Kang, Joohang; Choi, Byoungil; Lim, Chaehong; Eun, Joonyup
A icle
Coope a ion and compe i ion in an oligopolis ic and
ma u e indus y: A case s udy on he ca ionic eagen
indus y based on an op imiza ion model
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: Kang, Joohang; Choi, Byoungil; Lim, Chaehong; Eun, Joonyup (2025) :
Coope a ion and compe i ion in an oligopolis ic and ma u e indus y: A case s udy on he ca ionic
eagen indus y based on an op imiza ion model, Ope a ions Resea ch Pe spec i es, ISSN
2214-7160, Else ie , Ams e dam, Vol. 14, pp. 1-15,
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Coope a ion and compe i ion in an oligopolis ic and ma u e indus y:
A case s udy on he ca ionic eagen indus y based on an op imiza ion model
Joohang Kang , Byoungil Choi , Chaehong Lim, Joonyup Eun ∗
G adua e School o Managemen o Technology, Ko ea Uni e si y, Seoul 02841, Sou h Ko ea
ARTICLE INFO
Keywo ds:
Supply chain managemen
Supply chain op imiza ion model
Ca ionic eagen
Ma u e indus y
Oligopolis ic ma ke
ABSTRACT
A ca ionic eagen is an essen ial aw ma e ial in p in ing pape p oduc ion. The ma ke en i onmen o he
ca ionic eagen indus y is in luenced by he p in ing pape indus y. Owing o he COVID-19 pandemic,
he global expansion o emo e wo k and home educa ion has dec eased he demand o p in ing pape s.
Consequen ly, compe i ion among ma ke playe s (i.e., supplie s and buye s) in he ca ionic eagen indus y
is in ensi ying. This s udy ocuses on coope a ion be ween ma ke playe s in he ca ionic eagen indus y,
ep esen ing a ypical oligopolis ic and ma u e indus y. I p oposes a supply chain op imiza ion model
ha minimizes he cos s o he en i e supply chain, inco po a ing buye s’ isk hedge endency o add ess
ma ke unce ain y. The model is empi ically es ed using accessible and eliable da a o assess i s business
applicabili y. Nume ical expe imen s a e conduc ed o explo e scena ios ha can occu in eal ma ke
en i onmen , such as le els o isk hedging, ade dispu es, dec eases in demand, and changes in p oduc ion
capaci y. The expe imen al esul s p o ide manage ial implica ions. As buye s maximize he deg ee o which
hey di e si y hei pu chase quan i ies ac oss mul iple supplie s o educe isks, di e en ial cos s o he en i e
supply chain inc ease by 19%, which a e cos s ha canno be educed by supplie s’ capabili ies and ine i ably
a ise due o di e ences be ween supplie s (e.g., geog aphy, poli ics, and go e nmen policies). Howe e , in
un a o able ma ke condi ions, such as ade dispu es and dec eases in demand, less compe i i e supplie s
can su i e. This s udy shows ha when ma ke demand in he ca ionic eagen indus y dec eases, wo
supplie s may po en ially expe ience ope a ional ou ages. In eali y, hese wo supplie s de e io a ed unde
he challenging ma ke condi ions du ing he COVID-19 pandemic.
1. In oduc ion
The ca ionic eagen indus y ope a es in he business- o-business
sec o , whe e supplie s manu ac u e ca ionic eagen s o buye s. The
indus y is cha ac e ized as oligopolis ic and ma u e. Oligopolis ic ma -
ke s a e ypically domina ed by a small numbe o companies, o en
be ween wo and en. Se e al companies con ol a subs an ial ma ke
sha e, and hus ha e signi ican p icing powe and in luence [1]. The
ca ionic eagen indus y has an oligopolis ic na u e due o he limi ed
numbe o supplie s and buye s. Addi ionally, he indus y co esponds
o he ma u i y s age o he p oduc li e cycle, which consis s o in o-
duc ion, g ow h, ma u i y, and decline s ages [2]. The ma u e na u e
o he ca ionic eagen indus y is e idenced by he long his o y o
he indus y. The ca ionic eagen indus y aces i s o igins back o
he ea ly 20 h cen u y wi h he de elopmen o qua e na y ammo-
nium compounds [3]. In he 1970s, chemical companies such as Dow
and Degussa de eloped he mos common ca ionic eagen 3-chlo o-
2-hyd oxyp opyl ime hylammonium chlo ide. Mos o he demand
∗Co esponding au ho .
E-mail add ess: [email p o ec ed] (J. Eun).
o his ca ionic eagen is consumed o he p oduc ion o ca ionic
s a ch. Ca ionic s a ch enhances he bonding s eng h be ween mic o-
laye s o pape by ionizing pulp ibe , which enhances he bonding
s eng h be ween he mic o-laye s o pape by ionizing pulp ibe s.
Addi ionally, i imp o es o e all s eng h and p in abili y o pape s by
e enly dis ibu ing ille s. As an essen ial aw ma e ial in he p oduc-
ion o p in ing pape s, he ma ke en i onmen o he ca ionic eagen
indus y a e closely ied o hose o he p in ing pape indus y.
The p in ing pape indus y is cu en ly expe iencing an unp ece-
den ed c isis due o he COVID-19 pandemic. While he demand o
p in ed ma e ials such as o ice pape , magazines, and books had been
declining e en be o e he pandemic. The expansion o emo e wo k and
home educa ion, d i en by he pandemic, has u he accele a ed he
con ac ion o he p in ing pape ma ke . RISI, Inc., a consul ing i m
specializing in he pape indus y, has ocused he po en ial collapse
o he p in ing pape ma ke owing o he COVID-19 pandemic [4].
h ps://doi.o g/10.1016/j.o p.2025.100325
Recei ed 22 Augus 2024; Recei ed in e ised o m 23 Decembe 2024; Accep ed 14 Janua y 2025
Ope a ions Resea ch Pe spec i es 14 (2025) 100325
A ailable online 22 Janua y 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-NC-ND license ( h p://c ea i ecommons.o g/licenses/by-
nc-nd/4.0/ ).
J. Kang e al.
Moody’s, a global c edi a ing agency, has o ecas ed dec eased ope a -
ing p o i s o pape companies p ima ily selling p in ing pape s [5]. In
2020, 16 p in ing pape ac o ies in No h Ame ica ei he pe manen ly
closed o swi ched hei main p oduc o o he p oduc ocus due o he
lack o demand. The si ua ion in he Eu opean pape indus y is simila
o ha o No h Ame ica [6]. Oligopolis ic ma ke s can con ibu e o
economic s abili y by main aining p ice le els and educing ola ili y.
Howe e , excessi e ma ke dominance o collusion may lead o ma ke
dis o ions and hinde o e all economic e iciency [7,8]. Acco ding o
Po e [9] companies in ma u e indus ies end o lowe hei p oduc
p ices o secu e a la ge ma ke sha e, in ensi ying compe i ion wi h
o he companies. In ac , ma ke playe s (i.e., supplie s and buye s) in
he ca ionic eagen indus y, an oligopolis ic and ma u e indus y, ex-
pe ience educed p o i s due o excessi e compe i ion. Addi ionally, he
COVID-19 pandemic has c ea ed an un a o able ma ke en i onmen
o he p in ing pape indus y.
Oligopolis ic companies wield signi ican ma ke powe , enabling
hem o in luence p ices and ma ke ou comes o hei ad an age.
Howe e , his can lead o ine iciencies and inequali y wi hin he
ma ke , as smalle compe i o s s uggle o compe e [10]. This s udy
aims o explo e he s a egic decisions ha ma ke playe s can make o
he public good in an oligopolis ic indus y (i.e., he ca ionic eagen
indus y), which is cha ac e ized by s a egic in e ac ions [11]. One
po en ial s a egy o es ablish a compe i i e and obus supply chain in
he oligopolis ic and ma u e indus y is coope a ion be ween supplie s
and buye s. In his ega d, he e is he concep o compe i i e coop-
e a ion (i.e., co-ope i ion). Co-ope i ion is a business s a egy ha uses
insigh s gained om he game heo y o unde s and when i is be e
o compe i o s o wo k oge he [12]. The alue ne model, which con-
sis s o cus ome s, complemen o s, supplie s, and compe i o s, cen e ed
on he co-ope i ion, emphasized coope a ion among compe i o s [13].
