Zhou, Xingjian; Feng, Yan; Chen, Hongming; Cai, Lihua; Bashka e , Vladimi
A icle
P icing s a egy o supply chain conside ing esponse ime
o ex ended wa an y se ice
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: Zhou, Xingjian; Feng, Yan; Chen, Hongming; Cai, Lihua; Bashka e , Vladimi
(2025) : P icing s a egy o supply chain conside ing esponse ime o ex ended wa an y se ice,
Ope a ions Resea ch Pe spec i es, ISSN 2214-7160, Else ie , Ams e dam, Vol. 14, pp. 1-12,
h ps://doi.o g/10.1016/j.o p.2025.100330
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P icing s a egy o supply chain conside ing esponse ime o ex ended
wa an y se ice
Xingjian Zhou
a,b,c
, Yan Feng
a,c,*
, Hongming Chen
a
, Lihua Cai
d
, Vladimi Bashka e
a
a
School o Managemen , Wuhan Tex ile Uni e si y, Wuhan 430200, China
b
En e p ise Decision Suppo Resea ch Cen e , Key Resea ch Base o Humani ies & Social Sciences o Hubei P o ince, Wuhan 430073, China
c
Digi al & In elligen Logis ics & Tex ile & Ga men Supply Chain Managemen Resea ch Cen e , Indus y-Uni e si y-Resea ch Base o China Logis ics Socie y, Wuhan
430200, China
d
Ecological En i onmen Indus y College, Wuhan Uni e si y o Technology and Business, Wuhan 430065, China
ARTICLE INFO
Keywo ds:
Response ime
Ex ended wa an y se ice (EWS)
P icing s a egy
P oduc -se ice supply chain
ABSTRACT
Ex ended wa an y se ices (EWS) o e s a enues o new p o i sou ces and g ow h oppo uni ies. In a ime-
sensi i e ma ke , he esponse ime has an impo an impac on he p icing o EWS and sa is ying consume
u ili y. Applying S akelbe g Game heo y, a wo-echelon p oduc -se ice supply chain consis ing o a manu-
ac u e and wo e aile s (Sel -owned, F anchised) is cons uc . Conside ing he EWS esponse ime and p ice o
cha ac e ize he consume u ili y unc ion, he EWS p icing s a egies in di e en ma ke s ages a e s udied based
on he scena ios o iden ical esponse ime (IRT) and di e en esponse ime (DRT). The esea ch shows ha : (1)
unde IRT scena io, he op imal EWS p icing and cos o he sel -owned and anchised e aile s a e nega i ely
ela ed o he esponse ime, he e o e, bo h e aile s should conside a ade-o s a egy be ween he EWS p ice
and he esponse ime; (2) unde DRT scena io, an EWS esponse ime h eshold exis s, based on which he sel -
owned and anchised e aile s should de elop he op imal EWS p icing s a egies; (3) unde DRT scena io, he
e aile s’ op imal EWS p ices ha e a nega i e ela ionship wi h consume s’ p ice sensi i i y coe icien , and a
posi i e ela ionship wi h consume s’ ime sensi i i y coe icien . The manu ac u e and he sel -owned e aile
can signi ican ly educe EWS esponse ime wi h a limi ed inc ease in he p ices. While he anchised e aile
need o ollow he sel -owned e aile in de eloping i s p icing s a egy. The s udy cons uc a ime-sensi i e
consume u ili y unc ion by in eg a ing esponse ime and p icing, mo e accu a ely po aying he expec ed
alue o EWS. Based on he ma ke cha ac e is ics o EWS g ow h and ma u i y pe iods, he EWS p icing s a-
egies a e expanded ega ding esponse ime di e en ia ion in mul iple cycles. I helps companies be e un-
de s and consume demand o EWS, and assis s hem in o mula ing p icing s a egies o di e en s ages o
EWS ma ke de elopmen ,and imp o ing EWS supply chain managemen .
1. In oduc ion
The ex ended wa an y se ice (EWS), as an impo an pa o
p oduc -se ice supply chain (PSSC), is widely adop ed in du able goods
indus ies such as au omobiles, home appliances, and elec onics [1,2].
In some coun ies, e aile s p o ide EWS o consume s. Fo example, in
U.S.A., Squa eT ade Inc. se e s as a EWS e aile especially o elec-
onic p oduc s and appliances in Amazon, Cos co, Bes Buy, e c., and i s
pe o mance anks among he op h ee in he Amazon U.S. [3]. Al e -
na i ely, in o he coun ies, he EWS is p o ided by manu ac u e s (and
sel -owned e aile s) , such as BYD, Haie , Leno o, e c., in China [4]. The
anchised EWS e aile s licensed by he manu ac u e s a e also
a ailable o he consume s oge he wi h he p oduc s selling, such as
JD, TEMU, Tmall, Gome, e c. [5]. Consume s educe he pe cei ed isk
by pu chasing EWS and ob ain a be e p oduc using expe ience [6].
Some consume s decide whe he o pu chase co esponding p oduc s
based on he le el o EWS se ice, he eby changing he p o i s uc u e
o he companies’ p oduc and se ice.
The EWS has g adually become an impo an pa o companies’
p o i s [7]. Some companies ealize ha EWS is no jus subsidia y
se ices bundled wi h p oduc s o he pu pose o p omo ion. Ra he ,
enhancing he le el o EWS can imp o e companies’ p o i abili y and
compe i i eness in he ma ke [8]. Fo example, he au omo i e, com-
pu e , and mobile phone indus ies end o p e e p omp esolu ion
* Co esponding au ho .
E-mail add ess: [email p o ec ed] (Y. Feng).
Con en s lis s a ailable a ScienceDi ec
Ope a ions Resea ch Pe spec i es
jou nal homepage: www.else ie .com/loca e/o p
h ps://doi.o g/10.1016/j.o p.2025.100330
Recei ed 4 No embe 2024; Recei ed in e ised o m 17 Janua y 2025; Accep ed 10 Feb ua y 2025
Ope a ions Resea ch Pe spec i es 14 (2025) 100330
A ailable online 12 Feb ua 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-
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du ing a mal unc ion. In such scena ios wi h ime-sensi i e consume s,
some companies ha e implemen ed s a egies o expedi e he deli e y o
EWS. Fo ins ance, Tmall commi s o esponse in 24-hou and ul ill EWS
be o e he end o he day. Simila ly, Haie ’s esponse ime o EWS is
di ided in o 3 business days o appliances wi h spa e pa s in s ock and
a maximum o 10 business days o hose wi hou . Ob iously, he
companies’ ope a ing cos s o EWS a y unde di e en esponse imes,
and he EWS p icing will also di e .
