1
Scena io-Based Dynamic Nego ia ion o he Coo dina ion o Mul i-En e p ise
Supply Chains unde Unce ain y
Ke ah Hjaila1, José M. Laínez-Agui e2,Luis Puigjane 1 and An onio Espuña1*
1Chemical Enginee ing Depa men , Uni e si a Poli ècnica de Ca alunya, ETSEIB., A . Diagonal 647, 08028
Ba celona, Spain.
2Depa men o Indus ial and Sys ems Enginee ing, Uni e si y a Bu alo, NY, Uni ed S a es.
*co esponding au ho : an [email protected]
Abs ac
A no el Scena io-Based Dynamic Nego ia ion app oach is p oposed o he coo dina ion o
decen alized Supply Chains unde unce ain y. The ela ion be ween he in ol ed o ganiza ions
(clien , p o ide and hi d pa ies) and hei espec i e con lic ing objec i es is cap u ed h ough a
non-ze o-sum and non-symme ic oles SBDN nego ia ion. The clien (leade ) designs coo dina ion
ag eemen s conside ing he unce ain eac ion o he p o ide ( ollowe ) esul ing om he unce ain
na u e o he hi d pa ies, which is modeled as a p obabili y o accep ance. Di e en nego ia ion
scena ios a e s udied: i) Coope a i e, and ii) Non-Coope a i e and iii) S andalone cases. The use o he
esul ing models is illus a ed h ough a case s udy wi h di e en endo s a ound a “leade ” (clien ) in
a decen alized scena io. Al hough he usual coope a ion hypo hesis will allow highe o e all p o i
expec a ions, using he p oposed app oach i is possible o iden i y non-Coope a i e scena ios wi h
high indi idual p o i expec a ions which a e mo e likely o be accep ed by all pa ne s.
Keywo ds: Decen alized Supply Chain; Tac ical planning; Unce ain y managemen ;
Compe i i e managemen .
1. INTRODUCTION
Due o he ma ke dynamics, double ma ginaliza ion, and he ola ili y o he ma ke ,
he en e p ises decision-make s ha e o change hei way o managing hei Supply chains
(SCs). En e p ises in he chemical p ocess indus y seek “ alue p ese a ion” o emain
compe i i e and “ alue g ow h” o become mo e inno a i e (G ossmann, 2004). Many wo ks
in he li e a u e p opose di e en p ocedu es o help decision-make s o op imize hei SCs,
especially a he ac ical le el, which is he ocus o his pape . These wo ks, b ie ly discussed
below, a e de o ed o he op imiza ion o he whole sys em om a cen alized pe spec i e.
Howe e , holding a la ge scale SC o one en e p ise unde a cen alized decision-make may
no be easible, hus collabo a ing wi h o he en e p ises may add alue o all pa icipa ing
o ganiza ions, so ha all can emain compe i i e in he global ola ile ma ke . Such
collabo a ion is ha d o de elop as i depends on he coope a i e beha io o he pa icipan s.
Fu he mo e, a complexi y a ises when conside ing he di e en (possibly con lic ing)
objec i es o he o ganiza ions in ol ed, since hey a e eally ying o op imize i s own
bene i s wi hou conside ing he isks associa ed wi h he unce ain beha io o he o he
pa ne s.
F om a cen alized pe spec i e, Laínez e al. (2009) de elop an in eg a ed s a egic and
ac ical lexible MILP model aking in o accoun all possible easible links and ma e ial lows
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among he SC acili ies. Ama o and Ba bosa-Pó oa (2013) de elop a close-loop SC ac ical
model o mula ion (MILP), coo dina ing he di ec lows (new p oduc s) and he e e se
lows ( ecycled) wi hin a cen alized closed-loop pe spec i e whe e he di ec and e e se
echelons SCs belong o one o ganiza ion. Zama ipa e al. (2014) p opose a LP ac ical model
o op imizing mul i-si e mul i-p oduc SC ne wo ks, coo dina ing he di e en s eps h ough
he insu ance o he consis ency o he supply/demand SC. This wo k has been expanded la e
by Hjaila e al. (2016) by in eg a ing hi d pa ies’ inancial pe spec i es as new elemen s o
be conside ed in he decision making, hus esul ing in di e en (LP, NLP, MINLP) ac ical
cen alized models.
Typical SCM models ocus on he single low o in o ma ion biased by he decision-
make o one o ganiza ion (cen alizing playe ). Howe e , such in o ma ion is no su icien o
deal wi h he new ma ke compe i i e issues esul ing om he p esence o o he pa ne s,
such as coo dina ion/collabo a ion, nego ia ions, unce ain y. Bu , he inco po a ion o hi d
pa y decisions should be s udied in dep h.
All he abo e desc ibed wo ks ocus on he o e all objec i e o he sys em, esul ing
om he coo dina ion be ween he a ious echelons/pa ne s wi hin a global SC cen alized
pe spec i e, so ha he indi idual objec i es a e dis ega ded, al hough hey a e essen ial,
especially when SC supe s uc u e is decen alized and di e en o ganiza ions a e in ol ed,
including hi d pa ies wi h con lic ing objec i es and unce ain beha io .