Inspi ed by his concep , coope a ion among compe i o s (i.e., be ween
supplie s o be ween buye s) is also highligh ed in his s udy.
In his s udy, we p opose a supply chain op imiza ion model ha
minimizes cos s o imp o e he compe i i eness o he en i e indus y;
The e m en i e indus y e e s o all business and o ganiza ions engaged
in a pa icula p oduc o se ice. The buye s’ isk hedge endency is
inco po a ed in o he p oposed model o examine ma ke unce ain y.
The model subsequen ly analyzes he e ec s on supply chains based on
luc ua ions in he buye s’ isk hedge endency. The p oposed model
is empi ically es ed using accessible and eliable da a. Manage ial
implica ions a e de i ed h ough nume ical expe imen s unde a ious
ma ke en i onmen s. The esul s align wi h p ac ical e en s obse ed
du ing he s udy. Mo eo e , based on he expe imen al esul s, we
p esen he easons why eaching an ag eemen among ma ke playe s
o an ideal equilib ium, whe e coope a ion among ma ke playe s is
achie ed, is di icul . No ably, he expe imen al esul s, which show
ha wo supplie s a e unable o con inue hei businesses, align wi h
wha ac ually occu ed du ing his s udy.
The con ibu ions o his s udy a e s uc u ed in o heo e ical, man-
age ial, and me hodological aspec s and p esen ed as ollows. (i) F om
he heo e ical pe spec i e, his s udy p oposes a simple ye e sa-
ile supply chain op imiza ion model o an oligopolis ic and ma u e
indus y. This me hodology is e ec i e and solid because he model
conside s only di e en ial cos s ha ine i ably a ise due o di e ences
be ween supplie s. Gi en he minimal echnological and quali y di e -
ences be ween supplie s in a ma u e indus y, he op imiza ion model is
designed o be e ec i ely ac able by excluding non-di e en ial cos s
(i.e., con e gen cos s) a ec ed by echnological and quali y di e -
ences. (ii) F om he manage ial pe spec i e, by analyzing supply chains
o he con olled en i onmen o an oligopolis ic and ma u e indus y
unde a ious scena ios, he impo ance o coope a ion s a egy is high-
ligh ed. (iii) F om he me hodological pe spec i e, he op imiza ion
model is designed as an MILP (mixed in ege linea p og am). The
p oposed model is applicable as a p ac ical me hodology o making
decisions o ma ke playe s in a ious indus ial sec o s (e.g., aw ma-
e ials, pe ochemical, and a e ea hs indus y) ha ope a e in simila
business en i onmen (e.g., an oligopolis ic and ma u e indus y). By
manipula ing pa ame e s ha e lec changes in ma ke en i onmen
(e.g., ade dispu es, changes in demand, changes in supply), playe s’
s a us can be analyzed by obse ing he changes in decision a iables
(e.g., see Jeon e al. [14] and Cha e al. [15]). In his con ex , he busi-
ness en i onmen and ma ke en i onmen e e o he cha ac e is ics
o an indus y and he si ua ions o condi ions in which ma ke playe s
ope a e, espec i ely.
To ob ain clea manage ial insigh s om he expe imen al esul s,
se e al esea ch ques ions a e aised he e and answe ed in Sec ion 4.7:
1. How does coope a ion among ma ke playe s a ec he compe -
i i eness o he en i e indus y?
2. How do cos s o he en i e supply chain inc ease o dec ease in
esponse o di e en le els o isk hedging?
3. How do ade dispu es a ec sales quan i ies o supplie s and
cos s o he en i e supply chain?
4. How do dec eases in demand cause changes in cos s o he en i e
supply chain?
5. How does inc ease o dec ease in p oduc ion capaci y o supplie s
a ec s cos s o he en i e supply chain?
The emainde o his pape is o ganized as ollows: Sec ion 2
desc ibes he ela ed li e a u e. Sec ion 3in oduces a supply chain
op imiza ion model ha e lec s cha ac e is ics o an oligopolis ic and
ma u e indus y. In Sec ion 4, we empi ically es he p oposed model,
analyzing he expe imen esul s o de i e manage ial implica ions.
Sec ion 5concludes his s udy.
2. Rela ed li e a u e
Companies main ain a compe i i e ad an age by connec ing o
in eg a ing componen s o hei supply chains [16]. Selec ing he mos
sui able supplie s is c ucial because i signi ican ly in luences he sup-
ply chains componen s [17]. Acco dingly, a ious indus ial sec o s,
including manu ac u ing, p ocessing, and logis ics, ha e explo ed sup-
ply chain op imiza ion based on ma hema ical p og amming. This sec-
ion examines p e ious s udies om wo pe spec i es: i s , whe he
he s udies ocused on maximizing indi idual companies’ p o i s o
he en i e indus y’s p o i abili y, as well as on he ype o compe i-
i e s a egy (i.e., ei he compe i ion o coope a ion); second, whe he
ma ke unce ain y is inco po a ed in o a model. Ma ke unce ain y
e e s o luc ua ions in ma ke en i onmen , including eigh cos s,
aw ma e ial p ices, labo cos s, elec ici y a es, and impo a i s,
d i en by sudden e en s such as he COVID-19 pandemic o ade
dispu es. Table 1illus a es he cha ac e is ics o p e ious s udies and
he p oposed model in his s udy.
2.1. Supply chain pe spec i e and compe i i e s a egy
Jaya aman e al. [17] p oposed a supplie selec ion model ha
enables buye s o minimize ixed and a iable cos s when choosing
supplie s. The model pu sued he p o i o a single buye and as-
sumed a compe i i e si ua ion among mul iple supplie s and buye s.
Sakawa e al. [18] p oposed a supply chain model ha minimizes
p oduc ion and anspo a ion cos s, gi en supplie s’ p oduc ion ca-
paci ies and ma ke demand. They p esen ed a scheme o p o i s
and cos alloca ion among game pa icipan s om he pe spec i e o
coope a i e game heo y, employing uzzy logic o ensu e s able p o-
duc ion and anspo a ion in an unce ain en i onmen . Papageo giou
e al. [19] sugges ed a model o he pha maceu ical indus y, which
is an oligopolis ic and ma u e indus y, inco po a ing he cha ac e -
is ics o an oligopolis ic and ma u e indus y and he global ade
s uc u e. The model allowed a company o decide business s a egies
in he ma ke en i onmen . Vidal and Goe schalckx [20] p esen ed a
model ha maximizes he a e - ax p o i o a mul ina ional company.
Ope a ions Resea ch Pe spec i es 14 (2025) 100325
2
J. Kang e al.
The model included ans e p ices and he alloca ion o anspo a-
ion cos s as explici decision a iables. They de eloped an algo i hm
ha employed successi e linea p og amming based on elaxa ion,
yielding accep able-quali y solu ions. Thanh e al. [21] p oposed an
op imiza ion model o a p oduc ion-dis ibu ion sys em ha suppo s
decision-making p ocesses such as supplie selec ion and lows along
he supply chain, conside ing mul i-echelon and mul i-commodi y ac-
o s. In o he wo ds, he model helps companies make s a egic and
ac ical decisions. Companies pu sue a coope a ion s a egy in ha
supplie s o e pu chase cos discoun s when buye s pu chase mul iple
i ems in supplie selec ion. Chang e al. [22] p oposed a model ha
conside ed mul iple buye s and a single supplie while enhancing co-
ope a i e ela ionships ac oss he indus y. They ound ha a policy o
shipping small olumes o a ious i ems a he han la ge olumes o a
ew i ems could educe in eg a ed cos s, enhancing p o i s o bo h buy-
e s and supplie s. Jakha e al. [23] de eloped a pa ne selec ion and
low alloca ion model, p oposing sus ainable supply chain pe o mance
measu es. They conside ed he p o i o he en i e indus y and ap-
p oached compe i i e s a egy h ough coope a ion. Alikhani e al. [24]
p oposed a model ha conside s ac o s such as sus ainabili y and
isk a he same ime. The p oposed model uses in e al ype-2 uzzy
se s o quan i y he decision make ’s inpu and combines wi h DEA o
e icien ly selec a supplie . Guo e al. [25] p esen ed a mixed in ege
linea p og am and a dis ibu ed app oxima ion app oach o a sus ain-
able supply chain ne wo k design. This model s uc u ed he supply
chain o consis o supplie s, ans o me s, dis ibu o s, and cus ome s
o a ge he en i e indus y. Thei expe imen al esul s indica ed he
impo ance o connec i i y and collabo a ion among ma ke playe s.