The e o e, he EWS esponse ime is closely ela ed o business de-
cisions, and p icing is one o he mos c i ical ac o s o he decisions. In
he ime-sensi i e consume ma ke , he EWS esponse ime has g ea
impac on consume u ili y, EWS le el and p icing [9]. In di e en
ma ke s ages, companies may adop di e en EWS s a egies. In
coun ies whe e he EWS ma ke is expanding, such as China [10,11],
since 2006, TWG has in oduced i s au omo i e EWS o he Chinese
ma ke . Some OEMs, deale s, and p o essional au omo i e EWS agencies
ha e made a emp s and explo a ions in his ield, bu he de elopmen
is s ill ela i ely slow, and he a e age EWS pene a ion a e o au o-
mo i e indus y is only 10–20 %(can be conside ed as a g ow h s age in
he p oduc li e cycle). A ew high-end b ands o e EWS wi h selling,
and he pene a ion a e ba ely each 30–40 %. EWS p o ide s end o
adop iden ical p icing s anda ds and esponse ime in o de o p omo e
hei business and ea n mo e ma ke sha e. In coun ies whe e he EWS
ma ke is de eloped, such as Eu opean, he Uni ed S a es and Janpan
[11,12], he EWS pene a ion a e o au omobile indus y is much highe
(can be conside ed as a ma u i y s age in he p oduc li e cycle). The
pene a ion a e o EWS o au omo i e in he Uni ed S a es is abou 75
%, and in Eu ope i is abou 80 %. Japan ma ke is mo e ma u e, and he
EWS pene a ion a e o second-hand au omo i e is o e 90 %. The EWS
p o ide s o e lexible and di e si ied p icing s a egies and di e en-
ia ed esponse imes o enhance consume u ili y and company
compe i i eness. Howe e , ega dless o he ma ke s age, a easonable
de e mina ion o EWS esponse ime s a egy and p icing a e c ucial o
business decision-making.
As a eal- ime se ice h oughou he p oduc li e ime, i is di icul
o de ine he EWS esponse ime. The e o e, he esponse ime o he
p oduc ope a ion and main enance is adop ed o ep esen he EWS
esponse ime. The esponse ime o he p oduc ope a ion and main-
enance is de ined as he amoun o ime be ween he momen a se ice
is applied and he eques is ul illed [13]. In some indus ies, companies
implemen di e en ia ed esponse imes o mee di e en needs o
p oduc ope a ion and main enance. Fo example, ZTE ca ego izes he
le el o se ices in o h ee ie s—c i ical, impo an , and mino —based
on he esponse ime, and cha ge cus ome s based on ac ual cos s
incu ed. Boeing di ides he se ices in o High impac , C i ical eques
and Rou ine eques , and se s s anda ds o esponse ime and p ice o
di e en le els o eques s.
Gene ally, he p oduc ope a ion and main enance se ices cha ge
he cus ome s acco ding o he ac ual cos s incu ed and he u gency
deg ee o he esponse. While EWS p ice conside s he po en ial ailu es
in he use o he p oduc , combined wi h he u gency deg ee o he
esponse ime. Tha is, he p oduc ope a ion and main enance se ices
a e p iced in eal ime and EWS is p iced in ad ance [14]. In he o he
wo ds, he EWS is a p epaid model o he p oduc ope a ion and
main enance se ices. Concu en ly, he EWS esponse ime can be
ega ded as a p ede e mined alue. When hese wo ac o s a e supe -
imposed, hey ha e a p o oundly dele e ious e ec on he consume ’s
expec a ions ega ding he EWS alue. The cus ome ’s choice o he
p ice he is willing o pay depends on he alue expec ed o be de i ed
om use and he o al cos including he cos o wai ing. As o he
companies, he EWS p icing s a egy includes mo e unce ain y and
complexi y. On he one hand, i is necessa y o comp ehensi ely
conside he consume s’ expec a ions o EWS alue unde he e ec o
EWS esponse ime and p ice. On he o he hand, i is also necessa y o
conside he consume s’ EWS expec a ions unde he di e en s ages o
ma ke de elopmen . A p esen , adop ing di e en p icing s a egies
o EWS wi h di e en esponse imes o mee consume s’ expec a ions
and enable companies o ob ain op imal e enue is s ill ambiguous.
The e o e, u he esea ch on EWS p icing s a egies wi h he
conside a ion o esponse ime o ime-sensi i e consume s is in e -
es ing, bu he ollowing wo challenging issues need o be add essed:
(1) How o de e mine consume s’ expec a ions o he EWS alue wi h
he combined e ec o esponse ime and p ice.
{2) The impac o EWS esponse ime on he supply chain p icing
s a egy unde di e en s ages o p oduc li e cycle.
The possible con ibu ions a e mainly:
(1) Unlike he p oduc ope a ion and main enance se ices, which
conside s he ac ual cos incu ed and adop s a cos -plus
app oach o make he p icing decision, he p icing o EWS
conside he po en ial cos s. F om he pe spec i e o ime-
sensi i e consume s, comp ehensi ely conside s he esponse
ime and i s co esponding p ice, a consume u ili y unc ion is
cons uc ed o ca e he expec ed cos o EWS. This app oach
expands he adi ional unde s anding o EWS as subsidia y se -
ices bundled wi h p oduc s, and p oposes he consume u ili y
unc ion om he pe spec i e o he expec ed alue o EWS, o
be e dis inguish he esponse ime cha ac e is ics o EWS and
e lec he consume decision-making p ocess.
{2) To unde s and he ma ke cha ac e is ics o he EWS p oduc li e
cycle, ocusing on he g ow h and ma u i y pe iods, wo scena ios
wi h iden ical and di e en ia ed esponse ime a e conside ed,
and he EWS p icing s a egy in mul iple cycles is de eloped. This
app oach subdi ides he dynamic de elopmen cha ac e is ics o
he p oduc and se ice ma ke , and conduc s in ensi e esea ch
on EWS s a egies unde di e en ma ke de elopmen s ages,
speci ically whe e di e en EWS p icing s a egies a e adop ed
o new p oduc -se ice launch pe iod and popula p oduc -
se ice p omo ion pe iod.
{3) Unde he wo scena ios, om he company’s pe spec i e, he
demand unc ions and p o i unc ions a e de eloped based on
he consume u ili y. Conside ing o he impac o EWS esponse
ime, p icing, cos , e c.comp ehensi ely, he EWS p icing s a egy
is p oposed. This app oach u he quan i ies he in e nal impac
mechanism be ween esponse ime and p icing in mul iple sce-
na ios om he pe spec i e o ime sensi i e consume , which is
mo e in line wi h he companies’ p ac ical di icul ies in making
business decisions unde complex ma ke en i onmen s.