The esolu ion o con lic i e goals h ough nego ia ions has been sligh ly co e ed by
he PSE li e a u e. The app oaches discussed a he ba gaining li e a u e include he use o
quan i y discoun s, minimum commi men s, buy backs ( e u ns), penal ies, and e enue
sha ing (Cachon, 2003). I is wo h o commen he wo k by Cao e al. (2013) which sugges s a
ading me hod based on “ e enue sha ing” app oach o sol e he con lic s be ween one
manu ac u e and he a ious compe ing e aile s unde he leading ole o he manu ac u e .
The au ho s conside he unce ain y o he p oduc ion and inal ma ke s demands; howe e ,
in his wo k he manu ac u e p o ides he ini ial p oduc ion plan acco ding o i s unce ain y
beha io ega dless o he unce ain beha io o e aile s which can lead o SC dis up ions. In
o de o gua an ee some bene i s o he ollowe , Zhao e al. (2013) p opose a nego ia ion
me hod o op imizing a SC manu ac u e - e aile ne wo k h ough bi-di ec ional op ion
con ac s (call o pu ). Fo he call op ion, he manu ac u e mus buy a speci ic amoun o
p oduc s a a speci ic p ice while, o he pu op ion he e aile mus pay an allowance o he
cancella ion o e und o an o de .
Mul i-agen sys ems ha e been also p oposed o op imizing decen alized SC
ne wo ks. The wo k o Cao e al. (2007) de elop a Pinch Mul i-Agen Gene ic Algo i hm
(PMAGA) o ne wo k op imiza ion o wa e -use a he ac ical le el whe e s akeholde s
coope a e o minimize he o al used eshwa e . Banaszewski e al. (2013) p opose an
auc ion p o ocol ac ical model mul i-agen o a B azilian oil SC o iden i y he oil p oduc s
anspo plan ( ypes, amoun s, alloca ion). Howe e , he mul i-agen -based nego ia ions a e
o ien ed o coope a i e si ua ions, in which all pa icipa ing agen s coope a e owa ds a
common objec i e unc ion. This app oach dis ega ds indi idual objec i es and hei
unce ain na u e which can a ec he pe o mance o he en i e sys em.
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Many wo ks we e ca ied ou o op imize decen alized SCs h ough Game Theo y
(GT), based on coope a i e and non-coope a i e cases. Fo he coope a i e case, Henne and
A eda (2008) de elop a coo dina ion ag eemen o a p oduce and supplie SC h ough
coope a i e games based on sha ing he backo de cos s and capaci y ese a ion in o de o
main ain supply lows. Zhao e al. (2010) de elop a coope a i e game model o he
op imiza ion o a decen alized manu ac u e - e aile SC based on op ion-con ac s unde he
condi ion ha he manu ac u e maximum p oduc ion coincides wi h he e aile ese ed
quan i ies.
Whe eas indi idual goals h ough non-coope a i e SCs ha e been s udied so a , he
p oposed app oach is based on e y simpli ied SC s uc u es such as in he wo k o Li e al.
(2013). They p opose a coo dina ion con ac ag eemen based on “sho age penal y”
be ween one supplie and one buye (no ex e nal ma ke s), so ha he ollowe is obliged o
sell which gi es a high dominance o he leade . Yue and You (2014) conside mo e complex
s uc u es, in which di e en compe ing supplie s and e aile s pa icipa e. They mee he
compe i ion be ween he di e en supplie s and e aile s h ough coope a i e games based
on Nash Equilib ium, while he in e ac ions be ween he manu ac u e and he
supplie s/ e aile s a e modeled as non-coope a i e S ackelbe g games. Howe e , as a
coope a i e play, compe i i e supplie s a e conside ed obliged o sell o he manu ac u e
dis ega ding he compe i ion among di e en cus ome s. This gi es again a dominan
leade ship o he cus ome . Fu he mo e, in he p oposed non-coope a i e S ackelbe g game,
he supplie SC model has been simpli ied (as LP) in o de o be ep esen ed as cons ain s in
he manu ac u e op imiza ion model (bi-le el model), which canno be esol ed i he
supplie SC model is a non-con ex MINLP (Colson e al. 2007). This app oach would equi e
he use o non- ealis ic linea izing simpli ica ions i he supplie SC should conside aspec s
like p icing policies, e-design decisions, e c. Mo eo e , he unce ain beha io s o he
ollowe s SCs (supplie s and e aile s) a e no conside ed by he leade .
In summa y, mos o he li e a u e abou decen alized SCs ac ical decision-making,
ei he o coope a i e o non-coope a i e cases, ocuses on simple SC ne wo ks, whe e he
ollowe is o ced o coope a e wi h he leade , and/o p oposes linea ized models o
ep esen he beha io o some o he ac o s which can lead o losing some p ac icali y.
