Em oozi, Vahideh Ba andegan; Kazemi, Mos a a; Doos pa as , Mahdi
A icle
Enhancing indus ial main enance planning: Op imiza ion
o human e o educ ion and spa e pa s managemen
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: Em oozi, Vahideh Ba andegan; Kazemi, Mos a a; Doos pa as , Mahdi (2025) :
Enhancing indus ial main enance planning: Op imiza ion o human e o educ ion and spa e pa s
managemen , Ope a ions Resea ch Pe spec i es, ISSN 2214-7160, Else ie , Ams e dam, Vol. 14, pp.
1-24,
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Enhancing indus ial main enance planning: Op imiza ion o human e o
educ ion and spa e pa s managemen
Vahideh Ba andegan Em oozi
a,*
, Mos a a Kazemi
a
, Mahdi Doos pa as
b
a
Depa men o Managemen , Facul y o Economics and Adminis a i e Sciences, Fe dowsi Uni e si y o Mashhad, Mashhad, I an
b
Depa men o S a is ics, Facul y o Ma hema ical Sciences, Fe dowsi Uni e si y o Mashhad, Mashhad, I an
ARTICLE INFO
Keywo ds:
Human e o p obabili y
Main enance planning
In en o y con ol o spa e pa s
Manu ac u ing sys ems
ABSTRACT
Main enance is pi o al in he indus ial sec o , in luencing e iciency, eliabili y, sa e y, and p o i abili y. An
o ganized spa e pa s in en o y suppo s main enance e o s by minimizing down ime, ensu ing sa e y, and
op imizing main enance budge s. E ec i e spa e pa s managemen enhances main enance ope a ions and im-
p o es cash low. Con e sely, human e o can g ea ly diminish he e ec i eness o main enance e o s. This
pape p esen s a ma hema ical model aimed a minimizing cos s h ough op imized p e en i e main enance
(PM) planning, e ec i e spa e pa s in en o y con ol, and educ ion o human e o . The s udy p o ides
decision-make s wi h c ucial insigh s o s a egically managing main enance p ocedu es while accoun ing o
he e ec o human e o . The model is alida ed in eal-wo ld scena ios h ough sensi i i y analysis, ocusing on
he shape pa ame e o he Weibull dis ibu ion, and he equipmen ’s e ec i e a e. Findings e eal ha as he
numbe o pe iods inc eases, main enance ope a ions ollow a speci ic, p edic able cycle. Mo eo e , he op imal
human e o p obabili y (HEP) o cos minimiza ion is iden i ied as 0.02. These insigh s guide decision-make s
in ecognizing ac o s in luencing human e o and implemen ing p oac i e s a egies o enhance main enance
pe o mance.
1. In oduc ion
Main enance ope a ions a e c i ical o imp o ing o ganiza ional
e iciency and ensu ing eliable sys em pe o mance, especially when
subs an ial in es men s a e made in p oduc ion machine y [1–4]. Ine -
ec i e main enance can lead o machine ailu es, down ime, and
inc eased cos s, including oppo uni y cos s, epu a ional damage, and
dis up ions o p oduc ion schedules [5,6]. P e en i e main enance (PM)
is a widely adop ed s a egy o minimize unplanned b eakdowns and
down ime. Howe e , poo ly imed o inadequa ely execu ed PM can
nega i ely impac e iciency and incu addi ional cos s, such as esou ce
alloca ion and empo a y p oduc ion hal s. E ec i e planning and
execu ion o main enance a e he e o e essen ial o balance hese
ade-o s and op imize o ganiza ional pe o mance [7–10].
Op imal planning o main enance ope a ions depends hea ily on he
e ec i e managemen o spa e pa s in en o y. Excessi e spa e pa s
in en o y can lead o highe holding cos s and unnecessa y expendi-
u es, while insu icien in en o y can p olong down ime and esul in
g ea e losses due o machine inac i i y [8–10]. To add ess hese chal-
lenges, i is c ucial o op imize he spa e pa s in en o y con ol policy.
This p esen s a signi ican challenge in balancing cos s h ough op imal
in en o y managemen while ensu ing sys em eliabili y [11,12].
Bo h PM and co ec i e main enance (CM) signi ican ly in luence he
condi ion and i ual age o machine y. E ec i e main enance planning
mus accoun o hese ac o s o op imize he iming and equency o
PM ope a ions, he eby enhancing machine eliabili y. Howe e , e en
well-planned main enance can ail due o human e o , leading o
imp ope implemen a ion and inc eased sys em cos s. Human E o
P obabili y (HEP) is a quan i a i e measu e used o es ima e he likeli-
hood o human e o s occu ing in speci ic asks o sys ems [13,14]. I is
commonly employed in human eliabili y analysis (HRA) o e alua e
sa e y in indus ies such as a ia ion, nuclea powe , heal hca e, and
manu ac u ing. HEP is ypically exp essed as a p obabili y alue anging
om 0 (no chance o e o ) o 1 (ce ain y o e o ) [10,15].
HEP du ing PM, CM, o inspec ions can unde mine he e ec i eness
o main enance and in la e cos s. To mi iga e his, main enance plans
mus inco po a e s a egies o educe human e o , ensu ing bo h cos
e iciency and imp o ed machine eliabili y [16–18]. Gi en he signi -
ican impac o human e o on main enance ope a ion cos s and he
i ual age o machines, i is essen ial o conside human e o s when
* Co esponding au ho .
E-mail add esses: [email p o ec ed] (V. Ba andegan Em oozi), [email p o ec ed] (M. Kazemi), [email p o ec ed] (M. Doos pa as ).
Con en s lis s a ailable a ScienceDi ec
Ope a ions Resea ch Pe spec i es
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Ope a ions Resea ch Pe spec i es 14 (2025) 100336
A ailable online 1 Ap il 2025
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op imizing main enance plans.
In his s udy, da a on human e o , cos s, and he i ual age o
machines we e collec ed om his o ical da a in a case s udy. The cos o
human e o and he machine’s i ual age unc ions we e es ima ed
using a eg ession me hod based on HEP. Thus, he p oposed model
quan i a i ely inco po a es human e o , highligh ing i s e ec s on cos s
and he i ual age o he machine. When es ima ing he cos unc ion,
wo key challenges a ise. Fi s , he cos associa ed wi h human e o in
main enance ope a ions inc eases as he le el o e o ises. Second,
imp o ing con ex ual ac o s o mi iga e human e o also incu s addi-
ional cos s. Con ex ual ac o s, which include en i onmen al, o gani-
za ional, and ask- ela ed elemen s, play a c i ical ole in shaping HEP.
By iden i ying, assessing, and op imizing hese ac o s, indus ies can
e ec i ely educe human e o s, enhance sa e y measu es, and imp o e
o e all sys em eliabili y.
The e o e, he cos unc ion o human e o ela ed o main enance
ope a ions is es ima ed by conside ing bo h aspec s. Consequen ly,
op imizing main enance plans and minimizing human e o a e essen ial
o educing cos s and achie ing economic success ac oss a ious in-
dus ies. Al hough human e o signi ican ly a ec s main enance ope -
a ions, p e ious s udies ha e la gely o e looked his aspec , ocusing
ins ead on non-human ac o s. While spa e pa s ha e been examined in
some s udies, none ha e speci ically in es iga ed he epe cussions o
human e o in main enance ope a ions. The model p esen ed in his
pape quan i a i ely conside s he in luence o human e o , con ib-
u ing o a mo e comp ehensi e analysis o he p oblem.
The esea ch ocuses on a case s udy o a cemen company ha
ope a es con inuously, u ilizing hea y machine y wi h signi ican in-
es men . Gi en he cha ac e is ics o he indus y, p ope and op imal
main enance ope a ions a e c ucial o minimizing s ochas ic b eak-
downs and o al cos s. The model p esen ed o his case s udy is mul i-
p oduc , mul i-machine, and mul i-condi ion, p o iding a comp ehen-
si e app oach o he p oblem. The objec i e o his esea ch is o iden i y
he op imal alues o in en o y managemen o spa e pa s, as well as
o planning PM and CM ope a ions, while conside ing he impac o
associa ed human e o s. Acco dingly, in line wi h p e ious s udies in
his ield, we emphasize i e majo con ibu ions o his pape :
1. Impac o Human E o s on Equipmen U iliza ion and Vi ual
Age:
The s udy in es iga es how human e o s a ec he e ec i e a e
o equipmen u iliza ion and he i ual age o equipmen . By
modeling hese ela ionships, he esea ch o e s insigh s in o how
human e o s accele a e equipmen de e io a ion and p o ides
s a egies o minimize hei impac on ope a ional e iciency.
2. De elopmen o an In eg a ed Op imiza ion Model:
The s udy p oposes a no el op imiza ion model ha in eg a es
main enance ope a ions, spa e pa s in en o y con ol, and human
e o managemen in o a uni ied amewo k. This holis ic app oach
add esses he in e dependencies be ween hese componen s,
enabling mo e e icien and cos -e ec i e decision-making.
3. Inno a i e Main enance Planning Inco po a ing Equipmen
Li espan:
The esea ch pionee s a quan i a i e app oach o main enance
planning by in eg a ing equipmen condi ions and li espan in o he
decision-making p ocess. A no el cons ain is in oduced o accoun
o equipmen li espan, allowing o he de e mina ion o h eshold
limi s o main enance ac i i ies in an inno a i e and sys ema ic
manne .
4. Conside a ion o Machine Se up Cos s Du ing Down ime:
The s udy inco po a es machine se up cos s du ing p oduc ion line
down ime caused by PM and CM ope a ions. This inclusion allows
o mo e accu a e budge ing and esou ce alloca ion, op imizing
p oduc ion e iciency and minimizing inancial dis up ions du ing
main enance pe iods.