The e o e, his s udy mainly ocuses on wo objec i es: i s ly,
cons uc a consume u ili y unc ion by comp ehensi ely conside ing
he EWS esponse ime and p ice; secondly, de elop EWS p icing s a-
egies wi h di e en ia ed esponse ime unde mul iple cycles. This
pape is o ganized as ollows: Sec ion 2 e iews he li e a u e on
esponse ime and supply chain managemen , Sec ion 3 desc ibes he
p oblem and gi es he assump ion o he model, Sec ion 4 cons uc s he
unc ions and he model unde di e en scena ios, Sec ion 5 analyzes
he p icing s a egies o each scena io, Sec ion 6 exams he impac s o
a ious ac o s and Sec ion 7 d aws conclusion and shows he u u e
wo k.
2. Li e a u e e iew
P icing o p oduc -se ice wi h esponse ime is an impo an and
changeling b anch o he EWS supply chain s a egy ha has de eloped
apidly in he ecen yea s. The e a e mainly h ee ca ego ies o esea ch
ela ed o his a ea, namely he p icing s a egies o EWS supply chain,
he p oduc -se ice p icing issues conside ing esponse ime, and he
s a egies o supply chain managemen wi h ime conside a ions. Rele-
an esea ch is e iewed om hose pe spec i es.
X. Zhou e al.
Ope a ions Resea ch Pe spec i es 14 (2025) 100330
2
2.1. The p icing s a egies o EWS supply chain
The esea ch basis o he s udy is he EWS p icing s a egy, he e o e,
i is necessa y o i s e iew he exis ing wo k in his ield. The s udies
on supply chain s a egies o EWS ini ially ocus on he sales channel, i.
e., he op imal EWS p o ide decisions. The esea ch gene ally consid-
e ed a model, consis ing a e aile who sale he EWS, and a manu ac u e
o supplie who ca y ou he EWS. Desai & Padmanabhan [1] based on
he di ec , non-di ec , and dual-channel sales o EWS, conside ing he
in luence o double ma ginaliza ion and complemen a y goods e ec ,
p oposed he op imal design o EWS channel s a egy. Zhang e al. [15]
in es iga ed he op imal EWS p o ision wi h a pla o m supply chain,
ound ha he agen , who akes he owne ship o e he p oduc , ac s
mo e esponsi ely in p o iding he EWS ac oss he wo online channel
modes. Fu he , some schola s conduc ed esea ch on p icing s a egies
o EWS unde di e en channels. Wang e al. [6] p oposed ou kinds o
decision-making models and aims o s udy decisions o he elec onic
comme ce supply chain, including EWS p ice, sales p ice, and se ice
le el o e-pla o m. Fo elec onic comme ce supply chain en e p ises,
whe he o domina e he sys em o o p o ide EWS, i is conduci e o he
inc ease o p o i s. Zhang e al. [16] cons uc ed a manu ac u e -leading
supply chain sys em conside ing he EWS o s udy he in luence o se -
ice cos on he choice o he EWS p o ide , analyzed e ail p icing, EWS
p icing, EWS quali y, he manu ac u e ’s p o i , he e ail’s p o i and
he o al sys em p o i . The esul showed ha bo h he manu ac u e
and he e aile had o balance he a io o se ice cos . Zhang e al. [17]
p opose ou models based on wo assessmen s and wo supply chain
s uc u es, o in es iga e he p icing s a egies o p oduc and wa an y
sales. The s udy compa ed he op imal p ices o he wo supply chain
s uc u es unde unbiased assessmen s.
In he p icing s a egy o EWS supply chain, he se ice du a ion and
pu chasing poin a e also impo an in luence ac o s, which a ec he
cos and demand o EWS, and need o be conside ed in he design o
supply chain con ac s. Chang & Lin [18] s udied he op imal epai
s a egy and he op imal EWS du a ion du ing he p oduc li e cycle
om he pe spec i e o he selle in a wo-echelon supply chain con-
sis ing o a manu ac u e and a e aile ; Lam & Lam [19] ound ha
he e exis ed a decision o he op imal EWS du a ion when consume s
choose whe he o enew he con ac a e he end o he basic wa an y
pe iod; Tong e .al [20] in es iga ed he EWS du a ion p oblem in wo
scena ios: pu chasing EWS a he same ime as pu chasing he p oduc
and pu chasing EWS a e he end o he basic wa an y pe iod. Akseze
[21] analyzed he ailu e beha io o di e en classes o cell phone
p oduc s and hei ela ed cos s h ough a chain o consume elec onics
e aile ope a ing in Tü kiye. Wi hin di e en EWS du a ion, he cos s
o co e age o he hi d, ou h, and i h yea s we e de e mined.
The abo e li e a u e mainly ocused on he EWS channel, cos , de-
mand, du a ion e c. o s udy he EWS supply chain p icing s a egy. The
EWS was ega ded as a pa o he p oduc s ma ke ing policy, and he
objec i e o he EWS p o ide s was o maximize hei p o i s. These
s udies, om he pe spec i e o maximizing supply chain p o i s, e eal
he in luencing ac o s o EWS p icing decisions, and p o ide a esea ch
basis. Howe e , he e is less esea ch on he EWS s a egy ha conside s
maximizing bo h companies’ p o i s and consume u ili y. The e a e a
ew wo k on de eloping he EWS p icing s a egy om he pe spec i e
o consume , such as conside he impac o he esponse ime on he
ma ke o EWS.
2.2. The p oduc -se ice p icing issues conside ing esponse ime
Response ime is an impo an conside a ion ac o , and unde -
s anding i s impac mechanism on he EWS p icing s a egy is c i ical.
Cu en esea ch on his a ea a e mainly ocus on he ela ionship and
he co esponding s a egies o he esponse ime and p oduc -se ice
p icing. Zhang e al. [22] conside ed he impac o cus ome choice
beha io , in es iga ed how a monopoly se ice i m decides i s se ice
p oduc ’s esponse ime and p ice unde wo p oduc design s a egies.
The esul s indica ed ha he se ice i m should adop a segmen ed
p icing s a egy based on he cus ome pe cei ed alues and
ime-sensi i e deg ees. Emin & Ramazan [23] demons a ed he ela i e
impo ance o he esponse ime and discoun amoun acco ding o he
c i icali y le el o ailu es. I ocused on gende di e ences and de e -
mine whe he he esponse ime o discoun amoun is mo e impo an
o male and emale cus ome s in high o low-c i icali y si ua ions. Mo
e al. [24] conside ed wo di e en esponse ime, namely 24-hou and
48-hou , based on which cons uc ed a p ice disc imina ion s a egy.