Cu en nego ia ion me hods based on non-coope a i e SCs allow o p o ide indi idual
decisions based on s a ic cases wi hou add essing he ull SC pic u e, which should include
how pa ne s may eac , hus esul ing in incomple e nego ia ions, especially when he
nego ia ing pa ne s (and hei hi d pa ies) a e subjec o isk as he esul o ex e nal
unce ain y sou ces. Mo eo e , none o he li e a u e wo k on decen alized SCs op imiza ion
e alua es he nego ia ion ou come based on he bene i s p obabili ies in o de o help he
nego ia ing pa ne s o make a inal decision. Thus, e ec i e nego ia ions able o inco po a e
he con lic ing goals o all pa icipan s (including hi d pa ies) in ac ical models a e needed
o imp o e he o e all pe o mance o decen alized SC ne wo ks and o a oid SCs
dis up ions.
Consequen ly, his pape aims o de elop a no el Scena io-Based Dynamic Nego ia ion
me hod (SBDN) as a ool o decision suppo o p o ide he bes condi ions o coo dina ion
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be ween independen p oduc ion-dis ibu ion SCs wi h con lic ing objec i es wi hin
decen alized SC. The use o his app oach o suppo nego ia ions, aking in o accoun he
compe i ion be ween di e en supplie s/ma ke s and hei unce ain na u e, will imp o e he
capaci y o iden i y and manage new win- o-win scena ios, hus expanding he bounda ies o
he SC o in e es . Such expansion co e s bo h cus ome s and p o ide s, wi h hei espec i e
p oduc ion-dis ibu ion SCs, as pa o he o e all sys em.
In summa y, he objec i es o his wo k can be summa ized in he ollowing poin s:
- To analyze coope a i e and non-coope a i e decen alized SC h ough a nego ia ion
o ien ed app oach.
- To inco po a e in he sys em he unce ain na u e o he di e en in ol ed pa ies, and o
summa ize i in a single beha io al exp ession associa ed wi h he ollowe eac ion which
is conside ed in he leade SC objec i e unc ion.
- To ep esen all he in ol ed pa ne s in a comple e p oduc ion-dis ibu ion SCs.
- To p opose a decision-suppo s a egy o e alua e he o e all ou come, based on he isk
beha io and he expec ed bene i s o he pa ne s.
- To ep esen he a ia ions be ween he p o i s scena ios in one single app oach h ough
he p obabili y o accep ance.
- To c ea e a gene ic and lexible enough amewo k by implemen ing he esul ing s a egy,
able o be used in eal-sized cases o cen alized/decen alized SCs wi h simple/complex
s uc u es.
2. P oblem S a emen
The main SC o his wo k p oduces se e al p oduc s o inal cus ome s using
esou ces om di e en compe ing p o ide s. In o de o imp o e i s indi idual p o i s, he
main o ganiza ion (as a clien ) may conside o collabo a e wi h o he p oduc ion SCs, which
a e ecognized as independen o ganiza ions, wi h hei own compe ing p o ide s and
ma ke s, on he basis o a buying/selling esou ce which om now on will be conside ed an
“inne componen “ (Figu e 1). Since he alue o his inne componen is an income o he
main p o ide and a cos o he main clien , a con lic o in e es s a ises o iden i y he inne
componen lows (physical/economic) along he ac ical ime ho izon in his complex
compe i i e en i onmen . In o de o sol e his con lic , a coo dina ion comp omise is usually
p oposed, bu i s nego ia ion may be complex and may e en end wi hou an ag eemen .
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Figu e 1- Decen alized SC ne wo k and s akeholde s
2.1 SBDN me hodology
In he Scena io Based Dynamic Nego ia ion app oach (SBDN) p oposed in his wo k,
he pa ies in he nego ia ion a e he clien and he p o ide , bo h pa icipa ing as p oduc ion-
dis ibu ion SCs in he decen alized SC o in e es . The elemen s o nego ia ion a e he inne
componen physical lows be ween hei SCs, and ob iously i s uni ans e p ice. Ou SBDN
no el app oach is based on building a coo dina ion/collabo a ion con ac , and since any
con ac is be ween pai s o s akeholde s, wo main nego ia ing pa ne s a e conside ed o
signing he con ac : he Clien and he P o ide . The es o he pa icipan s o ganiza ions
(e.g. supplie s, cus ome s, ex e nal p o ide s, ex e nal clien s, e c.) in e ac ing wi h he
decen alized SC a e conside ed as 3 d pa ies (Figu e 2). Howe e , all 3 d pa ies pa icipa e
in he decision-making by means o hei p ice policies as will be explained la e .
Based on a non-symme ical ole, he clien (as leade ) will design a se o
coo dina ion con ac s based on i s bes condi ions and he p o ide (as ollowe ) expec ed
esponse unc ion (Figu e 2). This esponse unc ion is cha ac e ized by he unce ain
esponse o he ollowe 3 d pa ies o he quan i y and he i em p ice o e ed by he leade a
each ime slo o e he disc e e planning ime ho izon, and will be assessed on he basis o he
incomple e knowledge o he ollowe unce ain beha io and i s ex e nal condi ions (i.e.,
unce ain y o hi d pa ies’ beha io ).

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Figu e 2- SBDN pa ne s
Figu e 3 illus a es he SBDN con ex . The SBDN depends on many elemen s: i) he
economic con ex o he pa icipan s, especially a he s andalone case, ii) he ma ke si ua ion
(e.g. p ices, compe ing pa ne s, e c.,), iii) he main objec i es o each en e p ise s akeholde ,
i ) he quali y o he sha ed in o ma ion be ween pa ne s, ) he isk p opensi y o he main
en e p ise decision-make s, and inally i) he p obabili y o accep ance o he ollowe
pa ne o he decisions made by he leade pa ne .