5. Simul aneous Implemen a ion o Condi ion-Based Main enance
(CBM) and Time-Based Main enance (TBM):
Unlike adi ional PM models ha ely solely on ime- o usage-
based scheduling, his s udy in eg a es bo h CBM and TBM o
enhance main enance decision-making.
6. P ac ical Applica ion and Valida ion:
The model is applied o a eal-wo ld case s udy o a cemen ac o y,
u ilizing da a om main enance logbooks o alida e i s e ec i e-
ness. This p ac ical applica ion demons a es he model’s abili y o
add ess eal indus ial challenges and imp o e main enance p ac-
ices in complex ope a ional en i onmen s.
7. Quan i a i e Analysis o Human E o Cos s in Main enance:
The esea ch in oduces a no el ma hema ical model o quan i y
he cos s associa ed wi h human e o in main enance asks. Using
eg ession me hods, he s udy es ima es he cos unc ion linked o
he p obabili y o human e o , add essing a c i ical gap in exis ing
li e a u e. This app oach p o ides a sys ema ic way o e alua e and
mi iga e he inancial impac o human e o s.
The emainde o his pape is o ganized as ollows:
The second sec ion o e s a concise o e iew o p io esea ch on his
opic. The p oblem s a emen and case s udy a e p esen ed in Sec ion 3.
Sec ion 4 de ails he me hods employed in his s udy. The esea ch
indings a e p esen ed in Sec ion 5. Sec ion 6 examines he sensi i i y
analysis conduc ed o alida e he p oposed model. Las ly, Sec ion 7
p esen s manage ial insigh s, while Sec ion 8 discusses no able conclu-
sions and o e s sugges ions o u u e s udies.
2. Li e a u e e iew
Resea ch conduc ed in his ield ocused on main enance ope a ions
exclusi ely and igno ed human e o ’s impac on hese ope a ions. Liu
e al. [19] in oduced a model ha akes in o accoun bu e in en o y
and impe ec PM in p oduc ion sys em. Zheng e al. [6] highligh ed he
cos -e ec i eness o policies based on p oduc ion quan i y and
condi ion-based main enance o managing a de e io a ing p oduc ion
sys em. Lynch, e al. [20] in es iga ed he impac o an e ec i e main-
enance sys em on indus ial pe o mance. Bismu e al. [21] imp o ed
he main enance and inspec ion s a egies o he piping sys ems in
nuclea uel powe plan s. Emami-Meh gani e al. [22] examined he
e ec s o human e o s on epai able p oduc ion sys ems and p oposed
an op imal policy o educe p oduc ion cos s.. Mo a o e al. [23] in o-
duced op imal main enance planning o de e io a ing s uc u al com-
ponen s using a Dynamic Bayesian Ne wo k (DBN) and Ma ko decision
p ocess.
Szpy ko e al. [24] p oposed a compa ible and s aigh o wa d
simula ion app oach based on a isk assessmen model o op imize
main enance scheduling in di e en case s udies. Liu e al. [25] p o-
posed an in eg a ed model ha akes in o accoun bu e s ocks and
impe ec PM in p oduc ion sys ems. Sha i i and Taghipou [26] p o-
posed an in eg a ed model o p oduc ion and main enance planning.
Kim e al. [27] p esen ed a po en ial app oach o op imizing inspec ion
and main enance planning. Zhang e al. [12] explo ed he simul aneous
op imiza ion o main enance and spa e pa s in en o y o a
se ies-pa allel sys em wi h dual ailu e modes.
Nas a d e al. [28] in oduced a Pe i ne model ha conside s he
s a e o de e io a ion, inspec ion, age-dependen epai p ocesses, and
andom epai . B iˇ
s and Thuy T an [29] s udied he p oblem o
mul i-objec i e main enance op imiza ion o minimize cos s and maxi-
mize a ailabili y. Saleh e al. [30] in oduced an in elligen Pe i ne
algo i hm o op imize main enance ope a ions o wind u bines. Fek i
e al. [31] explo ed he wo kshop low scheduling p oblem wi h limi ed
mul i-skilled human esou ces in PM. Zhu e al. [32] in oduced an
op imiza ion model and algo i hm o spa e pa s, aking in o accoun
ade-o s be ween cos and ime as well as p ecedence cons ain s. Jiang
e al. [33] op imized PM in e al and he maximum in en o y le el,
V. Ba andegan Em oozi e al.
Ope a ions Resea ch Pe spec i es 14 (2025) 100336
2
wi h he ul ima e goal o minimizing sys em down ime and in en o y
holding cos s.
Cao e al. [34] examined an op imiza ion model o decision-making
aimed a he sus ainable main enance o in ica e oad ne wo ks. Thei
wo k in oduced a bi-le el p og amming app oach ha add esses he
di e se cha ac e is ics o subne wo ks, a ying main enance s anda ds,
and he alloca ion o main enance unds. Le i in e al. [35] ocused on
he op imiza ion o CM o mul is a e sys ems wi h s o age, pa icula ly
p oduc ion-s o age sys ems in a ious indus ies. They add essed he
impac o andom ex e nal shocks on sys em pe o mance and in oduce
a co ec i e main enance policy (CMP). Liu e al. [36] p o ided an
op imal condi ion-based main enance policy o leased equipmen ,
conside ing hyb id PM and pe iodic inspec ion. The au ho s add essed
he complexi y o leased equipmen s uc u es due o echnological
ad ancemen s, posing challenges o lesso s in de eloping main enance
policies. Lee e al. [37] de eloped an op imized scheduling model o
ailway lines using a sophis ica ed deep ein o cemen lea ning
algo i hm.
Liu e al. [38] in oduced wo inno a i e PM policies ha accoun o
subs an ial epai down ime. One policy is ime-based, scheduling p e-
en i e eplacemen s a one o wo p ede e mined calenda in e als,
con ingen on he sys em’s condi ion. Zhou and Zheng [39] in oduced a
mul i-objec i e decision op imiza ion model o p io i izing main e-
nance and epai o bus ailu es. Mikhail e al. [40] in oduced a
da a-d i en op imiza ion me hod ha conside s con ex ual condi ions.
They combined machine lea ning and ein o cemen lea ning ech-
niques wi h a eliabili y-based emaining use ul li e me hodology. Wang
e al. [41] in oduced a dynamic p edic i e main enance s a egy o
p edic ing he emaining use ul li e (RUL) o sys ems. Zheng e al. [42]
explo ed he join op imiza ion o main enance and spa e pa o de ing
om mul iple supplie s o sys ems wi h mul iple componen s.
Zeng e al. [43] add essed a no el challenge in in eg a ing PM wi h
obo disassembly line balancing (DLB) o enhance he e iciency and
s abili y o obo ic disassembly sys ems. Thei s udy ocuses on op i-
mizing bo h con en ional disassembly scena ios and PM scena ios,
while also imp o ing he ansi ion e iciency be ween hese wo con-
ex s. O’Neil e al. [44] in oduced a new esilience amewo k designed
o op imize he pe o mance o c i ical ne wo k in as uc u es, such as
powe g ids, elecommunica ions, and anspo a ion sys ems. This
amewo k ackles he challenges posed by dis up ions caused by s ess
e en s and aims o enhance ne wo k esilience h ough e icien
pos -dis up ion es o a ion. Lima e al. [45] p esen ed a no el model o
managing impe ec main enance in mul i-componen sys ems, speci -
ically add essing he Selec i e Main enance P oblem (SMP) by inco -
po a ing bo h pe ec PM and CM ac ions.
Tian e al. [46] in oduced a heu is ic algo i hm ha p o ides
nea -op imal solu ions o his complex issue, ocusing on e icien
esou ce u iliza ion and long- e m sys em pe o mance. They also
de eloped a Selec i e Se ial Main enance Sequence Planning (SSMSP)
model o op imize main enance ac i i ies o mechanical equipmen
wi h mul iple componen s. This model add esses ine iciencies, high
cos s, and esou ce was age by in eg a ing wo ke physical exe ion and
es ime in o main enance planning, he eby ensu ing sus ainable
schedules. Addi ionally, i employs a mul i-objec i e op imiza ion
app oach o balance main enance bene i s, cos s, and esou ce
cons ain s.
Zhang e al. [47] ocused on enhancing he eliabili y and main e-
nance e iciency o wind-pho o ol aic (PV) hyb id powe sys ems. They
de eloped a eliabili y model and a main enance op imiza ion model
ha inco po a es ene gy complemen a i y s a egies. This s udy ad-
d esses he in e mi ency o enewable ene gy sys ems and aims o
educe main enance cos s ac oss di e en ailu e modes and scena ios.
The p oposed main enance op imiza ion model in eg a es ene gy
complemen a i y s a egies o op imize sys em pe o mance and mini-
mize cos s. Wei and Cheng [48] de eloped a main enance policy op i-
miza ion amewo k o sel -se ice sys ems aimed a maximizing p o i
by balancing se ice e enue and main enance cos s. Thei model ac-
coun s o unique ailu e-induced demand-and-sys em in e ac ions and
employs a Tabu-sea ch algo i hm o op imize main enance policies.