Cao e al. [25] s udied cen alized and decen alized decision making in
a closed-loop supply chain, conside ing he impac o esponse ime,
de eloped he op imal p icing s a egies. A `
eche e al. [26] s udied
e enue-maximizing a i s ha depend on ealized lead imes o a
p o ide se ing mul iple ime-sensi i e cus ome ypes. Found ha
unde p ice and capaci y op imiza ion, lead- ime-dependen p icing
yields highe p o i s wi h less capaci y compa ed o la - a e p icing.
A `
eche e al. [27] designed p ice/lead- ime menus and he co e-
sponding scheduling policy o a p o i -maximizing se ice p o ide
se ing cus ome s wi h p i a e in o ma ion on hei p e e ences. Wang
e al. [28] conside ed he impac o consume ime p e e ences, and
e alua ed wo scena ios o commission a es cha ged by he e-comme ce
pla o m, o s udy he op imal p icing o paid membe s and in o ma ion
acquisi ion s a egies. Xu e al. [29] p oposed a mul i-le el p icing
scheme o mee he anspo demand o ime-sensi i e goods. A dy-
namic slo -in en o y con ol model conside ing he choice beha io o
goods owne s was es ablished o maximize he companie’s e enue.
The abo e s udies ocus on he e ec s o esponse ime and esponse
speed on p ice disc imina ion s a egy, p oduc -se ice p icing s a egy,
membe ship ee s a egy, e c. They mainly s udied he in insic ela-
ionship be ween esponse ime and p oduc -se ice p icing. These
s udies conside he p icing s a egies unde di e en consume de-
mands o esponse ime, and e i y he ela ionship be ween esponse
ime and p icing decisions. Bu less a en ion has been paid o he
esea ch o he speci ic p icing s a egies which can be di ec ly used by
he companies in eal business. The e is e en less li e a u e on he
p icing s a egies o EWS unde he in luence o esponse ime and a
di e en s ages o he ma ke .
2.3. The s a egies o supply chain managemen wi h ime conside a ions
Gene ally, companies pay mo e a en ion o he p icing s a egy o
EWS supply chain unde di e en ma ke s ages, which is also he pu -
pose o his s udy. This ield in ol es esea ch on supply chain man-
agemen s a egies wi h mul iple ime ac o s. The e a e some esea ch
ocusing on se ice p o isioning me hods and managemen s a egies
unde he in luence o ime. Qin e al. [30] s udied he p oblem o in-
en o y alloca ion op imiza ion, by op imally ading o he sa e y s ock
wi h he se ice esponse ime, so as o gene a e ecommended in-
en o y s a egies on a daily basis. Zha e al. [31] de eloped a
wo-echelon supply chain decision model o analyze he e ec s o
p oduc quali y, p icing, and in en o y managemen in he con ex o
ex ended wa an y se ices. The esul s indica ed signi ican di e ences
in op imal decisions be ween cen alized and decen alized supply
chains, especially conce ning p icing and in en o y con ol. Lin e al.
[32] p oposed a dynamic p icing mechanism conside ing he ac o s o
use eedback, se ice du a ion and se ice quali y le el, in o de o
enable he se ice p o ide o de e mine he op imal supply chain
s a egies. Wang & Zhou [33] designed a “one- o-many” supply chain
sys em which composed o one supplie and N e aile s, conside ing he
demand is sensi i e o p ice and ime, he easonable esponse ime o
cen alized and decen alized supply chain we e de e mined espec-
i ely. Feldman e al. [34] es ablished a queuing model whe e he se -
ice p o ide s and a ional consume s a e he e ogeneous in hei
demands o se ice du a ion, and p oposed ha he ime limi is a
use ul le e ha wo ks well when combined wi h he p ice mechanism.
X. Zhou e al.
Ope a ions Resea ch Pe spec i es 14 (2025) 100330
3
Guo e al. [35] implemen ed a S akelbe g Game model, consis ing o an
o e seas wa ehouse wi h online and o line dis ibu ion, and a
c oss-bo de e-comme ce pla o m wi h in o ma ion on ma ke demand,
o s udy he supply chain s a egy o o e seas wa ehouse ope a ion
mode based on deli e y ime and in o ma ion sha ing. Song e al. [36]
p oposed a join con ac o coo dina e he ime- a ying supply chain o
isk-a e se manu ac u e s and e aile s. The join con ac used p ice
educ ion subsidies and e enue-sha ing s a egies o enable manu ac-
u e s and e aile s o sha e isks and achie e o e all coo dina ion o he
supply chain. Rashid e al. [37] deal wi h he e aile ’s loca ion p ob-
lem, when in en o y cos s o e aile s and esponse ime cos s o
supplie s ha e been conside ed. B onzo e al. [38] analyzed he e ec s o
big da a analy ics capabili ies (BDACs) on companies’ eac ion ime, and
he e ec s o companies’ eac ion ime on supply chain esilience. This
s udy ound ha BDACs educe eac ion ime, which, in u n, imp o es
supply chain esilience.
The abo e s udies mainly ocused on supply chain managemen
s a egies, such as in en o y managemen , se ice quali y le el, se ice
p o ide s, p icing mechanism, acili y loca ion, e c., conside ing he
esponse ime, se ice du a ion, deli e y ime, ime alue, e c., and
de eloped he s a egies o maximize he companies’ e enue. These
s udies add ess a speci ic ma ke de elopmen s age om he pe spec-
i e o companies’ busisness, and e eal a supply chain managemen
s a egy ha conside s mul iple ime ac o s unde s a ic ma ke cha -
ac e is ics. The e ha dly exi s esea ch om he pe spec i e o con-
sume s’ demand cha ac e is ics in di e en ma ke de elopmen s ages,
conside ing he impac o consume s’ ime sensi i i y, he expec ed
alue o EWS, e c. on supply chain managemen s a egies.
All hose s udies show ha esponse ime has become a key ac o o
conside when p icing p oduc -se ice in bo h business p ac ice and
academic esea ch. EWS is a ypical p oduc -se ice app oach ha ex-
ends he p oduc li e cycle and can inc ease consume u ili y. Howe e ,
he e a e ewe s udies on how esponse ime simul aneously a ec s
p icing and sa is ies consume u ili y. The e o e, his pape akes he
consume ’s ime-sensi i e esponse ime as an impo an ac o a ec ing
he p icing o p oduc -se ice, and applies S akelbe g Game heo y o
explo e he p icing s a egy o EWS supply chain, so as o enable con-
sume s o ob ain a be e p oduc -se ice u ili y while companies ob ain
he op imal e enue.