SBDN
Economic
con ex
Ma ke
si ua ion
En e p ises
objec i es
In o ma io
n sha ing
Risk
p opensi y
P obabili y
o
accep ance
7
Figu e 3- SBDN con ex
The p oposed SBDN me hodology can be conside ed as di ided in o wo main pa s
(Figu e 4): he analysis o nego ia ion scena ios (iden i ica ion o he bes scena io o be used
o nego ia ing he inal ag eemen ), and he p epa a ion o he inal
coo dina ion/collabo a ion ag eemen .
2.1.1 Nego ia ion scena ios
Di e en nego ia ion scena ios a e analyzed in his wo k on he basis o h ee main
si ua ions i) S andalone, ii) Coope a i e, and iii) Non-Coope a i e ci cums ances (Figu e 4).
S andalone Scena io
(SS)
Coope a i e Nego ia ion
Scena io (CNS)
Nego ia ion Scena ios
Op imiza ionGlobal op imiza ion
Global
P o i
Unce ain
condi ions
P obabili y o
accep ance
Coo dina ion con ac
Leade Followe
Expec ed P o i
Final collabo a ion ag eemen
Expec ed P o i
P obabili y
dis ibu ion
Leade
non-Coope a i e Nego ia ion
Scena io (nCNS)
Followe
P ice scena ios
Op imiza ion
Cu en
P o i
Op imal
quan i y
Op imiza ion
Unce ain
condi ions
Cu en
P o i
Expec ed
P o i
Expec ed
ollowe P o i
Cu en
condi ions
P o i
Unce ain
condi ions
Expec ed
ollowe P o i
Cu en
condi ions
Cu en
condi ions
Imp o ed
expec ed p o i
Final esponse (accep / ejec )
Figu e 4- SBDN me hodology lowcha
i) Coope a i e Nego ia ion Scena io (CNS):
Bo h nego ia ing pa ies s udy he si ua ion unde a global pe spec i e, as hey we e
pa o a coali ion o maximize he o e all p o i o he SC. This will s ablish a second
benchma k, in he opposi e side. Be o e s a ing he nego ia ion p ocedu es, he logical s ep
8
o he pa ies is o analyze whe he hei e en ual coo dina ion ag eemen o e s po en ial
bene i expec a ions (o no ).
ii) Non-Coope a i e Nego ia ion Scena io (nCNS)
The leade designs he i s play by assessing a se o p ices and quan i ies o he
nego ia ion elemen s, based on he /his bes e ms and aking in o conside a ion he
compe i i e p ices o he ollowe SC ex e nal ma ke s (based on dynamic “sequen ial”
nego ia ions). Bo h pa ies independen ly op imize hei own SCs aking in o conside a ion
he low o a ba gaining (p ice s. quan i y) o e he planning ime ho izon.
iii) S andalone Scena io (SS):
The nego ia ing pa ne s op imize hei indi idual p o i s independen ly, i.e.: wi hou
conside ing he nego ia ion s ep. This scena io will es ablish indi idual benchma ks o all
me hods o nego ia ion.
2.1.2 The coo dina ion ag eemen
Based on he leade con ac o e s, bo h ading pa ne s analyze hei expec ed bene i s:
F om he leade side:
The bene i s o any educ ion in he unce ain y associa ed wi h he signa u e o a
coo dina ion ag eemen may be conside ed. The leade has o o ecas o wha ex en he
ollowe would accep each coo dina ion con ac o e by aking in o conside a ion he
unce ain eac ion associa ed wi h he ex e nal isk condi ions, and he endogenous
unce ain y in he ollowe model. As a esul , he p obabili y o accep ance o his ag eemen
by he ollowe is es ima ed. Addi ionally o he non- o mal knowledge ha each pa ne has,
p obably his o ically accumula ed abou he es o pa ne s, his p obabili y o accep ance,
may conside se o ex e nal easible scena ios ( ollowe SC) and he subsequen Mon e-Ca lo
sampling app oach. Then, he leade may use his p obabili y o accep ance unc ion o
calcula e he expec ed p o i s. The con ac p oposed by he leade will be ha one leading o
he mos p o i able leade ’s expec a ions, which in u n will depend on he manne he leade
manages unce ain y ( isk-seeking, isk-neu al, o isk-a e se).
F om he ollowe side:
On he basis o he coo dina ion ag eemen p oposed by he leade , he ollowe will
assess he isks associa ed wi h he accep ance o ejec ion o his coope a ion ag eemen .
The e alua ion will be based on he p obabili y dis ibu ion and cumula i e cu e o i s own
expec ed p o i s. These p obabili y cu es may be also ob ained by andomly gene a ing and
simula ing scena ios h ough a Mon e-Ca lo app oach (e.g.: assuming no mal o any o he
easonable p obabili y dis ibu ion unc ion). The esponse o he ollowe will also depend
on how he ela ed o ganiza ion manages unce ain y ( isk-seeking, isk-neu al, o isk-
a e se).