Leppinen e al. [49] ackled he challenge o op imizing main enance
schedules o mul i-componen sys ems by conside ing echnical s uc-
u al dependencies, which signi ican ly impac he cos -e iciency o
main enance policies. Thei s udy in oduced di ec ed g aphs as a ool o
ep esen he economic and s uc u al dependencies o he sys em,
including scena ios whe e main aining one componen necessi a es
disassembling o main aining o he s. The main enance scheduling
p oblem is modeled as a Ma ko Decision P ocess (MDP) and sol ed
using a modi ied policy-i e a ion algo i hm o de e mine he mos
cos -e icien main enance policy. Ba andegan Em oozi e al. [50]
assessed HEP in main enance asks using he Cogni i e Reliabili y and
E o Analysis Me hod (CREAM) and Sys em Dynamics (SD) modeling.
Thei s udy iden i ies and quan i ies ac o s in luencing HEP, explo es
hei in e ac ions, and es ima es associa ed cos s using machine lea ning
echniques. Ul ima ely, he esea ch de e mines he op imal HEP alue
o minimize cos s and acciden s, p o iding manage s wi h scena ios o
e ec i e budge alloca ion and imp o ed e gonomics. Table 1 p o ides
an o e iew o p e ious s udies on main enance.
•TBM is scheduled a ixed in e als o ensu e egula p e en i e ac-
ions and a oid unexpec ed ailu es.
•CBM is inco po a ed h ough eal- ime condi ion moni o ing o he
equipmen , allowing ea ly de ec ion o po en ial ailu es and
enabling adap i e main enance in e en ions be o e scheduled TBM
ac ions.
P e ious s udies ha e p o ided aluable insigh s in o main enance
ope a ions, as shown in Table 1. Howe e , hey did no conside he
impac o human e o on main enance me ics. This o e sigh is sig-
ni ican because he human ac o plays a c i ical ole in main enance
ope a ions, and neglec ing i may lead o inaccu a e esul s. P io
esea ch has p ima ily ocused on non-human ac o s, such as machine
eliabili y and ailu e a es, while o e looking he e ec s o human
e o . To add ess his gap, ou esea ch aims o examine how HEP a ec s
he o al cos and he i ual age o machines esul ing om main e-
nance ope a ions. This pape conduc s a quan i a i e analysis o de e -
mine he ex en o which human e o in luences hese cos s and
machine age. Addi ionally, we explo e in en o y con ol policies o
spa e pa s o enhance main enance planning.
Implemen ing an e ec i e in en o y con ol policy can help educe
down ime and main enance cos s by ensu ing ha spa e pa s a e
eadily a ailable when needed. I is impo an o no e ha p e ious
s udies ha e examined main enance ope a ions planning based on ei he
condi ion-based o ime-based main enance. Howe e , in ou s udy, we
in es iga e bo h condi ion-based and ime-based main enance simul a-
neously. This dual app oach allows us o iden i y which main enance
s a egy is mo e e ec i e o di e en ypes o machines and main e-
nance asks. O e all, ou esea ch aims o p o ide a comp ehensi e
unde s anding o he impac o human e o on main enance ope a ions
and he impo ance o an e ec i e in en o y con ol policy.
3. Me hodology
This sec ion ou lines a comp ehensi e and sys ema ic me hodology
o op imizing main enance ope a ions, spa e pa s in en o y con ol,
and human e o managemen wi hin a cemen ac o y. By in eg a ing
hese c i ical componen s in o a uni ied op imiza ion model, he
esea ch aims o achie e cos -e ec i e and e icien main enance p ac-
ices while igo ously adhe ing o ope a ional cons ain s. The inco -
po a ion o eal-wo ld da a om he cemen ac o y no only enhances
he model’s accu acy bu also ensu es i s p ac ical applicabili y and
ele ance o indus ial se ings. This app oach p o ides a obus
amewo k o balancing cos educ ion, ope a ional e iciency, and
V. Ba andegan Em oozi e al.
Ope a ions Resea ch Pe spec i es 14 (2025) 100336
3
equipmen eliabili y in complex main enance en i onmen s.
3.1. No a ion
This sec ion ou lines he symbols and no a ions used in he pape .
Table 2 p esen s he no a ions and de ini ions used h oughou he
ma hema ical model desc ibed in his pape .
3.2. P oblem s a emen and case s udy
The p ima y pu pose o his esea ch is o iden i y he op imal alues
o decision a iables ela ed o main enance ope a ions
(Voi ,Qi ,Bi ,Ii ,bBi ,bIi ), spa e pa s in en o y con ol
(zkj ,aj ,
ψ
cj ,ξcj,ξʹ
cj, [m]
kj , [p]
j ), and human e o (p, pk), aiming o educe cos s
while adhe ing o a ious cons ain s. I is impo an o no e ha ca -
ying ou PM and CM ope a ions can lead o p oduc ion line down ime
and dis up o ganiza ional p ocesses. In his model, he iming and
equency o each le el o PM ope a ions a e de e mined based on ma-
chine age, cos cons ain s, and o he o ganiza ional limi a ions.
In his s udy, ocusing on he case o a cemen ac o y, main enance
ope a ions a e examined o wo c i ical pieces o equipmen : a o a y
kiln and a clinke silo. The analysis includes ou key spa e pa s asso-
cia ed wi h his equipmen : bea ings, a side mo o , seals, and a pai o
b ushes. Addi ionally, he s udy conside s h ee di e en le els o PM
ope a ions and one ea u e o assess he condi ion o he equipmen (i.e.,
noise). I is wo h men ioning ha he model is speci ically designed o
epai able mechanical equipmen ha unde goes a de e io a ion p ocess
and ope a es independen ly. The da a used o he esea ch comes om
he main enance logbooks o he plan and is p esen ed in Tables 1A and
2A in he Appendix.
Simul aneously, he a ailabili y o spa e pa s is c ucial o ca ying
ou main enance e ec i ely and p omp ly, making spa e pa s in en o y
con ol a c i ical componen o he p ocess. This pape op imizes he
o de quan i y o spa e pa s. Fu he mo e, he op imal le el o human
e o is iden i ied based on he condi ions ha in luence human esou ce
e o s (i.e., Common Pe o mance Condi ions (CPCs)), as well as i s
impac on machine age and associa ed cos s. The cos o human e o in
main enance asks and i s e ec on machine age a e conside ed as a
unc ion o human e o . Fig. 1 illus a es he s uc u e and logic o he
model h ough a de ailed diag amma ic ep esen a ion.
3.3. Assump ion ela ed o he p esen ed model
The ollowing assump ions unde pin he model p esen ed:
Cons ained Time Ho izon
The model ope a es wi hin a ini e ime ho izon, wi h all ope a ions,
cos s, and ac i i ies analyzed o e his du a ion. This ensu es he model
Table 1
P e ious s udies on main enance.
No Re e ence Main enance
S a egy
Subca ego y Dis ibu ion o
ailu e unc ion
Func ion es ima ion
ela ed o HEP
In en o y
managemen o
spa e pa s
Solu ion app oach
Cos Reduc ionn
coe icien
1 [20] PM TBM –✖ ✖ ✔ Gene ic algo i hm (GA)
2 [33] PM, CM TBM Weibull ✖ ✖ ✔ Mon e Ca lo Simula ion
3 [16] PM, CM TBM Non-homogenous
Ma ko p ocesses
✖ ✖ ✖ Hamil on–Jacobi–Bellman (HJB)
4 [19] PM, CM TBM Uni o m ✖ ✖ ✖ Kushne and Dupuis’ me hod and alue
i e a ion o policy i e a ion algo i hms
6 [27] PM, CM TBM Log-No mal ✖ ✖ ✖ SAW, TOPSIS, ELECTRE
7 [25] PM, CM TBM Gamma ✖ ✖ ✔ A Lag angian elaxa ion-based heu is ic
app oach
8 [42] PM, CM CBM Weibull ✖ ✖ ✖ The policy-i e a ion algo i hm in he semi-
Ma ko decision p ocess (SMDP)
9 [26] PM, CM TBM Weibull ✖ ✖ ✖ GA, simula ed annealing (SA) algo i hm, and a
eaching–lea ning-based op imiza ion (TLBO)
10 [24] PM, CM TBM Weibull ✖ ✖ ✖ Pe i ne algo i hm
11 [21] PM, CM TBM Gamma ✖ ✖ ✖ Heu is ic pa ame e s op imiza ion
12 [23] PM, CM CBM Weibull ✖ ✖ ✖ he POMDP dynamics
14 [12] PM, CM CBM Gamma ✖ ✖ ✔ Mon e Ca lo simula ion
15 [32] PM, CM CBM uni o m ✖ ✖ ✔ Heu is ic-based on a s anda d c i ical pa h
me hod.
16 [28] PM, CM CBM Weibull ✖ ✖ ✖ Pe i ne algo i hm
17 [29] PM, CM TBM Exponen ial ✖ ✖ ✖ Inno a i e and upda ed calcula ion
me hodology by MATLAB so wa e
19 [31] PM TBM –✖ ✖ ✖ Me aheu is ic me hod (GA)
20 [34] PM, CM CBM Exponen ial ✖ ✖ ✖ Me aheu is ic me hod (GA)
21 [35] CM CBM –✖ ✖ ✖ Me aheu is ic me hod (GA)
22 [40] PM, CM CBM Kaplan-Meie (KM) ✖ ✖ ✖ machine lea ning and ein o cemen lea ning
23 [37] PM, CM CBM Exponen ial ✖ ✖ ✖ Deep ein o cemen lea ning
24 [36] PM, CM CBM Gamma ✖ ✖ ✖ Me aheu is ic me hod
25 [38] PM, CM CBM Exponen ial ✖ ✖ ✖ Ma hema ical model
26 [41] PM CBM –✖ ✖ ✔ CNN
27 [42]– – Exponen ial ✖ ✖ ✔ Hyb id deep ein o cemen lea ning algo i hm
(HDRL)
28 [45] PM, CM SMP –✖ ✖ ✖ Heu is ic algo i hm
29 [46] PM, CM TBM –✖ ✖ ✖ Enhanced me aheu is ic (b ains o ming
op imiza ion +la ge neighbo hood sea ch)
30 [49] PM, CM TBM Exponen ial ✖ ✖ ✖ MDP model, Modi ied policy-i e a ion
algo i hm
31 [50] PM, CM – – ✔ ✔ ✖ SD modeling and machine lea ning
32 This
s udy
PM, CM TBM, CBM Weibull ✔ ✔ ✔ Ma hema ical model (GAMS)
Condi ion-Based Main enance: CBM, Time-Based Main enance: TBM, Selec i e Main enance P oblem (SMP).