3. P oblem desc ip ion
Conside a p oduc -se ice supply chain comp ising a manu ac u e
and wo e aile s (Sel -owned, F anchised), he manu ac u e wo ks as
he leade in he S akelbe g Game, while he wo e aile s a e ollowe s.
The decision-making sequence is as ollows: i s ly, he manu ac u e
de e mines he basic wholesale p ice o he pa s and suppo se ices
needed o EWS based on he gene al indus y esponse ime, as well as
he admission ee and a iable a e o he anchise e aile ; Then, sel -
owned and anchised e aile s se he e ail p ices and esponse ime o
EWS based on consume demand and wholesale p ices espec i ely.
The manu ac u e p o ides spa e pa s and suppo se ices o he
wo e aile s. Bo h e aile s pu chase he spa e pa s and suppo se -
ices om he manu ac u e o ul ill he EWS pe o mance. The con-
sume s a e ime-sensi i e o he esponse o he EWS, hey make he
EWS pu chasing decisions o maximize hei u ili ies, which a e
composed o he EWS p ices and esponse ime. The membe s o he
supply chain, as a ional economic agen s, a e d i en by he objec i e o
maximizing hei own p o i s when making decisions.
In p ac ice, e aile s can se he EWS esponse ime iden ical ac-
co ding o he gene al indus y pe o mance. While hey can also p o-
ide a ious EWS esponse ime ( 1< 2 o 1> 2). The o me mainly
conce ns he EWS ma ke jus launched, in which all e aile s a e
equi ed o p o ide se ices wi h he same s anda d in o de o gain
consume s’ ecogni ion and hus expand he ma ke . The la e con-
side s he ma u e EWS ma ke , in which he e aile s a e allowed o
p o ide EWS wi h di e en se ice le els o enhance he consume s’
expe ience and maximize he e enue. A he ma u e s age, he an-
chised e aile can adop a ollow- he-leade s a egy, i.e., ea ing he
sel -owned e aile s as a benchma k ( 1< 2), o hey can adop an
agg essi e s a egy, p o iding he EWS wi h a sho e esponse ime
han ha o he sel -owned e aile ( 1> 2).
The e o e, wo scena ios a e discussed. The i s scena io is consid-
e ing iden ical esponse ime (IRT). The manu ac u e m p o ide EWS
wi h wholesale p ice w o wo e aile s. The sel -owned e aile
1
/
anchised e aile
2
o e no di e ence EWS esponse ime 1/ 2
( 1= 2= 0), and p ice p
1
/p
2
espec i ely. The anchised e aile pay he
ixed anchise ee k o he manu ac u e . The scena io IRT is shown in
Fig. 1(a). In he second scena io wi h di e en esponse ime(DRT), he
sel -owned e aile
1
o e s EWS esponse ime 1, and he anchised
e aile
2
o e s EWS esponse ime 2 ( 1< 2 o 1> 2). The scena io
DRT is shown in Fig. 1(b) . The solid a ow indica es he decision-
making ela ionship be ween he game subjec s, while he dashed
a ow indica es he paymen ela ionship.
No a ions a e shown in Table 1 below.
4. Func ion cons uc ion
In his sec ion, he o mulas o each pa y a e cons uc ed.
4.1. U ili y unc ion
Since he EWS esponse ime wo ks as a c ucial indica o o he
se ice le el, he loga i hmic unc ion is used o desc ibe he ela ion-
ship be ween se ice le el and se ice u ili y [39]. Wi hou loss o
gene ali y, he EWS consume u ili y unc ion is cons uc ed, consid-
e ing bo h he esponse ime and he p icing. Two scena ios a e
discussed.
In he i s scena io, bo h sel -owned and anchised e aile s p o ide
iden ical esponse ime o EWS. The consume u ili y unc ions a e as
ollows:
U1= −
α
p1+βln 1
,U2=θ −
α
p2+βln 1
(1)
In he second scena io, he wo e aile s p o ide di e en esponse
ime o EWS. Assuming Δ ep esen s he di e ence be ween he wo
esponse ime, he consume u ili y unc ions a e as ollows:
U1= −
α
p1,U2=θ −
α
p2+βln 1
Δ (2)
When making decision o pu chasing EWS, he ime-sensi i e con-
sume s compa e he u ili y om he sel -owned e aile and anchised
e aile wi h ze o. The e o e, h ee cases a e discussed.
Case 1:u1=u2. The u ili ies om bo h e aile s a e iden ical, he
consume will pu chase EWS om ei he e aile . In p ac ice, he com-
bina ion s a egy o EWS esponse ime and p ice b ings equal u ili y o
consume s. Fo example, he consume u ili y unde he combina ion
s a egy o sho e esponse ime and highe p ice is equal o ha o
longe esponse ime and lowe p ice.
Case 2: u1<u2. The u ili y om he anchised e aile is g ea e han
om he sel -owned e aile , hen he consume will pu chase EWS om
he anchised e aile . In p ac ice, he combina ion s a egy o EWS
esponse ime and p ice p o ided by sel -owned and anchised e aile
has di e ences in u ili y o consume s.
Case 3: u1>u2. The u ili y om he sel -owned e aile is g ea e
han om he anchised e aile , hen he consume will pu chase EWS
om he sel -owned e aile .In p ac ice, his case is simila o Case 2.
Conside ing he h ee ex eme si ua ions, se he consume u ili y
equal o ze o (u1 =0, u2 =0, and u1-u2=0), hen he consume alu-
a ions o EWS can be ob ained. The alua ions wi h iden ical esponse
ime and di e en esponse ime a e as ollows:
X. Zhou e al.
Ope a ions Resea ch Pe spec i es 14 (2025) 100330
4
+
1=
α
p1−βln 1
, +
2=
α
p2−βln 1
θ, +
3=
α
(p1−p2)
1−θ(3)
+
1=
α
p1, +
2=
α
p2−βln 1
Δ
θ, +
3=
α
(p1−p2) + βln 1
Δ
1−θ(4)
4.2. Demand unc ion
The demand o EWS is ela ed o p oduc demand as well as he
cha ac e is ics o he se ice, he e o e, only consume s who ha e pu -
chased a p oduc will p obably pu chase EWS. The esponse ime has an
impo an impac on pu chasing willingness o ime-sensi i e con-
sume s, and hey make decisions based on he consume alua ions o
EWS. Conside ing di e en combina ions o he consume alua ions o
EWS, he ela ionship be ween wo e aile s’ p ices a e as ollows.