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3. Ma hema ical model
A gene ic ac ical MINLP has been de eloped o e alua e di e en nego ia ion
scena ios. Small changes in he model’s cons ain s allow o in oduce di e en coo dina ion
si ua ions which a e use ul o assess whe he a speci ic p oposal is likely o be accep ed o
ejec ed by he coun e pa s.
3.1 The ac ical base model
The base model is designed o be lexible enough o accep simul aneously all
necessa y pa ne s wi h hei espec i e SCs and 3 d pa ies, which enables hem o play
di e en oles (e.g. clien o one SC and p o ide o ano he SC) wi hin a global SC ne wo k.
This is done by conside ing he pa ne SC’s as a se in he ma hema ical o mula ion.
Acco dingly, o ep esen he nego ia ion s a egy, a se o supply chains (sc1, sc2… SC) is
conside ed linking each SC o i s co esponding nego ia ion pa ne ( ollowe F o leade L).
Fu he mo e, he model o mula ion includes a se o hi d pa ies D: leade ex e nal
p o ide s (x ), ollowe ex e nal clien s (xc), supplie s (s), and cus ome s (m). The model
includes a se o esou ces (RM, inal p oduc , ene gy, e c.), p oduc ion plan s pl, and
wa ehouses w as well. A subse w’ is conside ed o ep esen he wa ehouses belonging o
o he pa ne SCs.
Figu e 5 illus a es he main in e ac ions be ween he leade and he ollowe SCs,
including hei ela ions wi h 3 d pa ies. The mos impo an a iables a e illus a ed in he
igu e: ’ ep esen s he speci ic esou ce unde nego ia ion (inne componen ), which can be
pu chased om ex e nal endo s (x ) and/o sold o ex e nal clien s (xc).
, ', sc
Q
′
ep esen s
he quan i y o his nego ia ion i em ’ sen by he ollowe SC (F) o each p oduc ion plan
(pl) o he leade SC (L) along a disc e e planning ho izon T, a a ans e p ice pe uni
,'
sc
p
′
.
', , ', ,
w sc xc
C
and
, , , ', x w sc
V′
ep esen he lows o he same kind o esou ce ’ sold o he ex e nal
clien s (xc) and pu chased om he ex e nal endo s (x ) along he planning ho izon T,
espec i ely. The e ms
,, xc
pc ′
and
,, x
p
′
ep esen he applicable p ices o selling and
pu chasing o he ex e nal clien s (xc) and om he ex e nal endo s (x ), espec i ely.
16
he decision making o bo h nego ia ing pa ne s is conside ed, and he e alua ion o he
coo dina ion con ac s will be assessed based on he p obabili y o accep ance.
The unce ain eac ion o he ollowe pa ne esul ing om he unce ain beha io
o i s 3 d pa ies (supplie s s, cus ome s m, ex e nal clien x ) is p ojec ed in he leade SC
model as a p obabili y o accep ance. The p obabili y o accep ance
sc
p ob
is compu ed aking
in o accoun he expec ed bene i s and he p obabili ies o occu ence o each gene a ed
scena io. In his wo k a simple a io be ween he numbe o success ul scena ios and he o al
numbe o scena ios is p oposed o calcula e he p obabili y o accep ance
sc
p ob
(Eq.19).
sc
p ob
is es ima ed on he basis o he expec ed p o i s o he ollowe SC esul ing om he
di e en gene a ed scena ios compa ed wi h he expec ed p o i s esul ing om he
s andalone case (SS) using he same gene a ed scena ios. In his pa , a Mon e-Ca lo sampling
me hod is used o gene a e andom scena ios o he p ice policies o he 3 d pa ies (Eqs. (6, 8-
13):
,, xc
pc
′
,
,, sc m
p
, and
,, , s sc
m
.
'
'
'
.
.
sc
sc
sc
No o scena ios o imp o ed p o i s
p ob To al No o scena ios
=
' ;'sc SC sc F∀∈ ∈
(19)
The leade expec ed p o i
'sc
ExPROF
is hen ob ained (Eq. 20) based on he
p obabili y o accep ance
'
sc
p ob
.
' ''
'
'(1 )
i he ollowe accep
sc sc sc sc
s i he ollowe
scejec s
ExPROF p ob PROF p ob PROF= ⋅ +− ⋅
' ;'sc SC sc L∀∈ ∈
(20)
The ma hema ical model o mula ion leads o di e en MINLP models, which can be
applied o di e en con igu a ions o SCs ne wo ks wi h hei own compe i i e 3 d pa ies.
Fu he mo e, he in eg a ion o he 3 d pa y p ice polices in he decision making as (Eqs. 6, 7,
8-13), ega dless o he added complexi y o he model o mula ion, gi es he 3 d pa ies
enough eedom o manage hei inancial lows, hus allowing hem o pa icipa e in he
decision-making wi h hei unce ain condi ions. Subsequen ly, he equilib ium can be
achie ed om his nego ia ion: be ween he ex e nal clien (xc) and he leade pa ne (L) as
compe ing clien s o pu chase he esou ce ’, and be ween he ex e nal endo s (x ) and he
ollowe pa ne as endo s o he esou ce ’. Fu he mo e, he de eloped MINLP model
cons i u es a lexible decision-suppo ool o co e all ypes o SCs nego ia ions
(coope a i e/non-coope a i e), o cen alized/decen alized SC ne wo ks.