V. Ba andegan Em oozi e al.
Ope a ions Resea ch Pe spec i es 14 (2025) 100336
4
aligns wi h p ac ical planning pe iods, such as inancial yea s o p ojec
li espans.
Spa e Pa s Sho age Cos s
The cos implica ions o spa e pa s sho ages a e modeled based on
he cumula i e sho age o e he planning ho izon. This app oach ac-
coun s o a ia ions in demand and in en o y le els while ensu ing ha
down ime cos s esul ing om spa e pa una ailabili y a e comp e-
hensi ely cap u ed.
Main enance Cos Dependencies
Spa e pa cos s o main enance a e in luenced by dynamic in-
en o y le els and se ice-le el equi emen s, inco po a ing penal ies
o s ockou s and o e s ocking.
Cos o Co ec i e and P e en i e Ac ions
The cos o eplacing pa s pos - ailu e is explici ly highe han
p e en i e eplacemen cos s due o unplanned down ime and po en ial
seconda y damages. This di e ence is dynamically calcula ed based on
se e i y and ime-o - ailu e scena ios.
Failu e Ra e Dis ibu ion
The ailu e a e exhibi s an inc easing end o e ime, modeled
using a Weibull dis ibu ion wi h a shape pa ame e (β>1). The ini ial
pa ame e es ima es we e in o med by expe judgmen , ensu ing
alignmen wi h domain knowledge, and subsequen ly e ined and ali-
Table 2
No a ions.
Se s
MThe se o pe iods ep esen ed by he index ;
KThe se o di e en le el ypes o PM ep esen ed by he index k;
JThe se o equipmen indexed by j;
IThe se o spa e pa s indexed by i;
CThe se o equipmen condi ions indexed by c;
Decision a iables
p[ o al]Human e o p obabili y.
pkHuman e o p obabili y associa ed wi h conduc ing k hle el o PM ope a ions.
zkj The bina y a iable equals 1 i a PM ope a ion is pe o med on he machine j a he k h le el in pe iod ; O he wise, i equals 0.
aj The i ual age o he machine j in pe iod .
[p]
j The a ailable ime on machine j o ca ying ou p oduc ion ope a ions in pe iod .
[m]
kj P e en i e main enance ime on he machine j a he le el k in pe iod .
ψ
cj The le el o implemen a ion o PM ope a ions on machine j unde condi ion c in pe iod .
Voi The bina y a iable o o de ing o no o de ing spa e pa s i in pe iod .
bIi The bina y a iable equals 1 i he e is in en o y a ailable o i h spa e pa s in pe iod ; O he wise, i equals 0.
bBi The bina y a iable equals 1 i he e is a sho age o i h spa e pa s in pe iod . O he wise, i equals 0.
Bi The amoun o sho age o i h spa e pa s in pe iod .
Ii The amoun o holding o i h spa e pa in pe iod .
Q
i
The o de quan i y o i h spa e pa in pe iod .
Pa ame e s
Shi The cos o sho age o i h spa e pa in pe iod (each uni ).
hi The cos o holding o i h spa e pa in pe iod (each uni ).
Cse j Se up cos a e machine down ime esul ing om PM and CM ope a ions on j hmachine in pe iod .
dpikj The demand o i h spa e pa s o he implemen a ion o PM ope a ions a k hle el on machine j in pe iod .
dcij The demand o i h spa e pa s o implemen a ion o CM ope a ions on machine j in pe iod .
CO
i
The ixed o de ing cos o i hspa e pa in pe iod .
LT[E]
iThe lead ime o eme gency o de s o i h spa e pa s.
MTTRj CM ime on j h machine in pe iod .
Wa i The wa ehouse capaci y o i h spa e pa s in pe iod .
Nmkj The numbe o echnicians needed o pe o m PM ope a ions on he j h machine a k hle el in pe iod .
N j The numbe o echnicians needed o pe o m CM ope a ions on j hmachine in pe iod .
Nspij The numbe o i h spa e pa s o ca y ou CM ope a ion on j hmachine in pe iod .
Hmkj The cos associa ed wi h human esou ces o PM ope a ions on he j hmachine a k hle el in pe iod .
H j The cos associa ed wi h human esou ces o CM ope a ions on machine j in pe iod .
Clj The cos o he los oppo uni y o p oduc ion line down ime on machine j in pe iod .
Cui P ice o each uni o i h spa e pa in pe iod .
ACj The noise o j hmachine in pe iod .
COi O de ing cos o i h spa e pa in pe iod .
cdi pu chasing cos o each uni o i h spa e pa in pe iod .
Q[max]
i The maximum quan i y o o de ing i h spa e pa s in pe iod .
ϑcj The op imal le el o PM ope a ions on j hmachine unde c hcondi ion in pe iod .
ξʹ
cj The uppe h eshold o c hcondi ion on machine j.
ξcj The lowe h eshold o c hcondi ion on machine j.
The lea ning coe icien o human esou ces in he implemen a ion o PM ope a ions on machine j.
μ
The numbe o le els o PM ope a ions.
HLeng h o he planning ho izon.
βWeibull dis ibu ion shape pa ame e .
η
Weibull dis ibu ion scale pa ame e .
α
kThe e ec i e a e o i ual age h ough he execu ionk hle el o PM ope a ion.
lThe in e al leng h.
AEjThe minimum accessibili y*o j h machine.
TB The maximum alloca ed budge .
pcu en The p obabili y o human e o in he cu en s a e.
*
In his pape , machine’s accessibili y is conside ed as he a ailable and ope a ional ime o he equipmen .
V. Ba andegan Em oozi e al.
Ope a ions Resea ch Pe spec i es 14 (2025) 100336
5
da ed using Maximum Likelihood Es ima ion (MLE) o g ea e accu acy
and eliabili y.
Lea ning Cu e E ec s on PM Times
O e ime, pe sonnel imp o e in pe o ming PM, educing he ime
equi ed pe ask. This imp o emen ollows a e ined lea ning cu e,
inco po a ing pla eau poin s whe e skill imp o emen s diminish.
Co ec i e Main enance (CM) Cos s S abili y
CM cos s a e assumed cons an pe uni ask, bu addi ional cos s
such as logis ical delays, ma e ial su cha ges, o o e ime penal ies a e
conside ed in sensi i i y analyses.
Exclusion o Oppo unis ic Main enance
Oppo unis ic main enance ac ions a e excluded; howe e , he
model p o ides he lexibili y o in eg a e hem in u u e expansions.
Immedia e CM Ope a ions
CM ope a ions a e execu ed wi hou delays upon aul de ec ion. The
aul de ec ion sys em is assumed o be obus , wi h negligible lag be-
ween ailu e and esponse.
P e en i e Main enance Le els
PM is ca ego ized in o h ee le els—minimal, impe ec , and pe ec .
Each le el’s e ec i eness is p obabilis ically modeled, inco po a ing
bo h human e o and equipmen imp o emen ac o s. This p o ides
ealis ic a ia ions in ou comes based on e o and expe ise.
Impac o CM on Failu e Ra e
CM is modeled as minimal, assuming i es o es equipmen unc-
ionali y wi hou al e ing i s inhe en ailu e cha ac e is ics, which
emain Weibull-dis ibu ed wi h s able pa ame e s.
Single Le el o CM Ope a ions
The s udy assumes a uni o m CM app oach. Fu u e wo k may explo e
di e en ia ed CM le els based on ailu e se e i y.
In en o y Con ol Sys em
Spa e pa s o PM ollow a ixed-o de in e al (FOI) sys em, wi h
eo de poin s op imized o minimum o al cos , conside ing o de size,
holding cos s, and s ockou penal ies. Unde his app oach (FOI), o de s
a e placed a p ede e mined, egula in e als, a he han being ig-
ge ed by a eo de poin . The o de quan i y is de e mined based on he
in en o y posi ion a he e iew ime o ensu e su icien s ock un il he
nex e iew pe iod.
Alignmen o Inspec ion and PM Pe iods
In en o y inspec ions coincide wi h PM pe iods, op imizing sched-
uling and esou ce u iliza ion.
Dual Spa e Pa s O de ing Sys em
Spa e pa s a e p ocu ed h ough egula and eme gency o de s,
wi h eme gency o de s incu ing highe cos s bu ensu ing se ice
con inui y du ing unexpec ed demand spikes.
Fig. 1. Rep esen a ion o he ma hema ical model’s s uc u e.
V. Ba andegan Em oozi e al.
Ope a ions Resea ch Pe spec i es 14 (2025) 100336
6
The i ual age o a machine
The i ual age o a machine is de ined as he measu e o i s e ec i e
age, based on ac o s such as ope a ional his o y, main enance, and
usage, a he han i s ac ual ch onological age.
Homogeneous Weibull Pa ame e s Ac oss Equipmen
This s udy assumes iden ical scale (
η
) and shape (β) pa ame e s o
he Weibull dis ibu ion ac oss all equipmen ypes, implying consis en
ailu e cha ac e is ics unde simila ope a ional condi ions.