Gao and You [26] de eloped a wo-s age game- heo y-based s ochas-
ic mixed linea p og am. They examined how mul iple s akeholde s’
independen p o i -seeking beha io s a ec supply chain pe o mance
in non-coope a i e en i onmen s. Va aeenezhad e al. [27] p oposed a
mul i-objec i e linea p og am o a mul i-echelon and mul i-p oduc
supply chain managemen . The model was cha ac e ized by simul a-
neously conside ing en i onmen al, economic, and social impac s. This
esea ch was applied o a wood and pape indus y case. Expe imen al
esul s demons a ed ha decision-make s could plan a supply chain
ha bes aligned wi h he cha ac e is ics hey conside ed impo an
(i.e., economy, en i onmen , and socie y). Gholizadeh e al. [28] de-
eloped an op imiza ion model and heu is ic algo i hm o maximize
he o al p o i and minimize en i onmen al e ec s o a closed-loop
supply chain. This s udy e alua ed he model’s pe o mance using
da a om Saleh Indus ial Dai y G oup, a well-known dai y p oduc
p oduce in I an. The op imali y gaps ob ained by he heu is ic algo-
i hm o all expe imen s demons a ed an accep able ange (less han
5%). Fa hollahi-Fa d e al. [29] p oposed a uzzy mixed in ege linea
p og am o handle unce ain pa ame e s in supply chain ne wo ks.
This model inco po a es a dual-channel (online and o line) and mul i-
p oduc app oach o accoun o ecen consume pu chasing beha io
(i.e., Online o O line). Th ough expe imen s, hey demons a ed ha
o he success ul implemen a ion o an O2O policy, app op ia e p icing
o bo h online and o line channels mus be es ablished. O he wise, i
could lead o nega i e e ec s on he en i e supply chain. Chowdhu y
e al. [30] p esen ed a mixed-in ege p og am o a accine supply
chain ha ensu es he en i e ne wo k’s economic pe o mance. They
applied he model o he COVID-19 accine dis ibu ion sys ems o
a densely popula ed ci y in Bangladesh and e i ied ha he supply
chain ne wo k is e icien and well-designed. Mosallanezhad e al. [31]
p oposed an op imiza ion model in he medical supply chain o ensu e
he eliable dis ibu ion o pe sonal p o ec i e equipmen o medical
pe sonnel in si ua ions like a global epidemic. The objec i e unc ion
o he model is o simul aneously minimize he o al cos s and he
amoun o unsa is ied demand o pa icipan s such as manu ac u e s,
dis ibu o s, and hospi als.
2.2. Ma ke unce ain y
Sakawa e al. [18] add essed a eal p oblem ega ding he p oduc-
ion and anspo a ion o a housing ma e ial manu ac u e . In he eal
wo ld, ma ke demand and p oduc ion capaci y we e de e mined based
on expe judgmen , so hey we e no always p ecise alues. To ackle
his issue, his s udy inco po a ed uzzy goals and uzzy cons ain s in o
a mixed ze o–one p og am. Liu and Nagu ney [32] s udied he impac
o o eign exchange unce ain y and compe i ion in ensi y on a supplie
engaged in o e seas ou sou cing. They highligh ed ha companies’
decisions ega ding p icing, p ocu emen , ou sou cing, anspo a ion,
and p oduc ion can be in luenced by o eign exchange unce ain y and
compe i ion. Gao and You [26] inco po a ed a ious unce ain ies in o
hei wo-s age game- heo y-based s ochas ic mixed linea p og am
o supply chain ne wo ks in ol ing mul iple s akeholde s. In a case
s udy on shale gas supply chain, hey conside ed he p oduc i i y
unce ain y o shale gas p oduce s and he ope a ional unce ain y
o shale gas p ocesso s. S akeholde s showed a endency o choose
mo e conse a i e op ions when ma ke unce ain y, including he
unce ain ies o o he s akeholde s, was p esen . Yılmaz e al. [33]
p oposed a scena ios-based wo-s age s ochas ic op imiza ion model
o e e se supply chain design. They conside ed he ipple e ec
ha esul s om sudden dis up ions a one o mo e poin s in he
supply chain and a ec s he en i e ne wo k as a o m o unce ain y.
Expe imen al esul s showed ha he ipple e ec can inc ease he
emission le el and o al cos by up o 40%. Focusing on unce ain-
ies om he ipple e ec , Yılmaz e al. [34] de eloped a wo-s age
s ochas ic op imiza ion model o medical supply chain esilience by
employing lean ools and conside ing he ipple e ec , emphasizing
p epa edness s a egies o mi iga e pandemic- ela ed isks. Simila ly,
Özçelik e al. [35] also conside ed he ipple e ec . They de eloped a
obus op imiza ion model o e e se supply chain ne wo ks aligned
wi h g een p inciples. Gholizadeh e al. [28] p oposed a mixed in ege
linea p og am o a sus ainable closed-loop supply chain in he dai y
indus y. The demand, shipping and ope a ing cos s, acili y capaci y,
and p oduc e u n a es a e conside ed as unce ain pa ame e s. Fo
he unce ain pa ame e s, hey gene a ed pessimis ic, op imis ic, and
wo s -case scena ios and e alua ed he model pe o mance. Fa hollahi-
Fa d e al. [29] ackled he unce ain y pa ame e s using a uzzy
model. They conside ed all pa ame e s ela ed o p ices and he a e
o was e p oduc ion as unce ain. Chowdhu y e al. [30] conside ed
in en o y holding cos s, uni assembly cos s o packaged accines, uni
p ices o aw ma e ials, supplie capaci y, and anspo a ion cos s as
unce ain pa ame e s in he accine supply chain. These pa ame e s
we e de ined as p obabilis ic wi h a uni o m p obabili y dis ibu ion.
Na u ally, h ough expe imen s, i was con i med ha hese unce ain
pa ame e s impac p o i abili y.
3. P oblem de ini ion
This sec ion desc ibes a supply chain op imiza ion model ha in-
co po a es he cha ac e is ics o he a ge indus y (i.e., oligopolis ic
and ma u e indus y). The objec i e unc ion o he p oposed model is
o minimize he o al di e en ial cos s (TDCs) o he supply chains in
he indus y h ough coope a ion among ma ke playe s. Sec ions 3.1
and 3.2 de ine he e minologies and assump ions o he model, e-
spec i ely. The p oposed model is o mula ed as a mixed in ege linea
p og am (MILP) and p esen ed in Sec ion 3.3.
3.1. Te minologies
•Di e en ial cos s e e o he cos s ha ine i ably a ise due o
di e ences be ween supplie s. These cos s a e in luenced by ac-
o s such as geog aphy, poli ics, and go e nmen policies, which
canno be educed by supplie s’ capabili ies. In he p oposed
model, logis ics, elec ici y, labo , aw ma e ial cos s, and impo
a i s a e conside ed di e en ial cos s.
Ope a ions Resea ch Pe spec i es 14 (2025) 100325
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J. Kang e al.
Table 1
Rela ed pape s and hei conside a ions †.