Case ①: When 1≥ 2 and 3≤1, he consume ’s alua ion o he
sel -owned e aile is g ea e , meanwhile, he e aile s’ p ice o he EWS
is se o sa is y he consume ’s alua ion expec ed ange [0,1]. So ha
he consume ’s u ili ies o EWS p o ided by bo h e aile s a e g ea e
han ze o, and he consume makes decision based on maximiza ion o
he u ili y. The consume has he op ion o pu chasing EWS om ei he
sel -owned e aile o anchised e aile , and he ela ionship be ween
he EWS p ices o he wo scena ios (IRT and DRT) a e shown as ollows:
p1−1−θ
α
≤p2≤θp1+βln 1
(1−θ)
α
(5)
p1−1−θ−βln 1
Δ
α
≤p2≤θp1+βln 1
Δ
α
(6)
Case ②: When +
1≥ +
2 and +
3>1, he consume ’s alua ion o he
sel -owned e aile is g ea e , howe e , he e aile s’ p ice o he EWS is
se beyond he cons ain o he consume ’s alua ion expec ed ange
[0,1]. So ha he consume ’s u ili ies o EWS p o ided by bo h e aile s
maybe less han ze o, and he consume makes decision based on
minimizing u ili y loss. The consume will pu chase EWS om he
anchised e aile , and he ela ionship be ween he EWS p ices o he
wo scena ios (IRT and DRT) a e shown as ollows:
p2≤p1−1−θ
α
(7)
p2≤p1−1−θ−βln 1
Δ
α
(8)
Case ③: When +
1≤ +
2, he consume ’s alua ion o he anchised
e aile is g ea e , whe he he e aile s’ p ice o he EWS is se o sa is y
he consume ’s alua ion expec ed ange [0,1] o no . The consume
will pu chase EWS om he sel -owned e aile , and he ela ionship
be ween he EWS p ices o he wo scena ios (IRT and DRT) a e shown as
ollows:
p2≥θp1+βln 1
(1−θ)
α
(9)
p2≥θp1+βln 1
Δ
α
(10)
The ela ionships be ween P
1
and P
2
in Eqs. (5)-(10) a e shown in
Fig. 2 below.
In Fig. 2, he egion①②③ espec i ely display he ange o p ice
in e als based on he EWS esponse ime. I can be in ui i ely seen ha
in he egion③, he EWS p ice o anchise e aile is highe , so he
consume u ili y by sel -owned e aile is g ea e . In egion②, he EWS
p ice o sel -owned e aile is highe , hen he consume u ili y by
anchise e aile is g ea e . In egion①, he EWS p ice o wo e aile s is
in be ween he egion② and ③, and he consume u ili y by sel -owned
e aile is ei he g ea e o less han ha o anchise e aile .
The egion ① ep esen s Case ①. The consume will choose o pu -
chase EWS om ei he he sel -owned o he anchised e aile , hen he
demand unc ions o he EWS unde he wo scena ios (IRT and DRT)
a e as ollows:
D1=1−
α
(p1−p2)
1−θ,D2=
α
(p1−p2)
1−θ−
α
p2−βln 1
θ(11)
Fig. 1. The models o he supply chain wi h EWS esponse ime.
Table 1
No a ions.
Symbol Desc ip ion Symbol Desc ip ion
mManu ac u e
α
consume p ice sensi i i y
coe icien o EWS
i e aile i, i =1 sel -owned, i =
2 anchised
βconsume ime-sensi i e
coe icien o EWS
wwholesale p ice o EWS Δ esponse ime di e ence o
EWS
i esponse ime o EWS, i =1,2 0Iden ical esponse ime o
EWS
pi e ail p ice o EWS, i =1,2
η
cos a e o EWS
ccos o EWS Uiconsume s u ili y o EWS, i
=1,2
k a ixed anchise ee Didemand o EWS, i =1,2
λa a iable anchise a e
( a iable anchise ee λp2D2)
Πmp o i o manu ac u e
consume alua ion o EWS Π i p o i o e aile , i =1,2
θsubs i u e a io o EWS
X. Zhou e al.
Ope a ions Resea ch Pe spec i es 14 (2025) 100330
5
D1=1−
α
(p1−p2) + βln 1
Δ
1−θ,D2=
α
(p1−p2) + βln 1
Δ
1−θ−
α
p2−βln 1
Δ
θ
(12)
The egion ② and egion ③ ep esen Case ② and Case ③ espec-
i ely. In egion ②, he consume pu chases EWS om anchised
e aile . The demand unc ion o EWS unde he wo scena ios a e
shown below:
D1=1−
α
p1−βln 1
Δ
θ,D2=1−
α
p2+2βln 1
Δ (13)
Simila ly, in egion ③, he consume pu chases EWS om sel -
owned e aile . The demand unc ion a e shown below:
D1=1−
α
p1
θ,D2=1−
α
p2+βln 1
(14)
The consume ’s pu chasing decision o EWS is clea in egion ② and
egion ③. Howe e , in egion ①, he consume can choose ei he he
sel -owned o he anchised e aile . To u he analyze e aile ’s de-
cision in a compe i i e supply chain, we ocus on egion ①, discussing
he EWS s a egies unde wo scena ios (IRT and DRT).
5. S a egy analysis
5.1. Scena io IRT
In his scena io, as he ma ke o EWS is expanding, all e aile s a e
equi ed o adop he same se ice s anda ds. The sel -owned e aile
and anchised e aile implemen he iden ical EWS s a egy o he
consume s. Based on he demand unc ion in Eq. (11), he o al demand
unc ion o EWS is cons uc ed as:
D=D1+D2=1−
α
p+βln 1
Meanwhile, he EWS cos o mula is c=
η
2 2 [40]. To mo i a e he
anchised e aile , he manu ac u e only cha ges a ixed anchise ee
k. Then he p o i unc ions o he manu ac u e and he e aile s a e
shown below.
Πm=wD +F=w(1−
α
p+βln 1
)+k(15)
Π =D(p−w−c) − F=(1−
α
p+βln 1
)(p−w−
η
2 2)−k(16)
P oposi ion 1: The op imal e aile EWS p icep∗is nega i ely
ela ed o he esponse ime . Simila ly, he cos o he EWS cis nega-
i ely ela ed o he esponse ime .