4. Case s udy
The de eloped MINLP models ha e been implemen ed and sol ed o a case s udy
based on he cen alized SC sys em p oposed by Hjaila e al. (2016). The cen alized SC is
decen alized by assuming a decen alized SC supe s uc u e in o de o illus a e he

17
p oposed app oach. Addi ionally, he planning ho izon has been educed om 10 o 6 ime
pe iods and he capaci ies o he ene gy gene a ion plan s ha e been inc eased om 5MWe o
6MWe in o de o enhance he compe i i e p essu e among pa ne s. The nego ia ing pa ies
a e he polys y ene p oduc ion-dis ibu ion o ganiza ion (as leade ) and he ene gy
gene a ion o ganiza ion (as ollowe ), so he in e nal ene gy supplied/demanded is
conside ed as he i em o be nego ia ed (amoun and p ice). Each SC is assumed o also
nego ia e wi h o he own supplie s and ma ke s (Figu e 6), so bo h ollowe and leade ha e
he lexibili y o accep o ejec he o e s o hei espec i e coun e pa . The equilib ium
will be achie ed be ween he compe ing pa ne s: i) be ween he polys y ene p oduc ion SC
en e p ise s akeholde and he local G id and ex e nal ma ke s o he ene gy gene a ion SC
(3 d pa ies), and ii) be ween he Local G id (3 d pa y as ex e nal p o ide o he leade SC)
and he ene gy gene a ion SC en e p ise s akeholde .
Figu e 6- Nego ia ion pa ne s SCs
The ene gy gene a ion SC consis s o 6 enewable ene gy gene a o s (g1, g2... g6) ed
by one RM supplie (s1) o 4 al e na i e compe ing esou ces (wood pelle s b1, coal b2,
pe coke b3, and ma c was e b4). I is assumed ha he ene gy RM is s o ed in he ene gy
gene a ion si es i necessa y. The ene gy gene a ion en e p ise SC p o ides ene gy o he
Local G id and o wo ex e nal ma ke s (Figu e 7). The SC o p oduc ion-dis ibu ion o he
polys y ene consis s o 3 manu ac u ing si es (pl1, pl2 and pl3) p oducing wo di e en
p oduc s (A and B) using 4 al e na i e esou ces: m1 and m2 o p oduce p oduc A, and m3
and m4 o p oduce p oduc B. They a e p o ided by 4 compe i i e supplie s (sup1, sup2,
sup3, and sup4) and he ene gy is ob ained om he Local G id. The inal p oduc s (A and B)
a e s o ed in 2 wa ehouses (w1 and w2) o be dis ibu ed la e o h ee polys y ene ma ke s
(m1, m2, and m3) (Figu e 8). P ices o bo h SCs ex e nal esou ces ollow a piecewise p icing
model, as in Hjaila e al. (2016) wi h an elas ici y’s p ice o demand o (-20) o he aw
ma e ials o he polys y ene p oduc ion-dis ibu ion SC, and (-25) o he aw ma e ials o he
ene gy gene a ion SC.
18
Figu e 7- Followe SC (SS)
Figu e 8- Leade SC (SS)
Table 1 and Table 2 lis he dis ances ha he polys y ene RMs a el h ough he leade SC,
and he polys y ene p oduc ion cos using he di e en RMs. Table 3 lis s he ene gy
gene a ion SC p oduc ion a io and cos (ene gy plan s).
Table 1- Dis ance supplie s/polys y ene p oduc ion plan s (km) (Re e ence: Hjaila e al., 2016)
Polys y ene
SC supplie
Dis ance o p oduc ion plan s
(km)
pl1
pl2
pl3
sup
1
100
150
145
sup
2
200
120
130
sup
3
110
70
80
sup
4
170
220
215
Table 2- Polys y ene p oduc ion uni cos s
Uni p oduc ion cos (€/kg)
P oduc
A
m1
0.64
m2
0.62
P oduc
B
m3
0.58
m4
0.53
Table 3- Ene gy gene a ion plan s p oduc ion a io and cos
P oduc ion a io
P oduc ion cos
g1-g3
g4-g6
g1-g3
g4-g6
b1
0.73
1.50
0.26
0.13
b2
2.00
2.60
0.20
0.14
b3
0.85
1.80
0.21
0.15
b4
0.80
2.00
0.23
0.14
The ene gy p ices and cos s o and om he local G id a e gi en in Table 4 aking in o
conside a ion he cha ac e is ics o he Spanish public elec ici y (Minis y o Indus y,
Ene gy and Tou ism, 2015). These p ices a y acco ding o he a i ype and a es in Spain.).