Au ho s Me hodology ‡Pe spec i e Compe i i e s a egy Conside a ion o ma ke unce ain y
Indi idual
company
En i e
indus y
Compe i ion Coope a ion
Jaya aman e al. [17] MILP ✓ ✓
Sakawa e al. [18] MBIP ✓ ✓ ✓
Papageo giou e al. [19] MILP ✓ ✓
Vidal and Goe schalckx [20] MILP ✓
Thanh e al. [21] MILP ✓ ✓
Chang e al. [22] MILP ✓ ✓
Liu and Nagu ney [32] LP ✓ ✓ ✓
Jakha e al. [23] MILP ✓ ✓ ✓
Guo e al. [25] MILP ✓ ✓
Alikhani e al. [24] LP ✓ ✓ ✓
Gao and You [26] SMIP ✓ ✓ ✓
Va aeenezhad e al. [27] LP ✓
Yılmaz e al. [33] SMIP ✓ ✓
Özçelik e al. [35] ROM ✓ ✓
Gholizadeh e al. [28] MILP ✓ ✓
Fa hollahi-Fa d e al. [29] FMIP ✓ ✓ ✓
Mosallanezhad e al. [31] DOM ✓ ✓
Chowdhu y e al. [30] MIP ✓ ✓
Sawik [36] SMIP ✓ ✓
Yılmaz e al. [34] SOM ✓ ✓
This s udy MILP ✓ ✓ ✓
†No e ha any cha ac e is ics (i.e., pe spec i e, compe i i e s a egy, ma ke unce ain y) ha a e no explici ly desc ibed o canno be easonably in e ed in a pape ha e been
le blank.
‡LP: linea p og am, MIP: mixed in ege p og am, MILP: mixed in ege linea p og am, FMIP: uzzy mixed in ege linea p og am, SMIP: s ochas ic mixed in ege p og am, MBIP:
mixed bina y in ege p og am, ROM: obus op imiza ion model, SOM: s ochas ic op imiza ion model, DOM: de e minis ic op imiza ion model.
•Con e gen cos s a e he a ied cos s ha can be educed by
supplie s’ capabili ies and e o s.
•Di ec ma e ial cos s a e he cos s o di ec and aw ma e ials
iden i ied in he p oduc ion o p oduc s.
•Di ec labo cos s a e hose o explici ly iden i iable labo used o
p oduce p oduc s.
•Manu ac u ing o e head cos s a e he cos s ha a e challenging
o iden i y, encompassing all cos s equi ed o p oduce p oduc s
excep di ec ma e ial cos s and di ec labo cos s.
•Cos and eigh (CFR) is a deli e y condi ion ha includes eigh
cos s and impo a i s. Unde his condi ion, a supplie co e s all
cos s om hei loading loca ion o he buye s’ designa ed po .
•F ee on boa d (FOB) is a deli e y condi ion ha excludes eigh
cos s and impo a i s. Unde his condi ion, a supplie is e-
sponsible o co e ing he ela ed cos s and p ocedu es un il he
p oduc s a e loaded on o a ship a he po o expo . How-
e e , once he ship depa s, he buye is esponsible o he
anspo a ion cos s and isks.
•Buye s’ isk hedge endency is he deg ee o which a buye ’s pu -
chase quan i ies a e dis ibu ed ac oss mul iple supplie s. F om a
buye s’ poin o iew, ins abili y caused by monopolis ic supply
om a ew supplie s, p ice luc ua ions, un esponsi eness o a
buye ’ o de , and unce ain y in lead imes a e isks associa ed
wi h supplie s. Di e si ying supplie s is a way o mi iga e hese
isks. To quan i a i ely conside he isk in a supply chain [37],
he p oposed model sugges s a pa ame e called buye s’ isk
hedge endency, which con ols he maximum amoun o demand
ha is able o be assigned o a supplie .
3.2. Assump ions
•The a ge indus y is oligopolis ic and ma u e wi h mul iple
supplie s and buye s; The g ow h o supply and demand in a
ma u e indus y is slow, wi h ew echnological and quali y di e -
ences among supplie s. Al hough echnology con inues o e ol e,
educing cos s in he indus y is challenging. Due o he cha ac-
e is ics o he ma u e indus y, all buye s ha e an equal le el
o buye isk hedge endency. Due o he high p ice elas ici y
o demand and cha ac e is ics o oligopolis ic indus ies (i.e., in-
e dependence be ween companies, high simila i y o p oduc s,
buye ’s budge cons ain , supplie ’s p ice-d i en s a egy, buye ’s
expec a ion) [38,39], all buye s execu e p ice-o ien ed pu chas-
ing decisions. P ice-o ien ed compe i ion is o e hea ing, and he
possibili y o supply chain es uc u ing (e.g., wi hd awal om he
business due o low p o i abili y) exis s [2].
•P oduc cos s a e di ided in o di e en ial and con e gen cos s;
In manu ac u ing companies, h ee gene al ypes o p oduc cos s
a e di ec ma e ial, di ec labo , and manu ac u ing o e head
cos s [40]. In he p oposed model, hese p oduc cos s a e ede-
ined as uncon ollable di e en ial and con ollable con e gen
cos s. Due o he minimal echnological and quali y di e ences
be ween supplie s in a ma u e indus y, con e gen cos s a e
igno ed in he ma hema ical o mula ion o Sec ion 3.3.
•CFR and FOB a e adop ed based on In e na ional Comme cial
Te ms (INCOTERMS); INCOTERMS a e s anda ds o p oduc de-
li e y, cos alloca ion, isk ans e , anspo a ion, and liabili y
be ween pa ies in a ade ansac ion. I a supplie and a buye
ag ee o accep INCOTERMS, hey a e bound by he condi ions o
he ade con ac .
•F eigh cos s a e conside ed in e -coun y eigh a es; In an
oligopolis ic ma ke whe e buye s mus ollow p ice-o ien ed pu -
chasing om a ew supplie s, anspo a ion is usually conduc ed
by con aine ships a sea. Small- olume p oduc s can be ans-
po ed by less- han-con aine load (LCL) shipmen s. The in e -
coun y eigh a e pe uni weigh o p oduc s anspo ed by
LCL is assumed o be he same as ha cha ged o con aine
ships. When a supplie wi hin a coun y anspo s p oduc s o he
same coun y, eigh cos s a e no cha ged. In Eu ope, land ans-
po a ion be ween coun ies is conduc ed by uck o ail oad,
incu ing signi ican ly low eigh cos s.
•The numbe o wo ke s o each supplie is calcula ed using he
ull- ime equi alen (FTE) concep ; FTE is he o al hou s wo ked
di ided by he maximum numbe o compensable hou s in a
ull- ime schedule. Based on FTE [41], he numbe o wo ke s
equi ed o comple e a ask wi hin a gi en pe iod is calcula ed
as a eal numbe , no an in ege .
Ope a ions Resea ch Pe spec i es 14 (2025) 100325
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J. Kang e al.
Table 2
No a ions used in he p oposed model.
Se s
𝑆Se o supplie s
𝐵Se o buye s
Pa ame e s
𝑦𝑖Capaci y o supplie 𝑖(MT)
𝑑𝑗Demand o buye 𝑗(MT)
𝑓𝑖,𝑗 F eigh cos s o ou e pe uni o p oduc om supplie 𝑖 o buye 𝑗(USD/MT)
𝑟𝑖Raw ma e ial cos s pe uni o p oduc o supplie 𝑖(USD/MT)
𝑒𝑖Elec ici y cos s pe uni o p oduc o supplie 𝑖(USD/MT)
𝑏𝑗FOB p ice pe uni o p oduc o buye 𝑗(USD/MT)
𝑢𝑖USD sales pe employee o supplie 𝑖
𝑤𝑖Annual a e age wage o supplie 𝑖
𝑥𝑖,𝑗 Impo a i a e pe uni o p oduc om supplie 𝑖 o buye 𝑗
𝑚Numbe o supplie
𝛾Buye s’ isk hedge endency (0≤𝛾 <1 −1
𝑚)
Va iables
𝑡𝑖,𝑗 Quan i y anspo ed om supplie 𝑖 o buye 𝑗(MT)
•Me ic on (MT) is used as he ma e ial uni . Mo eo e , 1 MT is
equi alen o 1 on (2204,6 lb).