3.4. Ma hema ical model
3.4.1. The objec i e unc ion
The objec i e unc ion o his esea ch is so as o educe in en o y
con ol cos s associa ed wi h spa e pa s, down ime, human e o , and
CM and PM ope a ion cos s
In en o y con ol
The in en o y con ol sys em ensu es ha spa e pa s a e a ailable
when needed o main enance ope a ions. The model inco po a es
sa e y s ock le els and eo de poin s o p e en s ockou s.I he in-
en o y le el o spa e pa s alls below he sa e y s ock le el, an eme -
gency o de is igge ed. Eme gency o de s a e expedi ed o minimize
down ime, bu hey incu highe cos s compa ed o egula o de s. This
ensu es ha main enance ope a ions can p oceed wi hou signi ican
delays, e en in cases o unexpec ed spa e pa s sho ages.
In en o y holding cos o spa e pa s
Holding cos s a e de e mined by he spa e pa s o de ed in excess o
he demand a he end o each ime pe iod. Since he demand o hese
spa e pa s is in luenced by machine ailu es, i s quan i y is es ima ed
using he demand unc ion o machine ailu e, making i a andom
a iable. In eali y, he demand o spa e pa s de i es om he o e all
demand o CM and PM ope a ions ha equi e spa e pa s eplacemen .
Hence, he demand o spa e pa s is also a andom a iable, and he
ollowing equa ions a e employed o calcula e he a e age in en o y
and sho ages.
Ii =Qi +Ii( −1)−dci −∑k∈Kdpik −Bi( −1)(1)
Bi = − Qi −Ii( −1)+dci +∑k∈Kdpik +Bi( −1)
Qi =Q[max]
i −Ii( −1)(2)
Based on he s ochas ic beha io model p oposed by Xiang e al.,
2018 [51] in en o y and sho age a e o mula ed as a backo de wi h a
loss unc ion in Eq. (3).
l(ϑ,w) = E[max (ϑ−w,0)] (3)
E ep esen s he expec ed alue o he andom a iable
ω
and he scala
a iable ϑ. As p e iously men ioned, demand o spa e pa s is a andom
a iable, and he o de quan i y o spa e pa s, in en o y, and sho age
a e scala a iables. The e o e, Eqs. (4) and 5 can be p esen ed o
nonlinea es ima ion o in en o y and sho age.
Ii =l(Qi +Ii( −1)−∑k∈Kdpik −Bi( −1),dci )
=E[max(Qi +Ii( −1)−dci −∑k∈Kdpik −Bi( −1),0)]
=E(Qi +Ii( −1)−dci −∑k∈Kdpik −Bi( −1))+
(4)
Bi =l(−Qi −Ii( −1)+∑k∈Kdpik +Bi( −1),−dci )
=E[max(−Qi −Ii( −1)+dci +∑k∈Kdpik +Bi( −1),0)]
=E(−Qi −Ii( −1)+dci +∑k∈Kdpik +Bi( −1))+
(5)
Consequen ly, Eqs. (6) and 7 can be o mula ed as ollows:
E[Qi +Ii( −1)−Bi( −1)−∑k∈Kdpik −dci ]≤I
⇒Qi +Ii( −1)−Bi( −1)−∑k∈Kdpik −E[dci ] ≤ Ii
(6)
E[∑k∈Kdpik −dci −Qi −Ii( −1)+Bi( −1)]≤Bi
⇒∑k∈Kdpik −E[dci ] − Qi −Ii( −1)+Bi( −1)≤Bi
(7)
whe e
E[dci ] = ∑
j∈J
Nscij [((aj +l)β−aβ
j )
η
β]
The e o e, gi en he s ochas ic na u e o spa e pa s demand, he
in en o y a e age in each pe iod is mul iplied by he holding cos pe
uni acco ding o Eq. (8). I he andom demand su passes he numbe o
spa e pa s o de ed o ha pe iod, he cos o sho ages is included in
he o al cos . In his model, he o al sho age cos is calcula ed by
mul iplying he sho age by he cos o sho age in each uni , as speci ied
in Eq. (9).
∑i∈I∑ ∈Mhi bIi (Qi +Ii( −1)−Bi( −1)−∑k∈Kdpik −E[dci ])
+∑i∈I∑ ∈MShi bBi (∑k∈Kdpik −E[dci ] − Qi −Ii( −1)+Bi( −1))(8)
whe e
E[dci ] = ∑
j∈J
Nscij [((aj +l)β−aβ
j )
η
β](9)
Eq. (4) ep esen s he expec ed in en o y a e age as he di e ence
be ween he o de ed amoun o spa e pa s and hei demand. This
equa ion indica es ha i he o de ed quan i y o spa e pa s exceeds he
andom demand, he exp ession will ha e a posi i e alue, and i he
demand o spa e pa s exceeds he o de ed quan i y o spa e pa s, he
expec ed in en o y will be ze o. Simila ly, Eq. (5) shows he expec ed
sho age a e age. Eq. (10) is always non-nega i e I is e iden ha hese
wo equa ions canno simul aneously assign alues o hemsel es. In
o he wo ds, i he e is in en o y in any pe iod, he e will be no
sho age, and ice e sa. The e o e, Eq. (9) ep esen s his ac as
ollows:
bBi +bIi =0⇒bBi +bIi ≤1 (10)
O de ing cos o spa e pa s
The o de ing cos s in his s udy comp ise o wo di e en scena ios,
and he decision ega ding he ype o o de ing s a egy depends on he
in en o y le el. I he in en o y le el o spa e pa s is lowe han he
eo de poin bu highe han he sa e y s ock le el a he inspec ion
poin , he o de ing iming will ollow he usual p ocedu e. Ne e heless,
i he in en o y le el o spa e pa s alls below he sa e y s ock le el, he
o de ing will be done in an eme gency s a e, leading o a educ ion in
o de ing iming and an inc ease in cos s compa ed o he usual si ua ion.
The e o e, eme gency o de s a e a c i ical componen o he
V. Ba andegan Em oozi e al.
Ope a ions Resea ch Pe spec i es 14 (2025) 100336
7
main enance policy. When spa e pa s a e una ailable in he in en o y
and all below he sa e y s ock le el, he sys em ini ia es an eme gency
p ocu emen p ocess. This p ocess educes he lead ime o spa e pa s
deli e y bu inc eases he associa ed cos s. The decision o place an
eme gency o de is based on he u gency o he main enance ask and
he c i icali y o he equipmen . Fo example, CM asks ha equi e
immedia e a en ion a e p io i ized o eme gency o de s o minimize
p oduc ion down ime.
Fig. 2 clea ly and comp ehensi ely illus a es he p ocess o o de ing
spa e pa s and i s ela ionship wi h PM and CM ope a ions. Thus, o
calcula e he o de ing cos acco ding o he ype o o de ing s a egy, we
can exploi Eq. (11) ha :
COi =⎧
⎨
⎩
0i ROPi <Ii
NOi i SSi ≤Ii ≤ROPi
EOi i Ii <SSi
⇒COi
=⎧
⎨
⎩
0i ROPi +1≤Ii
NOi i SSi ≤Ii ≤ROPi
EOi i Ii ≤SSi −1
(11)
In o de o calcula e he o de ing cos , i needs o be mul iplied by
he decision a iable ha is ela ed o o de ing o no o de ing in each
pe iod. Consequen ly, he o al cos o di e en pe iods can be calcu-
la ed using Eq. (12), whe e he o de ing cos is assumed o be a ixed cos
in his s udy. Besides, he cos o pu chasing spa e pa s is also depen-
den on he bina y a iable o o de ing o no o de ing. The cos o
pu chasing spa e pa s in each pe iod is equal o he mul iplica ion o he
pu chasing cos pe uni o spa e pa s and he o de ed quan i y. I an
o de is placed in a speci ic pe iod, his cos will be added o he model.
O he wise, no cos will be included in he model o ha pe iod. The
o de quan i y in each pe iod is ob ained h ough he di e ence be ween
he in en o y le el and he maximum o de quan i y.
TOi =∑i∈I∑ ∈MVOi .COi +∑i∈I∑ ∈MCui Qi VOi (12)
Qi =Q[max]
i −Ii( −1)(13)
Eq. (14) de ines he cons ain ha is ela ed o he demand o spa e
pa s and i s dependence on he bina y a iable o o de ing o no
o de ing. This equa ion cla i ies ha i he bina y a iable VO equals
ze o, no o de will be placed, and as a esul , he alue o Q will be ze o.
Howe e , i VOi equals one, he alue o Q can a y om ze o o i s
maximum alue (Q[max]), depending on he cu en in en o y le el.
Qi ≤Q[max]
i VOi (14)
Down ime cos
Machine down ime can occu due o se e al easons, and his s udy
ocuses on h ee signi ican ac o s. Fi s , i in ol es he una ailabili y o
spa e pa s du ing main enance ope a ions. Second, i conce ns he
a e age ime equi ed o pe o m CM o es o e he machine o p o-
duc ion ope a ions. Thi d, i pe ains o he execu ion o PM ope a ions
a a ious le els, which necessi a es empo a y hal s in he p oduc ion
line. No ably, he ime equi ed o hese ope a ions will dec ease as
employees gain expe ience om pe o ming hem mo e equen ly.
To calcula e he cos o machine down ime, we begin by de e mining
he cos pe uni o ime o p oduc ion line down ime and hen mul iply
i by he du a ion o he machine down ime. The cos s associa ed wi h
machine down ime, speci ically he second and hi d ypes, will be
Fig. 2. The in en o y con ol sys em o spa e pa s.