19
Table 4- Cu en ex e nal ene gy p ices
Ene gy p ice
(€/kWh)
Ene gy p ice o he ixed ene gy ma ke s
0.20
Ene gy p ice o Local G id (demand <2GWh)
0.21
Ene gy p ice o Local G id (2GWh<demand< 4GWh)
0.20
Ene gy p ice o Local G id (4GWh<demand < 6GWh)
0.19
Local G id ene gy p ice o ene gy ma ke s
0.22
Local G id ene gy p ice o Polys y ene SC (demand>2GWh)
0.22
Local G id ene gy p ice o Polys y ene SC (2GWh<demand<4GWh)
0.21
Local G id ene gy p ice o Polys y ene SC (4GWh<demand<8GWh)
0.20
Figu e 9- Decen alized SC ne wo k
5. Resul s and discussion
As a i s s ep, he MINLP ac ical models o bo h nego ia ing pa ne s a e op imized as
s andalone cases, so ha he s andalone (SS) indi idual p o i s a e ob ained. Then, o bo h
CNS and nCNS cases (see Figu e 9 Decen alized SC), he nego ia ion is held o iden i y he
in e nal ene gy lows (nego ia ion i em) o e he whole planning ime ho izon. The leade
may o e se e al p ices o he in e nal ene gy in his case a ying om 0.14 o 0.22 €/kWh
(con ac p ices
,'
con ac
sc
p
′
in he ma hema ical model). These p ices a e es ima ed based on he
elec ical ene gy p ice a ia ions in Spain du ing he las en yea s. The leade may also o e
lowe p ices, bu his would esul in he ejec ion o he con ac by he ollowe pa ne . So,
hese o e s depend on he knowledge ha he leade has abou he ollowe and he 3 d
pa ies p ice a ia ions (local G id pu chase p ices om he ollowe , local G id selling p ice
20
o ex e nal ma ke s, and he enewable ene gy p ice o he ex e nal ma ke s). Fo he CNS and
nCNS, he o al and indi idual expec ed p o i s a e ob ained o each ene gy p ice o e o be
conside ed.
The p oposed SBDN esul ed in he di e en MINLP models o he di e en p oposed
cases (S andalone - SS, Coope a i e Nego ia ion - CNS and Non-Coope a i e Nego ia ion -
nCNS). They ha e been implemen ed using he Gene al Algeb aic Modeling Sys em GAMS
24.2.3, and sol ed o e he planning ime ho izon (6 ime pe iods; 1000 wo king hou s each)
on a Windows 7 compu e wi h an In el® Co e™ i7-2600 CPU 3.40GHz p ocesso wi h 16.0 GB
o RAM, using he Global mixed-in ege quad a ic op imize “GloMIQO” (Misene & Floudas,
2013).
The models s a is ics show ha he nCNS ma hema ical o mula ion is less complex as
i allows o iden i y be e solu ions in less compu a ional e o s; 32% less han he SS and
63% less han he CNS scena ios, espec i ely (Table 5).
Table 5- Models s a is ics
Single
equa ions
Single
a iables
Disc e
a iables
CPU (sec)
S andalone Scena io (SS)
2,166
2,942
306
15.6
Coope a i e Nego ia ion Scena io (CNS)
2,165
2,926
306
31.6
Non-Coope a i e Nego ia ion Scena io (nCNS)
2,166
2,942
306
11.8
The ac ical decisions achie ed a e he expec ed RM acquisi ion, in e nal p oduc
lows and p ices (con ac e ms), and expec ed p oduc ion, in en o y, and dis ibu ion le els
o each pa ne .
In he nex subsec ions, he esul ing SC indi idual and global p o i s o each
coo dina ion con ac a e discussed, and he e ec s o he unce ain eac ion o he ollowe
on he ac ical decisions o he decen alized SC a e analyzed, as well as he e ec s o he
ollowe esponse on he leade SC ac ical and economic decisions.
5.1 Nego ia ion Scena ios
On he one hand, conside ing a de e minis ic si ua ion based on he cu en ma ke
ene gy p ices (Table 4), he o al and indi idual SC P o i s (nominal) esul ing om he
di e en leade coo dina ion con ac o e s a e ob ained (Figu es 10 & 11). The pu ple line
ep esen s he SC nominal p o i s ensuing om he leade SC (Figu e 10) and he Followe SC
(Figu e 11) s andalone scena ios (SS); so he nego ia ion only makes sense when he p o i s
exceed hese lines. F om he leade side (Figu e 10), i seems ha he nCNS leads o be e
solu ions han he CNS a all nego ia ion p ices o e s, al hough he CNS leads o highe o e all
p o i s (Figu e 12).
21
Figu e 10- Leade SC nominal p o i s. nego ia ion p ice
F om he ollowe side, i is no iced ha o nego ia ion p ices abo e 0.17 €/kWh he
CNS would lead o be e p o i s (Figu e 12), i he isks associa ed wi h i s SC unce ain
ex e nal condi ions a e no conside ed.