3.3. Ma hema ical o mula ion
Table 2illus a es a summa y o pa ame e s and a iables. 𝑆and
𝐵a e he se s o supplie s and buye s, espec i ely. 𝑦𝑖 ep esen s he
manu ac u ing capaci y o supplie 𝑖, and 𝑑𝑗deno es he demand o
buye 𝑗.𝑓𝑖,𝑗 e e s o eigh cos s pe uni o p oduc om supplie 𝑖
o buye 𝑗.𝑟𝑖and 𝑒𝑖indica e aw ma e ial cos s pe uni o p oduc
and elec ici y cos s pe uni o p oduc o supplie 𝑖, espec i ely.
𝑏𝑗indica es a p oduc p ice (i.e., FOB p ice) pe uni o p oduc o
buye 𝑗.𝑢𝑖is USD sales pe employee o supplie 𝑖and 𝑤𝑖is annual
a e age wage o supplie 𝑖.𝑥𝑖,𝑗 e e s o impo a i a e pe uni
o p oduc om supplie 𝑖 o buye 𝑗.𝛾indica es buye s’ isk hedge
endency and ac s as a cons ain on he quan i y o p oduc pu chased
om a supplie .
The p oposed model aims o ind he anspo ed quan i ies ha
minimize he TDCs o he a ge indus y o imp o e i s o e all com-
pe i i eness (i.e., he equilib ium). The objec i e unc ion is o mula ed
as ollows:
𝑀 𝑖𝑛𝑖𝑚𝑖𝑧𝑒 ∑
𝑖∈𝑆[∑
𝑗∈𝐵
𝑓𝑖,𝑗 𝑡𝑖,𝑗 +𝑟𝑖∑
𝑗∈𝐵
𝑡𝑖,𝑗 +𝑒𝑖∑
𝑗∈𝐵
𝑡𝑖,𝑗
+∑𝑗∈𝐵(𝑏𝑗+𝑓𝑖,𝑗 )𝑡𝑖,𝑗 𝑤𝑖
𝑢𝑖
+∑
𝑗∈𝐵(𝑏𝑗+𝑓𝑖,𝑗 )𝑡𝑖,𝑗 𝑥𝑖,𝑗 ](1)
TDCs a e he summa ion o di e en ial cos s om all supplie s. The
di e en ial cos s o supplie i a e ca ego ized in o i e componen s:
o al eigh , o al aw ma e ial, o al elec ici y, o al labo cos s,
and o al impo a i s. To al eigh cos s o supplie i is exp essed
as ∑𝑗∈𝐵𝑓𝑖,𝑗 𝑡𝑖,𝑗 , o al aw ma e ial cos s o supplie 𝑖as 𝑟𝑖∑𝑗∈𝐵𝑡𝑖,𝑗 ,
o al elec ici y cos s o supplie 𝑖as 𝑒𝑖∑𝑗∈𝐵𝑡𝑖,𝑗 , o al labo cos s o
supplie 𝑖as ∑𝑗∈𝐵
(𝑏𝑗+𝑓𝑖,𝑗 )𝑡𝑖,𝑗 𝑤𝑖
𝑢𝑖
, and o al impo a i s o supplie 𝑖as
∑𝑗∈𝐵(𝑏𝑗+𝑓𝑖,𝑗 )𝑡𝑖,𝑗 𝑥𝑖,𝑗 , espec i ely.
∑
𝑗∈𝐵
𝑡𝑖,𝑗 ≤𝑦𝑖,∀𝑖∈𝑆(2)
∑
𝑖∈𝑆
𝑡𝑖,𝑗 ≥𝑑𝑗,∀𝑗∈𝐵(3)
𝑡𝑖,𝑗 ≤(1 −𝛾)𝑑𝑗,∀𝑖∈𝑆 ,∀𝑗∈𝐵(4)
Eq. (2) ensu es ha he o al sales quan i y o a supplie canno
exceed he supplie ’s p oduc ion capaci y 𝑦𝑖. Eq. (3) gua an ees ha
he o al pu chase quan i y o a buye sa is ies he buye ’s demand 𝑑𝑗.
Eq. (4) o ces he quan i y anspo ed om supplie 𝑖 o buye 𝑗is less
han o equal o he buye ’s demand conside ing 𝛾.
Fig. 1illus a es how he supply chain wo ks in he p oposed model.
In his example, we assume ha he e a e only wo supplie s and wo
buye s in he supply chain. The USD sales pe employee o supplie s A
and C a e $1,000,000 each. P oduc s om supplie s A and C a i e a
each expo po ia land ou es, wi h deli e y condi ions speci ied as
FOB. La ge quan i ies o p oduc s a e anspo ed by con aine ships
and small quan i ies a e anspo ed by LCLs om expo po s o
he buye s’ designa ed po s. A his s age, he deli e y condi ions a e
speci ied as CFR. To explain he TDCs calcula ion in de ail, using he
eigh olume in Fig. 1and he da a om Sec ion 4.2, an example o
calcula e TDCs is p esen ed as ollows.
𝐷 𝑖𝑓 𝑓 𝑒𝑟𝑒𝑛𝑡𝑖𝑎𝑙 𝑐 𝑜𝑠𝑡𝑠 𝑜𝑓 𝑆 𝑢𝑝𝑝𝑙 𝑖𝑒𝑟 𝐴
=4146
20 × 20 +1166
20 × 8 + 456 × 28 + 69 × 28
+((1140 +4146
20 )× 20 × 63093)+((1056 +1166
20 )× 8 × 63093)
1000000
+((1140 +4146
20 )× 20 × 0 +(1056 +1166
20 )× 8 × 0.039)
= 21922.6
𝐷 𝑖𝑓 𝑓 𝑒𝑟𝑒𝑛𝑡𝑖𝑎𝑙 𝑐 𝑜𝑠𝑡𝑠 𝑜𝑓 𝑆 𝑢𝑝𝑝𝑙 𝑖𝑒𝑟 𝐶
=3053
20 × 2 +315
20 × 40 + 867 × 42 + 98 × 42
+((1140 +3053
20 )× 2 × 39472)+((1056 +315
20 )× 40 × 39472)
1000000
+((1140 +3053
20 )× 2 × 0 +(1056 +315
20 )× 40 × 0.039)
= 44931.44
𝑇 𝐷 𝐶 𝑠=𝐷 𝑖𝑓 𝑓 𝑒𝑟𝑒𝑛𝑡𝑖𝑎𝑙 𝑐 𝑜𝑠𝑡𝑠 𝑜𝑓 𝑆 𝑢𝑝𝑝𝑙 𝑖𝑒𝑟 𝐴
+𝐷 𝑖𝑓 𝑓 𝑒𝑟𝑒𝑛𝑡𝑖𝑎𝑙 𝑐 𝑜𝑠𝑡𝑠 𝑜𝑓 𝑆 𝑢𝑝𝑝𝑙 𝑖𝑒𝑟 𝐶
= 66854.04 (𝑈 𝑆 𝐷)
4. Case s udy: Ca ionic eagen indus y
4.1. Backg ound
A ca ionic eagen is conside ed as a ma u e p oduc . The ca ionic
eagen indus y is oligopolis ic wi h only se en supplie s sp ead ac oss
Ope a ions Resea ch Pe spec i es 14 (2025) 100325
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J. Kang e al.
Fig. 1. A schema ic example o he supply chain in his s udy.
Fig. 2. Capaci y u iliza ion and sales quan i y in he ideal equilib ium.
i e coun ies. In 2019, he o al p oduc ion capaci y o hese suppli-
e s was 170,000 ons, while he o al demand om all buye s was
127,654 ons. In o he wo ds, he ma ke is expe iencing an o e supply
o ca ionic eagen s, leading o in ense compe i ion among supplie s.
Ca ionic eagen s a e ypically aded in 230-kg d ums, 1,100-kg in-
e media e bulk con aine s, and 20,500-kg lex bags, and a e usually
anspo ed in 20- oo d y con aine s wi h a capaci y o 20 ons.
4.2. Da a
This case s udy uses publicly a ailable and accessible da a om he
ca ionic eagen indus y [42]. The global supply chain o ca ionic
eagen s includes se en supplie s and wen y-six buye s. Table 3and
Table 4illus a e he da a o he supplie s and buye s, espec i ely.
The p ima y aw ma e ial o ca ionic eagen s is p opylene [43].