V. Ba andegan Em oozi e al.
Ope a ions Resea ch Pe spec i es 14 (2025) 100336
8
zk ,VOi ,bIi ,bBi ,y[1]
i ,y[2]
i ,y[3]
i ∈ {0,1}
0.00005 ≤pk,pCM,pins,p[ o al]≤pcu en
ψ
[ o al]
,
ψ
c ∈In
(44)
As a esul , he esea ch model is o mula ed as ollows:
subjec o
Qi +Ii( −1)−Bi( −1)−∑k∈Kdpik −E[dci ] ≤ Ii ∀i, (46)
∑k∈Kdpik +E[dci ] − Qi −Ii( −1)+Bi( −1)≤Bi ∀i, (47)
bIi +bBi ≤1∀i, (48)
Qi ≤Q[max]
i VOi ∀i, (49)
Qi =(Q[max]
i −Ii( −1))VOi ∀i, (50)
[m]
kj =γkjzkj
⎛
⎜
⎜
⎜
⎜
⎜
⎝
1+∑
l∈M
l≤M−1
ʹ
zkjl
⎞
⎟
⎟
⎟
⎟
⎟
⎠
ln
ln2∀k,j, (51)
aj =(aj( −1)+l)(1−∑k∈Kzkj
α
k(1−pk))∀j, (52)
ξʹ
cj −ξʹ
cj −ξcj
μ
−2(
ψ
cj −1)≤ϑcj ≤ξʹ
cj −ξʹ
cj −ξcj
μ
−2(
ψ
cj −2),
μ
>2∀c,j,
(53)
∑k∈Kzkj =1∀j, (54)
ψ
[ o al]
j =∑k∈Kkkzkj ∀j, (55)
ψ
[ o al]
j ≤
ψ
cj ∀c,j, (56)
Qi +Ii( −1)−Bi( −1)−dpik −E(dci ) ≤ Wa i ∀i, (57)
Qi +Ii( −1)−Bi( −1)≤dpik +E(dci ) ∀i, (58)
[p]
j =l−∑
k∈K
zkj [m]
kj −MTTRj [((aj +l)β−aβ
j )
η
β]
−LT[E o al]
bBi( −1)[((aj +l)β−aβ
j )
η
β]∀j, (59)
LT[E]
ibBi ≤LT[E o al]
∀i, (60)
∑k∈Kdpik =∑k∈KNspik zk ∀i, (61)
−Q[max]
i ∑j∈Jzkj ≤∑k∈Kdpik ≤ − Q[max]
i ∑j∈Jzkj ∀k,j, (62)
∑
∈M
[p]
j ≥AEj∀j(63)
VOi ≥1−y[3]
i ∀i, (64)
(ROPi +1) − My[1]
i ≤Ii ≤Q[max]
i∀i, (65)
SSi −My[2]
i ≤Ii ≤ROPi +My[2]
i ∀i, (66)
Ii ≤ (SSi −1) + My[3]
i ∀i, (67)
y[1]
i +y[2]
i +y[3]
i =2∀i, (68)
EOi (1−y[3]
i )+NOi (1−y[2]
i )=COi ∀i, (69)
−Q[max]
i(bBi ) ≤ Ii ≤ (1−bBi )Q[max]
i∀i, (70)
−Q[max]
i(bIi ) ≤ Bi ≤ (1−bIi )Q[max]
i∀i, (71)
min∑
i∈I∑
∈M
hi bIi (Qi +Ii( −1)−Bi( −1)−∑
k∈K
dpik −E[dci ])
+∑
i∈I∑
∈M
Shi bBi (∑
k∈K
dpik −E[dci ] − Qi −Ii( −1)+Bi( −1))
+∑
i∈I∑
∈M
VOi .COi +∑
i∈I∑
∈M
Cui Qi VOi +∑
i∈I∑
j∈J∑
∈M(Clj LT[E o al]
i+EOi )bBi( −1)[((aj +l)β−aβ
j )
η
β]
+∑
i∈I∑
kʹ,k∈K
kʹ<k∑
j∈J∑
∈M(Clj LT[E]
i+EOi )bBi( −1)zkʹj + (p)
+∑
k∈K∑
j∈J∑
∈M((CLj +Hmkj Nmkj ) [m]
kj +Cse j )zkj
+∑
j∈J∑
∈M((Clj +H j N j )MTTRj +Cse j )[((aj +l)β−aβ
j )
η
β]
(45)
V. Ba andegan Em oozi e al.
Ope a ions Resea ch Pe spec i es 14 (2025) 100336
15
p[ o al]=1−(∏k∈K(1−pk))(1−pco ec i e)(1−pins)(72)
To al cos ≤TB (73)
zkj ,VOi ,bIi ,bBi ,y[1]
i ,y[2]
i ,y[3]
i ∈ {0,1}(74)
0.00005 ≤pk,pco ec i e,pins,p[ o al]≤pcu en (75)
ψ
[ o al]
j ,
ψ
cj ∈In (76)
Qi ,Ii ,Bi ,dpik ,dci ,a ,COi , [p]
j , [m]
kj ≥0 (77)
4. Findings
The model is o mula ed as a mixed-in ege nonlinea p og amming
(MINLP) p oblem and sol ed using GAMS so wa e. The compu a ions
a e ca ied ou on a sys em equipped wi h an AMD Ryzen 32200U
p ocesso unning a 2.5 GHz, 8 GB o RAM, and a 64-bi ope a ing
sys em. The esul s ob ained om sol ing he model, which u ilizes da a
om a case s udy in ol ing mul iple machines, spa e pa s, condi ions,
and h ee di e en le els o PM ope a ions ac oss a ious pe iods, a e
p esen ed in Table 5. In his model, he PM app oach is designed such
ha di e en le els o main enance ope a ions, each wi h a ying
e ec i eness a es, in luence he equipmen ’s li espan. Based on he
o e all esul s, he mos e ec i e le el o PM ope a ions is selec ed.
Since one o he p ima y objec i es o PM is o p e en sys em ailu es
and unexpec ed p oduc ion line shu downs, he model inco po a es
cos s ela ed o p oduc ion line dis up ions ha may occu due o he
implemen a ion o speci ic le els o PM and CM ope a ions, as well as
sho ages o ce ain spa e pa s.
The esul s ob ained om sol ing he model indica e he op imal
le els o PM ope a ions o di e en pe iods, aking in o accoun bo h
cos s and he e ec i e a e o he equipmen . Implemen ing PM ope a-
ions a he lowes le el (Le el 3) equi es less cos , ime, and esou ces,
such as manpowe and spa e pa s, compa ed o highe le els o PM
ope a ions. Con e sely, execu ing PM ope a ions a he highes le el
(Le el 1) demands he mos ime, cos , and esou ces. Based on da a
om he case s udy company, pe o ming Le el 1 PM ope a ions o
es o e equipmen o an “as good as new” condi ion in ol es signi ican
expenses. The e o e, as obse ed in he model esul s, Le el 2 o Le el 3
PM ope a ions ha e been selec ed o a ious pe iods. As he numbe o
pe iods inc eases, i becomes e iden ha main enance ope a ions begin
o ollow a speci ic and p edic able cycle. This cyclic pa e n allows o
mo e e icien planning and alloca ion o esou ces, ul ima ely
enhancing he o e all main enance s a egy. The esul s o sol ing he
p oblem o he a iables o PM ope a ions a e p esen ed in Table 5.
Fu he mo e, he ypes o spa e pa s equi ed o each le el o PM
ope a ions a e de ailed in Table 5. As e iden om he esul s, no spa e
pa s a e needed o unselec ed le els o PM ope a ions. Fo he selec ed
le els in each pe iod, he app op ia e spa e pa s a e de e mined based
on he chosen le el o main enance. The ime equi ed o execu ing PM
ope a ions is in luenced by he lea ning cu e e ec , leading o a
educ ion in ime o each subsequen execu ion o he same PM le el.
Consequen ly, as illus a ed in Table 5, he du a ion o pe o ming
Le el 2 and Le el 3 PM ope a ions dec eases o e ime. Speci ically, he
ime o Le el 2 PM ope a ions dec eases om 0.083 h o 0.031 h, while
he ime o Le el 3 PM ope a ions dec eases om 0.025 h o 0.011 h.
This educ ion e lec s he e iciency gained h ough expe ience,
imp o ed echniques, and he cumula i e impac o he lea ning cu e.
These indings highligh he impo ance o conside ing lea ning e ec s
in main enance planning o op imize esou ce u iliza ion and enhance
Table 6
The esul s o sensi i i y analysis (
η
).
No. Δzcos
η
Δ
η
1−0.10285 36 0.285714
2−0.10296 35 0.25
3−0.001206 34 0.232143
4−0.000980 33 0.178571
5−0.000815 32 0.142857
6−0.000727 31.5 0.125
7−0.000540 30.5 0.089286
8−0.000421 30 0.071429
9−0.000338 29.5 0.053571
10 −0.000230 29 0.035714
11 −0.000118 28.5 0.017857
12 0 28 0
13 0.000123 27.5 −0.01786
14 0.000252 27 −0.03571
15 0.224561 26 −0.07143
16 0.653825 24 −0.14286
Fig. 8. The impac o changes in
η
pa ame e s on he objec i e unc ion.
Fig. 9. The a io o changes in o al main enance cos s o changes in he scale
pa ame e (
η
).
V. Ba andegan Em oozi e al.
Ope a ions Resea ch Pe spec i es 14 (2025) 100336
16
ope a ional e iciency.