P oo : The EWS p ice can be de e mined by he backwa d induc ion
me hod. Fi s , calcula e he e aile p o i Π in Eq. (16) o second
pa ial de i a i e wi h espec o he EWS p ice p. As
∂
Π 2
∂
p2= − 2
α
<0,
he e is an op imal EWS p ice ha maximizes he e aile p o i . calcu-
la e he manu ac u e p o i Πmin Eq. (15) o second pa ial de i a i e
wi h espec o wholesale p ice w. As
∂
Πm2
∂
w2= −
α
2<0, he e is an op imal
EWS p ice ha maximizes he manu ac u e p o i . Second, le he
pa ial de i a i e o Πm wi h espec o w be ze o, he op imal wholesale
p ice o EWS is:
w∗ =
−
αη
+2 2(a+βln 1
)
4
α
2(17)
Then, subs i u ing w∗in o Eq. (16), he op imal e aile EWS p ice p∗
is:
p∗ =
αη
+6 2(1+βln 1
)
8
α
2(18)
Finally, calcula e he pa ial de i a i e o p∗and cwi h espec o he
esponse ime .
∂
p∗
∂
= −
η
4 2−3β
4
α
<0;
∂
c
∂
= −
η
3<0 (19)
In o he wo ds, bo h he op imal EWS p ice p∗and he cos c a e
mono onically dec easing unc ions o he esponse ime . Q.E.D.
P oposi ion 1 indica es ha when a ce ain EWS newly en e s he
consume ma ke , companies end o coope a e,and se iden ical EWS
esponse ime in o de o expand ma ke sha e. This si ua ion is an
app oxima e heo e ical s a e, whe e he gi en esponse ime di ec ly
a ec s he EWS cos and p ice.
P oposi ion 2: Fo a gi en EWS esponse ime , he e aile can
always op imize he manu ac u e and he e aile p o i s by p icing he
EWS app op ia ely.
P oo : Fi s , ake he pa ial de i a i es o Eq. (16) wi h espec o
he EWS p ice p and he esponse ime .
∂
Π
∂
p=1−2p
α
+w
α
+
αη
2 2+βln 1
Fig. 2. Rela ionship be ween p
1
and p
2
.
X. Zhou e al.
Ope a ions Resea ch Pe spec i es 14 (2025) 100330
6
∂
Π
∂
= − β
(p−w−
η
2 2)+
η
3(1−
α
p+βln 1
)
Fu he mo e, calcula e he second pa ial de i a i es o he e aile
p o i Π wi h espec o p and .
∂
Π 2
∂
p2= − 2
α
∂
Π 2
∂
2=β
2(p−w) − 3
η
4(1−
α
p+βln 1
)−5β
η
2 4
Calcula e he second mixed de i a i e o he e aile p o i Π wi h
espec o p and .
∂
Π 2
∂
p
∂
=
∂
Π 2
∂
∂
p=−
αη
3−β
Cons uc he Hessian ma ix, he i s -o de p incipal mino de e -
minan D1= − 2
α
<0, he second-o de p incipal mino de e minan
D
2
is:
D2=
⎛
⎜
⎜
⎜
⎜
⎝
∂
Π 2
∂
p2
∂
Π 2
∂
p
∂
∂
Π 2
∂
∂
p
∂
Π 2
∂
2
⎞
⎟
⎟
⎟
⎟
⎠
=⎛
⎜
⎜
⎜
⎝
−2
α
−
αη
3−β
−
αη
3−β
β
2(p−w)− 3
η
4(1−
α
p+βln1
)−5β
η
2 2
⎞
⎟
⎟
⎟
⎠
=− 2
α
[β
2(p−w)− 3
η
4(1−
α
p+βln1
)−5β
η
2 2]−(−
αη
3−β
)2
(20)
In Eq. (20), in o de o make he Hesse ma ix nega i e de ini e, D
2
should be posi i e.
−2
α
[β
2(p−w) − 3
η
4(1−
α
p+βln 1
)−5β
η
2 2]−(−
αη
3−β
)2
>0 (21)
hen
p<
α
2[2wβ+6
η
(1+βln 1
)−2
η
β]+β 4(5
αη
−β) −
α
2
η
2
2
α
2(β 2+3
αη
)(22)
The e o e, wi h a gi en esponse ime , he e aile can always se
he p ope EWS p ice o sa is y he cons ain i.e. Eq. (22), and maximize
he p o i s o bo h he manu ac u e and he e aile . Q.E.D.
P oposi ion 2 indica es ha wi h iden ical EWS esponse ime,
companies can design app op ia e p icing s a egies based on he ela-
ionship be ween EWS esponse ime and p ice in P oposi ion 1 o
achie e maximum p o i s, and p omo e he con inuous g ow h o he
EWS ma ke .
5.2. Scena io DRT
In his scena io, as he ma ke o EWS is ma u e, he e aile s can
o e EWS wi h di e en ia ed se ice le els, while he sel -owned and
he anchised e aile s each de eloping hei own EWS s a egies. Based
on he demand unc ion in Eq. (12), he EWS cos o mula is c =
η
2Δ 2
[40]. To maximize he p o i , he manu ac u e cha ges a a iable
anchise ee based on sales o EWS, in addi ion o he ixed anchise ee
k. Then he p o i unc ions o he manu ac u e and he e aile s a e
shown below.
Max∏∗
m=
w∗
w⎡
⎢
⎣1−
α
(p1−p2) + βln 1
Δ
1−θ⎤
⎥
⎦
+ (w+λp2)⎡
⎢
⎣
α
(p1−p2) + βln 1
Δ
1−θ−
α
p2−βln 1
Δ
θ⎤
⎥
⎦+k(23)
Max∏∗
1 =
p1∗,p2∗
(p1−w)[1−
α
(p1−p2)
1−θ](24)
Max∏∗
2 =
p1∗,p2∗[(1−λ)p2−w−
η
2Δ 2]⎡
⎢
⎣
α
(p1−p2)
1−θ−
α
p2−βln 1
Δ
θ⎤
⎥
⎦−k(25)
P oposi ion 3: The wo e aile s op imal EWS p ices a e nega i ely
ela ed wi h he p ice sensi i i y coe icien , and posi i ely ela ed wi h
he esponse ime-sensi i e coe icien .
P oo : By he backwa d induc ion me hod, he op imal EWS p ices o
bo h e aile s a e as ollow:
p∗
2=
αη
(θ−1) + Δ 2{ − 6+4λ+θ[6+λ(λ−4)]}(θ+βln 1
Δ )
4
α
Δ 2(θ−1)(λ−2)
(27)
Calcula e he i s pa ial de i a i es o he op imal EWS p ices p∗
1
and p∗
2 wi h espec o
α
and β espec i ely.