The aw ma e ial p ice (i.e., he p ice o p opylene) illus a ed in
Table 3is based on he second week o Oc obe 2020 [44]. I equi es
0.2 MT o p opylene o syn hesize 1 MT o ca ionic eagen s. The
annual labo cos s o each supplie a e e e enced om he da a o
hei espec i e coun ies, published by he OECD in 2020 [45]. To
s anda dize he uni o annual labo cos s in o U.S. dolla s (USD), we
use he exchange a e om 2019. While eliable da a on he labo
p oduc i i y o supplie s A, B, D, E, F, and G a e lacking, we do ha e
eliable da a o supplie C. Gi en he ma u e na u e o he indus y,
wi h minimal echnological and quali y di e ences among supplie s,
supplie C’s labo p oduc i i y is assumed o be ep esen a i e o he
o he supplie s (𝑢𝐶=𝑢𝑖, whe e 𝑖∈𝑆). Indus ial elec ici y p ices a e
ob ained om he da a o each supplie ’s coun y [46]. Fo e e ence,
his case s udy se s he elec ici y equi emen o p oducing one uni
o ca ionic eagen s a 250 kWh. F eigh cos s om supplie s o buye s
a e collec ed om ele an online sou ces [47,48]. The impo a i
a e o each coun y is based on he HS-CODE 2923.90 o ca ionic
eagen s. The HS-CODE is an in e na ionally s anda dized sys em o
classi ying aded p oduc s and acili a ing global cus oms p ocesses
and ade egula ions [49].
4.3. Ideal equilib ium and pu pose o ma ke playe s
The ideal equilib ium, achie ed h ough coope a ion among ma ke
playe s, is ob ained by sol ing he MILP desc ibed in Sec ion 3.3 wi h
𝛾se o ze o. The esul s, which minimize TDCs in he ca ionic eagen
indus y, a e p esen ed in Table 5and Fig. 2. Supplie s B, C, E, F, and G
achie e ull u iliza ion, while supplie s A and D show low u iliza ion.
I ma ke playe s make mul ila e al concessions and coope a e, TDCs
in he ca ionic eagen indus y can be educed, he eby inc easing he
compe i i eness o he en i e indus y.
Howe e , achie ing he ideal equilib ium is challenging due o ma -
ke playe s pu suing hei indi idual in e es s. To es his hypo hesis,
expe imen s a e conduc ed o maximize he p o i s o ma ke playe s.
Gi en ha he a ge indus y is oligopolis ic and compe i o s a e well-
in o med abou each o he , he objec i e unc ions a e se o maximize
he o e all sales o supplie s and minimize he o e all cos s o buye s.
Fi s , an expe imen is conduc ed o maximizes supplie s’ sales
(i.e., FOB sales) e lec ing supplie s’ in e es s. In his expe imen , Eq. (5)
Ope a ions Resea ch Pe spec i es 14 (2025) 100325
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J. Kang e al.
Table 3
Da a on supplie s.
Supplie 𝑖Loca ion Capaci y
(MT/Yea )
Raw ma e ial p ice
(USD/MT)
Labo cos s
(USD/Yea )
Indus ial elec ici y p ice
(USD/MWH)
A No h Ame ica 30,000 456 63,093 69
B No h Ame ica 25,000 456 63,093 96
C No h Eas Asia 25,000 867 39,472 98
D Wes e n Eu ope 20,000 920 54,262 86
E Wes e n Eu ope 20,000 920 44,111 74
F No h eas Asia 30,000 899 10,941 40
G No h Eas Asia 20,000 899 10,941 40
Table 4
Da a on buye s.
Buye 𝑗Loca ion Demand
(MT/Yea )
Sale p ice
(USD)
F eigh cos s (USD/20 con aine )
when pu chasing om supplie 𝑖
Impo a i s (%)
when pu chasing om supplie 𝑖
A B C D E F G A B C D E F G
A’ USA 29,960 1,140 0 0 3,539 2,058 2,503 3,406 3,406 0 0 0 6.2 6.2 6.2 6.2
B’ Canada 4,674 1,140 4,146 4,613 3,053 2,495 2,695 2,949 2,949 0 0 0 0 0 0 0
C’ B azil 2,133 1,208 796 2,190 3,650 420 834 3,650 3,650 2 2 2 2 2 2 2
D’ Mexico 1,823 1,208 1,095 2,929 3,815 1,780 1,835 3,815 3,815 0 0 0 0 0 0 0
E’ Res o La in Ame ica 3,182 1,208 685 1,882 3,650 420 834 3,650 3,650 0 0 0 0 0 0 0
F’ Ge many 5,674 1,163 491 993 892 7 8 839 839 6.5 6.5 0 0 0 6.5 6.5
G’ I aly 4,355 1,163 622 1,755 950 14 34 950 950 6.5 6.5 0 0 0 6.5 6.5
H’ F ance 2,879 1,163 472 811 867 4 12 839 839 6.5 6.5 0 0 0 6.5 6.5
I’ UK 4,625 1,163 491 940 1,307 4 11 1,339 1,339 6.5 6.5 0 0 0 6.5 6.5
J’ Spain 2,305 1,163 682 1,046 1,265 9 28 1,097 1,097 6.5 6.5 0 0 0 6.5 6.5
K’ Benelux 2,622 1,163 497 993 867 0 10 839 839 6.5 6.5 0 0 0 6.5 6.5
L’ Russia 5,136 1,163 1,319 1,852 1,485 516 N/A 1,427 1,427 3 3 3 3 3 3 3
M’ Res o Eu ope 3,225 1,163 472 993 867 3 17 839 839 6.5 6.5 0 0 0 6.5 6.5
N’ India 7,452 1,091 1,309 1,652 1,075 923 1,939 1,075 1,075 10 10 0 10 10 10 10
O’ ASEAN 9,655 1,091 1,077 1,177 65 950 1,123 125 125 0 0 0 0 0 0 0
P’ Res o Sou h Asia 5,272 1,091 1,010 1,170 410 1,027 1,198 260 260 5 5 0 5 5 0 0
Q’ China 14,046 1,056 877 890 120 800 1,048 0 0 10 10 0 6.5 6.5 0 0
R’ Japan 5,623 1,056 1,166 1,166 315 1,060 1,298 300 300 3.9 3.9 3.9 0 0 3.9 3.9
S’ Sou h Ko ea 5,210 1,056 777 1,002 0 800 1,048 300 300 0 0 0 0 0 2.6 2.6
T’ Aus alia 2,065 1,116 1,661 1,661 1,145 958 958 1,345 1,345 0 0 0 0 0 0 0
U’ New Zealand 556 1,116 1,661 1,661 1,145 958 958 1,345 1,345 0 0 0 0 0 0 0
V’ GCC 2,340 1,228 1,048 1,336 586 689 1,089 855 855 5 5 5 5 5 5 5
W’ Tu key 396 1,228 972 1,209 1,325 595 1,161 1,325 1,325 6.5 6.5 0 0 0 6.5 6.5
X’ No h A ica 865 1,228 1,272 1,256 1,682 686 1,320 1,714 1,714 2 2 2 0 0 2 2
Y’ Sou h A ica 940 1,228 1,880 2,363 1,069 N/A N/A 1,620 1,620 0 0 0 0 0 0 0
Z’ Res o Middle Eas 641 1,228 1,201 1,299 882 739 1,064 1,024 1,024 5 5 5 5 5 5 5
Table 5
Expe imen al esul s o he ideal equilib ium (uni s: million USD).
Cos s Supplie
A B C D E F G To al
Di e en ial cos s 7.13 35.94 26.35 3.98 23.04 14.58 9.66 120.69
F eigh cos s 0 0 0.74 0.06 0.02 0.02 0.94 3.31
Impo a i 0 0 0.24 0.05 0 0 0.19 0.72
Raw ma e ial cos s 0.45 2.28 4.34 0.50 3.68 3.68 3.60 20.24
Elec ici y cos s 0.09 0.43 0.61 0.06 0.37 0.37 0.20 2.06
Labo cos s 6.59 33.22 20.43 3.32 18.97 18.97 4.74 94.36
eplaces Eq. (1) as he objec i e unc ion, as desc ibed in Sec ion 3.3.
