSP wi h SDST and de el-
oped a new heu is ic based on se up imes and he Enhanced Mig a ing
Bi ds Op imisa ion (EMBO) o minimise he makespan. A a ie y o
imp o ed compu a ional mechanisms we e embedded in o EMBO o
show he compe i i eness o EMBO o combina o ial op imisa ion.
4.6. B anch VI
Roo ing om PanGLG2017 [30] on he global main pa h, which
wo ked on hyb id FSSP wi h SDSTs, MengZSZRL2020 [72] began his
b anch, and LiLGZPTM2021 [73] is i s closing poin . This b anch con-
e ges in o he global main pa h h ough MengP2021 [33], which ex-
plo es he dis ibu ed pe mu a ion FSSP wi h SDSTs and he e ogeneous
ac o ies. This pa h b anched o again om MengP2021 [33], esul ing
in a b ie bu impo an pa h h ough GuoSZML2022 [74]. The e u n o
he main pa h ook place h ough HanHZQLLG2022 [35], which is
ocused on he dis ibu ed blocking FSSP wi h SDSTs.
MengZSZRL2020 [72] s udied hyb id FSSP wi h SDSTs. They p o-
posed eigh MILP models whe e he makespan is he op imisa ion
objec i e. The ex ended o mula ions accoun o no-wai and blocking
se ings o un ela ed pa allel machines. They also conduc ed nume ical
expe imen s using CPLEX o e alua e he compu a ional complexi y o
he models. LiLGZPTM2021 [73] explo ed he dis ibu ed hyb id FSSP
wi h SDSTs while in ol ing mul iple ac o ies, mul iple s ages, and
mul iple pa allel machines; he modi ied disc e e ABC algo i hm was
used o minimise he makespan in he p oposed model. In hei
app oach, an inno a i e machine posi ion-based ma hema ical model
was showcased o acili a e he encoding and decoding me hods o he
solu ion algo i hm. MengP2021 [33] in es iga ed he dis ibu ed pe -
mu a ion FSSP wi h SDSTs and he e ogeneous ac o ies, ecei ing a new
ex ension in o he ABC algo i hm wi h he goal o minimising he
K.-C. Ying e al.
Ope a ions Resea ch Pe spec i es 14 (2025) 100340
8
open shop en i onmen s. Mo eo e , u he esea ch may explo e he
applica ion o SDSTs in high- olume manu ac u ing indus ies o ali-
da e hei impac and e ine he models as needed. P ac ical imple-
men a ions in hese sec o s will enhance ou unde s anding o he
applicabili y and scalabili y o SDSTs in di e en p oduc ion se ings.
Digi al echnologies. Explo ing he cu en de elopmen ajec-
o ies o SDST con i ms a g owing end o in eg a ing eme ging digi al
echnologies, such as machine lea ning and big-da a analysis, in o
op imisa ion app oaches. This may help educe a oidable se ups and
op imise ope a ions ha a e o en in angible and non- alue-adding. The
inco po a ion o such echniques could u he imp o e he e ec i eness
and e iciency o scheduling sys ems beyond he cu en op imali y
no ms and o e no el solu ions o exis ing challenges in SDSTs.
Eme ging challenges. The e a e echnical challenges in inco po-
a ing SDSTs wi h he new indus ial landscapes, no ably Indus y 5.0
and cybe -physical sys ems. A b oade discussion is equi ed o highligh
he ele ance o SDSTs wi hin he digi al ans o ma ion con ex . Ad-
di i e manu ac u ing is ano he a ena whe e SDST equi es new de-
elopmen s. Finally, unde s anding he impac o se ups on au oma ed
manu ac u ing en i onmen s and human- obo collabo a ions will be
c i ical o ad ancing he ield and ensu ing ha mode n demands a e
well add essed.
6.3. Limi a ions o he exis ing e iew
While his s udy u ilized MPA and CA o iden i y b oad pa e ns o
knowledge de elopmen , i did no p o ide he g anula i y needed o
de ailed analyses o speci ic esea ch subg oups and s udies. In pa ic-
ula , esea ch a eas such as SDST scheduling in di e en p oduc ion
en i onmen s equi e a mo e in-dep h examina ion o hei unique
challenges, me hodologies, and ad ancemen s. Due o space cons ain s
and he me hodological na u e o MPA and CA, ou analysis p ima ily
ocuses on o e a ching ends a he han p o iding a comp ehensi e
e iew o each subg oup. Fu u e esea ch may add ess his limi a ion by
employing mo e a ge ed e iew me hodologies, such as sys ema ic
li e a u e e iews o bibliome ic analyses ha ocus on indi idual
sub ields. These app oaches would enable a deepe explo a ion o spe-
ci ic esea ch a eas, helping o unco e nuanced insigh s and iden i y
c i ical gaps wi hin each segmen o he li e a u e.
Due o he ex ensi e olume o he li e a u e analysed— o aling
2195 a icles—conduc ing a ho ough analysis and d a ing he manu-
sc ip was ime-consuming. Addi ionally, as he s a is ical analysis was
based on annual publica ions, i was no easible o include he mos
ecen li e a u e beyond 2023 in his s udy. Fu u e esea ch may add ess
his limi a ion by conduc ing he MPA e e y 5–10 yea s o pe iodically
upda e he esea ch landscape ela ed o SDSTs and inco po a e he
la es ad ancemen s in he ield.
CRediT au ho ship con ibu ion s a emen
Kuo-Ching Ying: W i ing – e iew & edi ing, Valida ion, Supe i-
sion, So wa e, P ojec adminis a ion, Me hodology, Concep ualiza-
ion. Pou ya Pou hejazy: W i ing – o iginal d a , In es iga ion,
Fo mal analysis. Zhi-Rong Lin: Visualiza ion, Me hodology, Fo mal
analysis, Da a cu a ion.
Decla a ion o compe ing in e es
The au ho s decla e ha hey ha e no known compe ing inancial
in e es s o pe sonal ela ionships ha could ha e appea ed o in luence
he wo k epo ed in his pape .
Da a a ailabili y
Da a will be made a ailable on eques .
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