The esul s ob ained om sol ing he i s model o bina y a iables
ela ed o spa e pa s indica e ha in en o y is consis en ly a ailable
ac oss all examined pe iods, wi h no sho ages eco ded. This ou come is
logical, as he cos o main aining spa e pa s is ypically lowe han he
cos associa ed wi h sho ages, which is no ably highe in he con ex o
he cemen ac o y case s udy.
Al hough PM ope a ions a e p e-scheduled, and auxilia y lines and
side mo o s a e u ilized o p e en p oduc ion s oppages and kiln
shu downs, signi ican cos s can s ill a ise i spa e pa s a e no a ailable
in he equi ed quan i ies and he lead ime o p ocu emen exceeds he
a ailabili y o hese auxilia y esou ces. Fu he mo e, he o al cos o
main enance ope a ions o e he 36-mon h pe iod amoun s o
3501,281,000 uni s o cu ency. Addi ionally, he op imal HEP o
minimizing human e o - ela ed cos s is de e mined o be 0.02. These
indings unde sco e he impo ance o main aining adequa e spa e pa s
in en o y and op imizing main enance s a egies o mi iga e cos s and
ensu e ope a ional e iciency.
5. Sensi i e analysis
Sensi i i y analysis is a widely used echnique o e alua e he impac
o a ia ions in one o mo e inpu pa ame e s on one o mo e desi ed
ou pu s. I plays a c ucial ole in enhancing he unde s anding o a
model’s beha io and esul s, p o iding insigh s in o i s p ecision and
e ec i eness. In his sec ion, a sensi i i y analysis me hod is employed
o assess he obus ness o he designed model. This is accomplished by
sys ema ically a ying key pa ame e s o c ea e a ange o scena ios,
including bo h educ ions and inc eases in hei alues. Speci ically, a
comp ehensi e sensi i i y analysis was conduc ed on wo c i ical model
pa ame e s:
1. The pa ame e
η
o he Weibull dis ibu ion: The scale pa ame e
(
η
) is o en e e ed o as he cha ac e is ic li e o li e ime cha ac-
e is ic o he equipmen .
2. The e ec i e a e o equipmen
By analyzing hese pa ame e s unde di e en scena ios, he sensi-
i i y analysis p o ides aluable insigh s in o how changes in hese in-
pu s a ec he model’s ou pu s, such as main enance cos s, op imal PM
Table 7
The changes in o al main enance ope a ion cos s o a ious e ec i e a es o
equipmen .
E ec i e a e
α
kΔ
α
kΔzcos
K ¼1(0.825, 0.5, 0) −0.175 0.0721044
(0.85, 0.5, 0) −0.150 0.0613767
(0.875, 0.5, 0) −0.125 0.057943
(0.9, 0.5, 0) −0.100 0.0403553
(0.925, 0.5, 0) −0.075 0.0300581
(0.95, 0.5, 0) −0.050 0.01999009
(0.975, 0.5, 0) −0.025 0.009882
(1, 0.5, 0) 0 0
K ¼2(1, 0.25, 0) −0.500 0.033876
(1, 0.3, 0) −0.400 0.027060
(1, 0.35, 0) −0.300 0.020264
(1, 0.4, 0) −0.200 0.013488
(1, 0.45, 0) −0.100 0.006734
(1, 0.5, 0) 0 0
(1, 0.55, 0) 0.100 −0.006713
(1, 0.6, 0) 0.200 −0.111557
(1, 0.65, 0) 0.300 −0.115236
(1, 0.7, 0) 0.400 −0.118907
(1, 0.75, 0) 0.500 −0.122570
K ¼3(1, 0.5, 0) 0 0
(1, 0.5, 0.05) 0.050 −0.00427
(1, 0.5, 0.1) 0.100 −0.00852
(1, 0.5, 0.15) 0.150 −0.012777
(1, 0.5, 0.2) 0.200 −0.01701
(1, 0.5, 0.25) 0.250 −0.02125
(1, 0.5, 0.3) 0.300 −0.02547
(1, 0.5, 0.35) 0.350 −0.02969
(1, 0.5, 0.4) 0.400 −0.03389
(1, 0.5, 0.45) 0.450 −0.03809
(1, 0.5, 0.5) 0.500 −0.04228
(1, 0.5, 0.55) 0.550 −0.04647
Fig. 10. The changes in cos s ela i e o he e ec i e equipmen a e o Le el
1 PM.
Fig. 11. The changes in cos s ela i e o he e ec i e equipmen a e o Le el
2 PM.
Fig. 12. The changes in cos s ela i e o he e ec i e equipmen a e o Le el
3 PM.
V. Ba andegan Em oozi e al.
Ope a ions Resea ch Pe spec i es 14 (2025) 100336
17
le els, and in en o y managemen s a egies. This p ocess helps alida e
he model’s eliabili y and adap abili y o a ying ope a ional
condi ions.
5.1. Sensi i i y analysis wi h espec o he scale pa ame e (
η
)
The scale pa ame e
η
, o en e e ed o as he li e ime cha ac e is ic,
is di ec ly associa ed wi h he mean ime o ailu e (MTTF), which is
calcula ed as MTTF=
η
Γ(1 +1/β). An inc ease in he scale pa ame e
η
leads o a longe MTTF, meaning he equipmen can emain ope a ional
o a mo e ex ended pe iod, he eby delaying he occu ence o ailu es.
As a esul , bo h CM and PM cos s dec ease wi h a highe
η
, as he need
o main enance in e en ions is educed. Table 6 p o ides de ailed
in o ma ion on he a ia ions o he scale pa ame e
η
and i s impac on
main enance cos s. Addi ionally, Fig. 8 illus a es hese a ia ions and
hei in luence on main enance cos s, o e ing a isual ep esen a ion o
how changes in
η
a ec he o e all main enance s a egy. This analysis
highligh s he impo ance o he scale pa ame e in de e mining
equipmen eliabili y and main enance planning, demons a ing ha
highe alues o
η
con ibu e o educed main enance equency and
cos s.
Fig. 9 illus a es no only he in e se ela ionship be ween he scale
pa ame e
η
and o al main enance cos s bu also emphasizes a mo e
signi ican educ ion in cos s as he alues o
η
inc ease. The igu e
clea ly depic s cos a ia ions wi hin he ange 27.5<
η
<32.5, encom-
passing all obse ed cos alues. Addi ionally, he igu e e eals ha
cos changes a e less p onounced o highe alues o
η
compa ed o
lowe alues, indica ing a diminishing ma ginal e ec as
η
inc eases.
The ci cles in Fig. 9 highligh shi s in he op imal solu ion o spe-
ci ic alues o he scale pa ame e
η
. These shi s demons a e how
changes in
η
in luence he model’s ou comes, pa icula ly in e ms o
cos op imiza ion and main enance s a egy adjus men s. This isuali-
za ion unde sco es he impo ance o he scale pa ame e in de e mining
main enance cos s and p o ides aluable insigh s in o he sensi i i y o
he model o a ia ions in
η
.
5.2. Sensi i i y analysis wi h espec o he e ec i e a e o equipmen
As desc ibed, a ious le els o PM ope a ions ha e a ying e ec s on
he li espan o equipmen . Speci ically, each PM le el impac s he i ual
li espan o he sys em di e en ly, e lec ing hei dis inc in luences on
equipmen du abili y. This s udy in es iga es how he e ec i eness o
PM ope a ions anges om minimal o pe ec . Each PM le el a ec s he
e ec i e a e o he equipmen in a unique way, he eby al e ing he
sys em’s i ual li espan acco dingly. The changes in o al main enance
ope a ion cos s o a ious e ec i e equipmen a es a e illus a ed in
Table 7.
Based on he esul s ob ained om sol ing he model, as shown in
Table 7, inc easing he e ec i e equipmen a e leads o a educ ion in
cos s. This ou come aligns wi h he assump ions o he p oblem and is
en i ely logical. An inc ease in he e ec i e equipmen a e ypically
esul s in a dec ease in he equipmen ’s i ual age, which in u n e-
duces he equipmen ’s ailu e a e and, consequen ly, he associa ed
main enance cos s. Figs. 10–12 illus a e his ela ionship: as he e ec-
i e equipmen a e inc eases, he i ual li espan o he equipmen
dec eases, and ice e sa. In o he wo ds, a longe e ec i e li espan o
he equipmen shi s PM om a minimal o a mo e comp ehensi e le el
o implemen a ion. This ansi ion enhances he equipmen ’s li espan
and educes i s ailu e a e, u he con ibu ing o lowe main enance
cos s. These indings highligh he impo ance o op imizing he
e ec i e equipmen a e o achie e cos -e icien and eliable main e-
nance s a egies.
I is c ucial o no e ha a ia ions in he e ec i e a e o any
main enance le el can in luence he op imal solu ion. Fo example, i
he e ec i e a e o Le el 2 PM inc eases om 0.5 (impe ec ) o 1
(pe ec ), he op imal solu ion may change. Ins ead o pe o ming Le el
2 main enance in jus one pe iod, i migh become op imal o apply his
le el o main enance ac oss mul iple pe iods. This is because he cos -
e ec i eness o Le el 2 main enance, gi en i s cos and e ec i eness,
could be mo e bene icial compa ed o o he main enance le els when
ex ended o e a g ea e numbe o pe iods.
As shown in con ou Figs. 10–12, egions wi h une en bounda y
cu a u e indica e whe e he op imal solu ion alues change. Speci -
ically, he op imal solu ions o PM ope a ions a y wi hin he ollowing
e ec i e equipmen a e anges:
•Fi s le el o PM: Changes occu when
α
1<0.85.
•Second le el o PM: Adjus men s a e obse ed wi hin 0.5<
α
2≤0.6.