6illus a es ha maximizing supplie sales diminishes he compe i i e-
ness o he en i e indus y. Speci ically, maximizing FOB sales inc eases
TDCs by $11.06 million compa ed o he ideal equilib ium. Addi ion-
ally, Table 6indica es a signi ican ise in impo a i s o supplie s
B, E, F, and G, who ha e low le els o FTAs. Fu he mo e, supplie D’s
labo cos s signi ican ly inc ease, educing i s cos compe i i eness.
𝑀 𝑖𝑛𝑖𝑚𝑖𝑧𝑒 ∑
𝑖∈𝑆∑
𝑗∈𝐵
𝑏𝑗𝑡𝑖,𝑗 (5)
Second, simila o p e ious s udies [17,18,22], an expe imen is
conduc ed o minimize he cos s o buye s (i.e., CFR sales) e lec ing
buye s’ in e es s. In his expe imen , Eq. (6) eplaces Eq. (1) as he
objec i e unc ion, as desc ibed in Sec ion 3.3. CFR sales encompass
he sum o FOB sales, eigh cos s, and impo a i s paid by buye s
ep esen ing he ac ual pu chase cos s. Table 7illus a es ha minimiz-
ing buye s’ ac ual pu chase cos s esul s in a $20.83 million inc ease
Table 6
Expe imen al esul o maximizing sales o supplie s (uni : million USD).
Cos s Supplie
A B C D E F G To al Inc ease †
Di e en ial cos s 0 21.72 25.00 27.83 28.28 17.33 11.58 131.75 11.06
F eigh cos s 0 0.90 0.28 0.50 2.30 2.49 1.83 8.30 4.99
Impo a i 0 0.59 0.24 0 1.44 1.90 0.88 5.05 4.33
Raw ma e ial cos s 0 1.16 4.32 3.68 3.68 5.39 3.60 21.84 1.60
Elec ici y cos s 0 0.22 0.61 0.43 0.37 0.30 0.20 2.13 0.07
Labo cos s 6 18.85 19.55 23.22 20.49 7.25 5.07 94.43 0.07
†Inc ease e e s o he ise in each ype o cos s compa ed o wha is seen in he ideal
equilib ium.
in TDCs compa ed o he ideal equilib ium. This inc ease is p ima ily
due o a signi ican ise in labo cos s o supplie s A and D, making
hem less cos -compe i i e. The compe i i eness o he ca ionic eagen
Ope a ions Resea ch Pe spec i es 14 (2025) 100325
7
J. Kang e al.
Table 7
Expe imen al esul o minimizing buye s’ ac ual pu chase cos s (uni s: million USD).
Cos s Supplie
A B C D E F G To al Inc ease †
Di e en ial cos s 43.95 6.94 26.46 29.36 23.07 11.72 0 141.51 20.83
F eigh cos s 0.20 0 0.66 0.81 0.006 0.17 0 1.90 −1.41
Impo a i 0 0 0.19 0.24 0 0.23 0 0.66 −0.07
Raw ma e ial cos s 2.74 0.44 4.34 3.68 3.68 5.00 0 19.88 −0.36
Elec ici y cos s 0.52 0.08 0.61 0.43 0.37 0.28 0 2.29 0.23
Labo cos s 40.49 6.42 20.66 24.21 18.97 6.03 0 116.78 22.42
†Inc ease e e s o he ise in each ype o cos s compa ed o wha is seen in he ideal
equilib ium.
indus y is he e o e ad e sely a ec ed by ma ke playe s’ e o s o
maximize hei indi idual p o i s.
𝑀 𝑖𝑛𝑖𝑚𝑖𝑧𝑒 ∑
𝑖∈𝑆∑
𝑗∈𝐵
(𝑏𝑗+𝑓𝑖,𝑗 )(1 +𝑥𝑖,𝑗 )𝑡𝑖,𝑗 (6)
4.4. Risk managemen
This subsec ion in es iga es supply chain isk managemen h ough
wo expe imen s. The i s examines how TDCs inc ease o dec ease
in esponse o di e en le els o isk hedging. The second assesses he
impac o ade dispu es on supply chains and TDCs. The equilib ium
is ob ained by sol ing he MILP desc ibed in Sec ion 3.3 changing 𝛾.
4.4.1. Impac o isk hedging on TDCs
Buye s wan o educe he isk om supplie s ailing o deli e
p oduc s when designing hei supply chains. E en i addi ional cos s
a e needed, concessions and coope a ion be ween ma ke playe s can
lowe isks [50]. Apa om concession and ma ke playe s coope a -
ing, di e si ying supplie s is an e ec i e s a egy o educing he isk
o buye s. In Sec ion 3.2, i is assumed ha buye s ha e an equi alen
le el o isk hedge endency (𝛾) in hei pu chasing s a egies. In his
expe imen , adjus ing 𝛾in Cons ain (4) yields changes in TDCs. As
𝛾app oaches ze o, he quan i y ha a buye ecei es becomes mo e
concen a ed on a single supplie . Con e sely, as 𝛾app oaches 1 −1
𝑚,
supplie s become mo e di e si ied. Fo example, i 𝛾is 0.5, a buye
does no pu chase mo e han 50% o he demanded quan i y om any
single supplie . Wi h 7 supplie s, he minimum pe cen age equi ed o
sa is y mo e han 100% o he o al demand is 15% when conside ing
only in ege s. Howe e , unde his condi ion, a buye has o pu chase
simila amoun s close o 15% om each o he 7 supplie s, making i
ha d o obse e changes in sales quan i ies depending on he ma ke
en i onmen . The e o e, he maximum 𝛾is limi ed o 0.84 in his s udy.
TDCs a e lowes when a buye can pu chase he en i e demanded
quan i y om a single supplie (𝛾= 0), as shown in Fig. 3. TDCs
and eigh cos s gene ally inc ease when supplie s a e di e si ied.
This is because when buye s di e si y hei supplie s, hey e en ually
pu chase he emaining quan i ies om supplie s loca ed a away.
Howe e , despi e he inc eases in TDCs and pu chase cos s, buye s
can ensu e supply chain s abili y by es ablishing business ela ionships
wi h a ious supplie s, making i challenging o he ca ionic eagen
indus y o each he ideal equilib ium. No e ha eigh cos s sligh ly
dec ease when 𝛾is 0.4 compa ed o 0.3. This is because, as he buye ’s
pu chase limi om a supplie is educed om 70% o 60%, supplie E,
loca ed in Wes e n Eu ope, di e si ies expo s o buye s D’ (Mexico), E’
( he es o La in Ame ica), T’ (Aus alia), and U’ (New Zealand), whe e
eigh cos s a e highe . (see Fig. 4).
4.4.2. Impac o ade dispu e on supply chains
When ade dispu es a ise be ween coun ies, ade ba ie s such as
a i s a e o en imposed on p oduc s and se ices om he a ec ed
coun e pa s. Fo example, when a ade dispu e be ween he Uni ed
S a es and China e up ed in Oc obe 2019, bo h coun ies imposed
e alia o y a i s on each o he ’s p oduc s [51]. In his subsec ion, we
examine he e ec s o inc eased e alia o y a i s be ween he Uni ed
S a es and China on supply chains. P io o he dispu e, a 10% impo
a i was applied o p oduc s om US-based supplie s A and B when
expo ed o China, while a 6.2% impo a i was applied o p od-
uc s om Chinese-based supplie s F and G when expo ed o he US.
Following he ade dispu e, bo h coun ies inc eased he e alia o y
a i o 30%. Fig. 5illus a es ha when 𝛾is ze o, he inc ease in
TDCs is negligible because each coun y has i s domes ic supplie s,
and no ade exis s be ween he wo coun ies. As 𝛾inc eases, he
impac o ade dispu es on TDCs inc eases. This end in ensi ies when
a hypo he ical 100% e alia o y a i is imposed on bo h coun ies.