∂
p1∗
∂α
=(θ+βln 1
Δ ){4λ+θ[2+λ(λ−4)]} + 2(θ−βln 1
Δ −2)
8
α
2(1−θ)(28)
∂
p2∗
∂α
=(θ+βln 1
Δ ){ − 6+4λ+θ[6+λ(λ−4)]}
4
α
2(θ−1)(λ−2)(29)
∂
p1∗
∂
β=ln 1
Δ { − 2+4λ+θ[2+λ(λ−4)]}
8
α
(θ−1)(30)
∂
p2∗
∂
β= − ln 1
Δ { − 6+4λ+θ[6+λ(λ−4)]}
4
α
(θ−1)(λ−2)(31)
Obse ing Eq.(26), p1∗should be g ea e han ze o, as θ<1, he e o e
p1∗ =
−
αη
(θ−1) + Δ 2[θ+βln 1
Δ ]{4λ+θ[2+λ(λ−4)]} + 2Δ 2(θ−βln 1
Δ −2)
8
α
Δ 2(θ−1)(26)
X. Zhou e al.
Ope a ions Resea ch Pe spec i es 14 (2025) 100330
7
−a
η
(θ−1) + Δ 2[θ+βln(1
Δ )]{4λ+θ[2+λ(λ−4)]
+2Δ 2[θ−βln(1
Δ )−2]
<0
Since −
αη
(θ−1)>0, hen
(θ+βln 1
Δ ){4λ+θ[2+λ(λ−4)]) + 2(θ−βln 1
Δ −2)}<0
in ha case,
∂
p1∗
∂α
<0.
Simila ly in Eq.(27), p2∗should also be g ea e han ze o, bo h θ and
λ<1, he e o e
{ − 6+4λ+θ[6+λ(λ−4)]}(θ+βln 1
Δ )<0
in ha case,
∂
p2∗
∂α
<0.
Likewise, i can be p o ed ha Eq. (30) and Eq. (31) a e bo h g ea e
han ze o, i.e.
∂
p1∗
∂
β>0 and
∂
p2∗
∂
β>0.
Hence, he op imal EWS p ices p1∗and p2∗a e dec easing unc ion o
he p ice sensi i i y coe icien
α
, and inc easing unc ion o he esponse
ime-sensi i e coe icien β. Q.E.D.
P oposi ion 3 indica es ha as he EWS ma ke de elops o a ma u e
s age, companies ude s and he consume demands be e and engage in
compe i ion. Based on he p icing s a egy in P oposi ion 2, companies
need o conside consume p ice sensi i i y and esponse ime sensi-
i i y, and se a mo e complex combina ion p icing s a egy.
P oposi ion 4: When 1< 2, he op imal EWS p ice o he sel -owned
e aile p1∗is posi i ely ela ed o he di e en ial esponse ime Δ . The
op imal EWS p ice o he anchised e aile p2∗is nega i ely ela ed o
he di e en ial esponse ime Δ . When 1> 2, p1∗is nega i ely ela ed
o Δ , and p2∗is posi i ely ela ed o Δ .
P oo : Take he i s pa ial de i a i es o he op imal EWS p ices p
1
*
and p
2
* wi h espec o Δ in Eq. (26) (27):
∂
p1∗
∂
Δ =2
αη
(θ−1) − Δ βln 1
Δ { − 2+4λ+θ[2+λ(λ−4)]}
8
α
Δ 3(θ−1)(32)
∂
p2∗
∂
Δ =2
αη
(θ−1) + Δ βln 1
Δ { − 6+4λ+θ[6+λ(λ−4)]}
4
α
Δ 3(θ−1)(λ−2)(33)
Based on he p oo o P oposi ion 3, bo h he nume a o s in Eq. (32)
and Eq. (33) a e less han ze o, he e o e,
∂
p1∗
∂
Δ >0and
∂
p2∗
∂
Δ <0.
Δ is de ined as | 1− 2|, consis ing wo kinds o si ua ion, 1< 2 and
1> 2. When 1< 2, he op imal EWS p ices p
1
* is g ea e han p
2
*, and
he mo e di e ence o esponse imes be ween he wo e aile s, he
highe he p ice p
1
*, i.e., p1∗is an inc easing unc ion o Δ . Simila ly, p2
∗is a dec easing unc ion o Δ . when 1> 2, p
1
* is less han p
2
*, and he
mo e di e ence o esponse imes be ween he wo e aile s, he lowe
he p ice p
1
*, i.e., p1∗is a dec easing unc ion o Δ , and p2 ∗is an
inc easing unc ion o Δ . Q.E.D..
P oposi ion 4 indica es ha in he compe i ion o he EWS ma ke ,
based on he EWS combina ion p icing s a egy in P oposi ion 3, com-
panies can design hei own op imal p icing s a egy and ob ain a p ice
compe i i e ad an age by adjus ing he di e ence o esponse ime wi h
hei compe i o s.
6. Sensi i i y analysis
Based on he e i ica ion o he p e ious ou p oposi ions, his
sec ion ocus on obse ing he impac s on he EWS s a egies unde he
combina ion o esponse ime and p ice h ough wo pa ame e s: con-
sume p ice sensi i i y coe icien o EWS
α
and consume ime-
sensi i e coe icien o EWS β. The pa ame e s such as cos a e o
EWS
η
, a iable anchise a e λ, and subs i u e a io o EWS θ a e mainly
used o suppo he acquisi ion o nume ical calcula ion esul s. The
changes in hese pa ame e s do no a ec he conclusions, so he
de ailed analysis is omi ed. Acco ding o he e e ence [40], wi hou
lossing o gene ali y, se he pa ame e s as ollows:
α
=0.2, β=0.3,
η
=
0.1, λ=0.2, θ=0.4. Among hem,
α
and β a e ini ial alues selec ed. In
sensi i i y analysis, di e en combina ions o hese wo pa ame e s a e
ca ied ou . As o
η
, λ and θ, he selec ion o he alues a e acco ding o
heo e ical li e a u e e iew, as well as empi ical business p ac ices.
Hence, he sensi i i y analysis is conduc ed o exam he impac s o
he p ice and esponse ime on EWS supply chain s a egies in scena io
IRT and scena io DRT.
6.1. Sensi i i y analysis in scena io IRT
6.1.1. The impac s o esponse ime on EWS s a egy
Calcula e he EWS p ices, cos s and p o i s wi h a ious ime. In
Fig. 3, bo h he EWS p ice p∗and cos c inc ease wi h dec easing o he
esponse ime , and he EWS p ice w∗dec eases wi h dec easing o he
esponse ime . The e exis s a h eshold alue o he esponse ime .
When <0.2, he EWS cos s inc ease apidly as he esponse ime
Fig. 3. The impac s o on p∗,w∗and c.
Fig. 4. The impac s o on Πm∗and Π ∗.
X. Zhou e al.
Ope a ions Resea ch Pe spec i es 14 (2025) 100330
8