•Thi d le el o PM: Va ia ions a e e iden wi hin 0.3<
α
3≤0.5.
E en i he op imal solu ions emain s able in o he anges, a ia-
ions in he e ec i e equipmen a e can s ill impac he op imal alue o
he objec i e unc ion (cos ). This is because he equipmen ’s li espan
a ec s he ailu e a e, which consequen ly in luences he o e all
main enance cos s.
6. Manage ial insigh s
The esul s o his s udy p o ide aluable insigh s in o de e mining
he mos app op ia e iming and in ensi y o PM ope a ions, conside ing
hei impac on equipmen li espan, condi ions, and associa ed expen-
di u es. O e all, his pape p esen s a cos - educ ion s a egy o in-
dus ies, aimed a imp o ing equipmen a ailabili y and educing he
HEP. The indings o his s udy assis manage s in making in o med
decisions ega ding he op imal le el o HEP, aking in o accoun he
cos s associa ed wi h human e o , esou ce alloca ion o human e o
educ ion, and he o ganiza ion’s o e all budge . Manage s can plan
o ganiza ional and pe sonnel condi ions in a way ha main ains he
le el o e o a a desi ed and op imal h eshold.
In o he wo ds, hey can es ablish desi able h esholds o each o he
Common Pe o mance Condi ions (CPCs) co esponding o human e -
o s. Fu he mo e, he esul s o he p oposed model signi ican ly
con ibu e o enhancing main enance ope a ions planning by inco po-
a ing human e o in o he decision-making p ocess. This, in u n, leads
o op imal decision-making ega ding a ious le els o PM ope a ions
and imp o ed managemen o spa e pa in en o y. As a esul , he cos s
associa ed wi h CM ope a ions and o e all o ganiza ional expenses can
be managed in a cos -e ec i e manne .
The p esen ed model o e s signi ican bene i s o o ganiza ions
whe e PM plays a c ucial ole, and he cos s associa ed wi h human e o
and equipmen ailu e a e subs an ial. Addi ionally, his model p o ides
conside able ad an ages o o ganiza ions ha p e e o pe o m PM
ope a ions based on bo h equipmen age and condi ions. The simul a-
neous execu ion o PM ope a ions based on bo h condi ions and ime can
g ea ly enhance decision-making ou comes. This app oach p o es o be
a eliable s a egy o o ganiza ions ha mus conduc PM ope a ions
while conside ing ime cons ain s and equipmen condi ions, ensu ing
a balance be ween cos e iciency and ope a ional eliabili y.
V. Ba andegan Em oozi e al.
Ope a ions Resea ch Pe spec i es 14 (2025) 100336
18
7. Conclusions and sugges ions
This pape is no able o i s inno a i e app oach in es ima ing he
cos unc ion ela ed o human e o s in main enance asks by le e aging
eg ession analysis and his o ical da a. The s udy highligh s he signi -
ican e ec o HEP on he e iciency and e ec i eness o main enance
ope a ions. Fo he i s ime, i demons a es how human e o can
in luence he e ec i e a e o equipmen li espan, p o iding a no el
pe spec i e on he in e play be ween human ac o s and equipmen
eliabili y. In his s udy, a limi ed selec ion o spa e pa s has been
analyzed based on he equipmen unde conside a ion. The esea ch
ocuses exclusi ely on e alua ing he spa e pa s ypically u ilized o
bo h PM and CM ope a ions o wo speci ic machines. Es ablishing
p io i ized ankings and selec ing he mos essen ial spa e pa s—guided
by ac o s such as equi ed quan i y, signi icance o ope a ional ob-
jec i es, lead ime, supplie accessibili y, epai abili y, p icing, and
o he ele an conside a ions—can signi ican ly enhance he e iciency
and e ec i eness o spa e pa s in en o y managemen .
Fu he mo e, u u e in es iga ions could del e in o explo ing how
pe sonnel aining impac s no only PM bu also CM ope a ions, as
imp o ed aining may educe human e o s and enhance main enance
ou comes. Addi ionally, he s udy assumes a cons an cos o CM and
PM ope a ions ac oss all ime pe iods. I is sugges ed ha u u e esea ch
endea o s should accoun o eal-wo ld dynamics by inco po a ing
ac o s such as in la ion a es, luc ua ions in spa e pa s in en o y
le els, and o he economic a iables o be e e lec ac ual condi ions.
Such e inemen s would u he imp o e he model’s applicabili y and
accu acy in eal-wo ld indus ial se ings. This s udy ocuses p ima ily
on de e mining he op imal alue o HEP, wi hou p oposing speci ic
s a egies o enhancing and mi iga ing human e o s ac oss a ious
CPCs. To add ess his limi a ion, i is ad isable o de elop a no el
ma hema ical model ha dynamically adjus s based on he op imal HEP.
Such a model would p o ide a mo e comp ehensi e and impac ul
app oach o educing human e o s and hei associa ed cos s.
In p ac ical e ms, his would in ol e implemen ing enhancemen s
in he CPCs, aking in o accoun he cu en o ganiza ional con ex ,
inancial limi a ions, and he in luence o hese ac o s on human e o s.
This app oach should acili a e he iden i ica ion o op imal in-
e en ions o modi ying each sub-condi ion and o e all pe o mance
c i e ia, ensu ing a mo e a ge ed and e ec i e educ ion in human e -
o s. Fu he mo e, o u u e esea ch endea o s, i is ecommended o
inco po a e he conside a ion o a iable a iance in andom ac o s
du ing p oblem-sol ing p ocesses. By es ablishing h eshold limi s o
hese a iances, esea che s can o e mo e p ac ical and ac ionable
insigh s o add essing human e o s in eal-wo ld scena ios. This would
no only enhance he obus ness o he model bu also p o ide decision-
make s wi h clea e guidelines o implemen ing e o - educ ion s a-
egies in dynamic and unce ain en i onmen s.
A aluable di ec ion o u u e esea ch would be o de elop a mo e
comp ehensi e model ha in eg a es bo h lea ning and o ge ing p o-
cesses in he con ex o PM ope a ions. This amewo k would quan i y
he a e a which skills a e acqui ed and los o e mul iple main enance
cycles, conside ing ac o s such as ask complexi y, equency o p ac-
ice, and wo k o ce expe ience. By explo ing how lea ning- o ge ing
dynamics in luence main enance scheduling, HEP, and associa ed
cos s, his esea ch could p o ide ac ionable insigh s in o op imizing
wo k o ce aining p og ams and ope a ional e iciency.
To u he ad ance he unde s anding o human e o in main e-
nance ope a ions and i s economic implica ions, a u u e s udy could
ocus on de eloping a dynamic cos -bene i op imiza ion model o HEP
educ ion ac oss di e se main enance domains. This model would
in eg a e a de ailed classi ica ion o human e o s (e.g., slips, lapses,
mis akes, iola ions) and e alua e he impac o speci ic con ex ual
ac o s—such as aining p og ams, p ocedu al imp o emen s, human-
machine in e ace (HMI) design, and en i onmen al condi ions—on
HEP and associa ed cos s.
The s udy could also explo e domain-speci ic HEP h esholds, iden-
i ying he poin a which u he in es men s in e o educ ion yield
diminishing e u ns. By inco po a ing eal-wo ld case s udies and
simula ion-based scena ios, he esea ch would p o ide a decision-
suppo amewo k o help o ganiza ions p io i ize cos -e ec i e s a-
egies o minimizing human e o s in inspec ion, PM, and CM ac i i ies.
Fu he mo e, he s udy could in es iga e he ole o eme ging ech-
nologies, such as AI-d i en p edic i e main enance sys ems and
augmen ed eali y (AR) ools, in educing human e o s and op imizing
main enance e iciency. These echnologies could enhance decision-
making, imp o e ask execu ion, and educe he cogni i e load on
main enance pe sonnel. By in eg a ing hese ools in o he model, o -
ganiza ions could align hei main enance ope a ions wi h p ede ined
a ge s while balancing he ade-o s be ween e o educ ion cos s and
sys em eliabili y.
Such a amewo k would o e p ac ical, da a-d i en insigh s o
enhancing main enance pe o mance ac oss indus ies, enabling o ga-
niza ions o achie e highe eliabili y, lowe cos s, and imp o ed sa e y
s anda ds. By add essing he in e play be ween human ac o s, echno-
logical ad ancemen s, and economic conside a ions, his esea ch
would con ibu e signi ican ly o he ield o main enance op imiza ion
and human e o managemen .
CRediT au ho ship con ibu ion s a emen
Vahideh Ba andegan Em oozi: Concep ualiza ion, Me hodology,
So wa e, W i ing – o iginal d a , Visualiza ion. Mos a a Kazemi: Su-
pe ision, Da a cu a ion. Mahdi Doos pa as : W i ing – e iew &
edi ing, Valida 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 .
V. Ba andegan Em oozi e al.
Ope a ions Resea ch Pe spec i es 14 (2025) 100336
19
Appendix
The da a ela ed o his pape , de i ed om he case s udy, is p esen ed in Tables 1A o 2A.
Table 1
A. Da a ela ed o case s udy.
(con inued on nex page)
V. Ba andegan Em oozi e al.
Ope a ions Resea ch Pe spec i es 14 (2025) 100336
20
Table 1 (con inued)
V. Ba andegan Em oozi e al.
Ope a ions Resea ch Pe spec i es 14 (2025) 100336
21
Table 2
A. Da a ela ed o case s udy.
(con inued on nex page)
V. Ba andegan Em oozi e al.
Ope a ions Resea ch Pe spec i es 14 (2025) 100336
22
Da a a ailabili y
Da a will be made a ailable on eques .
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