Wi h a 100% e alia o y a i applied, when 𝛾exceeds 0.6, changes
in sales quan i ies o each supplie be o e and a e he dispu e s a
o occu , as shown in Fig. 6. This means ha as 𝛾inc eases, he ade
ne wo k be ween buye s and supplie s becomes signi ican ly complex,
and e alia o y a i a es be ween wo coun ies owing o he ade
dispu e also a ec o he ma ke playe s.
4.5. Dec ease in demand
The ou b eak o COVID-19 has led a con ac ion in global economic
ac i i y and majo downs eam sec o s o he ca ionic eagen indus y,
such as he p in ing pape indus y, ha e signi ican ly de e io a ed. As
non- ace- o- ace social ac i i ies we e encou aged, emo e wo k and
home educa ion sp ead, dec easing he p oduc ion o p in ed p omo-
ional ma e ials. Pandemics, such as COVID-19, accele a ed he isk
o dis up ions in p oduc ion lines, dec easing p oduc demand o all
ma ke pa icipan s [50].
This subsec ion examines he e ec s o a dec ease in demand in sup-
ply chains. The equilib ium is ob ained by sol ing he MILP desc ibed
in Sec ion 3.3, changing 𝛾in Eq. (4) and 𝑑𝑗in Eqs. (3) and (4). Sales
quan i ies a e obse able when demand om all buye s dec eases by
15% and 30%, espec i ely.
When 𝛾is ze o, a 15% dec ease in demand esul s in sales quan i ies
o supplie s A and D d opping o ze o, leading o hei ope a ions
being hal ed, as shown in Fig. 7. A 30% dec ease in demand esul s
in supplie ’s ope a ion (i.e., supplie B) being hal ed in addi ion o
supplie s A and D. When 𝛾is 0.6, a 15% dec ease in demand does no
cause any supplie o cease ope a ions. Howe e , a 30% dec ease in
demand o ces supplie s A, B, and D o cease hei ope a ions. When 𝛾
is 0.84, no supplie needs o hal ope a ions e en in he e en o a 30%
dec ease in demand.
Since he o al sales quan i y dec eases wi h a dec ease in demand,
he concep o TDCs pe uni is used in his subsec ion o obse e he
e ec o a dec ease in demand on TDCs. TDCs pe uni a e ob ained by
di iding TDCs by he o al sales quan i y. As demand dec eases, TDCs
pe uni also dec ease, as shown in Fig. 8. This means ha dec eased
demand inc eases he oppo uni y o educe di e en ial cos s, including
logis ics cos s, elec ici y cos s, labo cos s, aw ma e ial cos s, and
impo a i s. Howe e , as 𝛾inc eases, TDCs pe uni dec eases less
signi ican ly. This means ha he oppo uni y o educe di e en ial
cos s diminishes because buye s a e compelled o di e si y supplie s.
No e ha 𝛾a which luc ua ions in sales quan i ies occu inc eases
as demand dec eases by 15% o 30%. This is because buye s ha e o
educe hei pu chases as demand dec eases, while supplie s’ supply
emains unchanged, allowing o he buye s o pu chase mo e p oduc s
om cos -compe i i e supplie s. As shown in Table 8, he p oduc s
o non-compe i i e supplie s A, B, and D a e no longe pu chased by
buye s as demand dec eases by 30%.
Ope a ions Resea ch Pe spec i es 14 (2025) 100325
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[33] Yilmaz OF, Ozcelik G, Yeni FB. Ensu ing sus ainabili y in he e e se supply
chain in case o he ipple e ec : A wo-s age s ochas ic op imiza ion model. J
Clean P od 2021;282:124548.
[34] Yilmaz OF, Yeni FB, Yolmaz BG, Ozcelik G. An op imiza ion-based me hodology
equipped wi h lean ools o s eng hen medical supply chain esilience du ing
a pandemic: A case s udy om Tu key. T ansp Res E Logis T ansp Re
2023;173:103089.
[35] Ozcelik G, Fa uk Yilmaz O, Be ul Yeni F. Robus op imisa ion o ipple e ec on
e e se supply chain: an indus ial case s udy. In J P od Res 2021;59(1):245–64.
[36] Sawik T. S ochas ic op imiza ion o supply chain esilience unde ipple e ec :
A COVID-19 pandemic ela ed s udy. Omega 2022;109:102596.
[37] da Cunha RA, Rangel LAD, Rudol CA, dos San os L. A decision suppo
app oach employing he PROMETHEE me hod and isk ac o s o c i ical supply
assessmen in la ge-scale p ojec s. Ope Res Pe spec 2022;9:100238.
[38] Maskin E, Ti ole J. A heo y o dynamic oligopoly, III: Cou no compe i ion. Eu
Econ Re 1987;31(4):947–68.
[39] F iedman J. Oligopoly heo y. Handb Ma h Econ 1982;2:491–534.
[40] Lu TY, Wang SL, Wu MF, Cheng FT. Compe i i e p ice s a egy wi h
ac i i y-based cos ing–case s udy o bicycle pa company. P ocedia CIRP
2017;63:14–20.
[41] Wicaksono S, Fadlillah AM. Implemen a ion o ull ime equi alen me hod in
de e mining he wo kload analysis o logis ics admin employees o PT X in
Jaka a, Indonesia. Eu J Bus Manag Res 2021;6(5):159–62.
[42] Pe sis ence Ma ke Resea ch. 3-chlo o-2-hyd oxyp opyl ime hyl ammonium
chlo ide (CHPTAC) ma ke . 2019.
[43] Reimschuessel HK, Kocu MA. P ocess o he p epa a ion o anhyd ous N-(3-
chlo o-2-hyd oxyp opyl) ialkylammonium sal s. 1986, U.S. Pa en No. 4, 594,
452.
[44] FIBRE2FASHION. 2020, h ps://www. ib e2 ashion.com/ [accessed July 28,
2024].
[45] OECD. A e age annual wages: 2020. 2020, h ps://s a s.oecd.o g [accessed July
28, 2024].
[46] S a is a. Elec ici y p ices o en e p ises wo ldwide in decembe 2023, by selec
coun y. 2020, h ps://www.s a is a.com/ [accessed July 28, 2024].
[47] iCon aine s. Ocean eigh calcula o : Ins an shipping a es. 2020, h ps://www.
icon aine s.com/ocean- eigh -calcula o / [accessed July 28, 2024].
[48] F eigh os. F eigh ha jus wo ks. 2020, h ps://www. eigh os.com/ [accessed
July 28, 2024].
[49] In e na ional T ade Adminis a ion. Ha monized sys em (HS) codes. 2024, h ps:
//www. ade.go /ha monized-sys em-hs-codes [accessed July 28, 2024].
[50] Shen W, Yang C, Gao L. Add ess business c isis caused by COVID-19 wi h
collabo a i e in elligen manu ac u ing echnologies. IET Collab In ell Manu
2020;2(2):96–9.
[51] Li M, Balis e i EJ, Zhang W. The US–China ade wa : Ta i da a and gene al
equilib ium analysis. J Asian Econ 2020;69:101216.
[52] Dunn RF, El-Halwagi MM. P ocess in eg a ion echnology e iew: backg ound
and applica ions in he chemical p ocess indus y. J Chem Technol Bio echnol
2003;78(9):1011–21.
[53] O’ha a M. Ma ke mic os uc u e heo y. John Wiley & Sons; 1998.
[54] Lo AW. The adap i e ma ke s hypo hesis. J Po Manag 2004;30(5):15–29.
[55] Fede al Rese e Boa d o Go e no s. Indus ial p oduc ion and capaci y
u iliza ion. 2020, h ps://www. ede al ese e.go / [accessed July 28, 2024].
[56] Pepall L, Richa ds D, No man G. Indus ial o ganiza ion: Con empo a y heo y
and empi ical applica ions. John Wiley & Sons; 2014.
[57] Eun J, Tiwa i V, Sandbe g WS. P edic ing daily su gical olumes us-
ing p obabilis ic es ima es o p o ide s’ u u e a ailabili y. Decis Sci
2022;53(1):124–49.
[58] Hassan NM, Abbasi MN. A e iew o supply chain in eg a ion ex en s, con-
ingencies and pe o mance: A pos Co id-19 e iew. Ope Res Pe spec
2021;8:100183.
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