Figu e 11- Followe SC P o i s. nego ia ion p ice
Figu e 12- O e all SC P o i
5.2 Mon e-Ca lo sampling
The use o Mon e-Ca lo sampling as pa o he op imiza ion p ocedu e is a p ac ical
way o educe he complexi y o he model o mula ion, by conside ing a se o ealiza ions o
he unce ain a iables as ep esen a i e o he global sys em beha iou . I helps in ob aining
he p obabili y o accep ance o he di e en o e s, he p obabili y dis ibu ion o expec ed
p o i s and he cumula i e p obabili y cu es. In his case, in o de o ob ain he p obabili y o
accep ance o each o he di e en con ac o e s ( lows and p ices), he p oposed MINLP

22
ac ical model o he ollowe is sol ed o each con ac o e a he di e en gene a ed
scena ios, in o de o ob ain each one emula ing a ealiza ion o he ex e nal ene gy p ices o
he 3 d pa ies a ound he ollowe SC as ollows (Figu e 13). Each scena io includes speci ic
andom alues o :
(a) he local G id ene gy p ice o he ex e nal ma ke s (Figu e 13a),
(b) he enewable ene gy p ice om he ollowe o local G id a p ice zone 1 (Figu e 13b),
(c) he enewable ene gy p ice om he ollowe o local G id a p ice zone 2 (Figu e 13c),
(d) he enewable ene gy p ice om he ollowe o local G id a p ice zone 3 (Figu e 13d),
(e) he enewable ene gy p ice om he ollowe o he ex e nal ma ke s (Figu e 13e).
a)
b)
c)
d)
23
e)
Figu e 13- Ene gy p ices gene a ion (Mon e-Ca lo)
Fo simplici y, he gene a ion o p ice scena ios is based on a no mal dis ibu ion. The
s anda d de ia ion o p ices gene a ed (σ) is assumed o be 0.03 € / kWh o all p ice anges,
while he a e age (μ) o each p ice gene a ion is equal o i s cu en nominal p ice, as shown
in Table 4. Indeed, a co ela ion be ween hese p ices is assumed, so ha o he i s p ice (a:
local g id o ex e nal ma ke s) a no mal dis ibu ion is gene a ed (Figu e 13a), and hen he
emainde dis ibu ions a e gene a ed assuming a signi ican co ela ion wi h his i s one.
The a ia ions in hese p ice p edic ions a e jus i ied by he ola ile changes in he
ene gy p ices, so hei compu a ion should be based on he pe cep ion o he ma ke ola ili y
by he leade decision make . The alues assumed in his wo k a e based on he pe cep ion o
he ene gy p ice ola ili y in he Spanish ma ke by he au ho s; ob iously his pe cep ion
signi ican ly a ec s he speci ic esul s ob ained in he p esen ed case s udy, al hough his
does no comp omise he use ulness o he p esen ed me hodology: om he di e en
gene a ed scena ios, he co esponding eac ions om he ollowe can be an icipa ed.
5.3 Coo dina ion Con ac
In he nCNS nego ia ion scena io, he leade would design he inal coo dina ion
con ac conside ing he unce ain eac ion o he ollowe in o de o es ima e i s SC
expec ed bene i s. Then he esul s will be analyzed om bo h leade and ollowe sides.
5.3.1 The leade o e
The leade es ima es i s expec ed SC bene i s a each nego ia ion p ice, based on he
ollowe p obabili y o accep ance alues. To calcula e he p obabili y o accep ance a each
nego ia ion p ice, he ollowe nCNS model is sol ed o he 500 gene a ed scena ios, and he
numbe o a o able scena ios is ob ained ( he expec ed bene i s ha exceed he S andalone
SS expec ed bene i s). Then he p obabili y o accep ance (Eq. 19) is calcula ed o each
nego ia ion p ice (Table 6). I is no iced ha he p obabili y o accep ance is ze o i he o e ed
con ac p ices a e in he ange (0.14-0.16 €/kWh), while i inc eases om o e s abo e (0.17
24
€/kWh), ill eaching he highes alue (100 %) a con ac p ice 0.22 €/kWh (see also Figu e
11).
Table 6- P obabili y o accep ance
0.14
0.15
0.16
0.17
0.18
0.19
0.2
0.21
0.22
No o scena ios whe e he
ollowe ob ains imp o ed
P o i (con ac s. SS)
0
0
0
89
314
393
440
477
498
P obabili y o Accep ance
0
0
0
0.18
0.63
0.79
0.88
0.95
1.00
Based on hese p obabili ies o accep ance, he leade assesses i s SC expec ed bene i s
(Eq. 20) conside ing i s SC bene i s in case ha he ollowe accep s o ejec s each con ac
o e (Table 7 and Figu e 14). Figu e 14 shows he leade p oduc ion-dis ibu ion SC expec ed
bene i s s. he p obabili y o accep ance. I can be no iced ha 24.71 GWh o o al ene gy is
needed o he leade SC p oduc ion in o de o ul ill he inal ma ke s demands. F om Table
7, i is demons a ed ha is be e o he leade o pu chase his amoun om he ollowe a
all con ac p ices, excep a 0.22 €/kWh, whe e is be e o he leade o pu chase a la ge
pa om he Local G id (21.96 GWh) a lowe p ice, be ween 0.20 and 0.22 €/kWh (see Table
4).
Table 7- Coo dina ion con ac s and Leade expec ed bene i s
Con ac
p ice
(€/kWh)
In e nal
ene gy
(GWh)
Ene gy
om G id
(GWh)
P o i i he
ollowe
accep s (M€)
P o i i he
ollowe
ejec s (M€)
P obabili y
o
accep ance
Expec ed
p o i
(M€)
0.14
24.71
0
9.25
7.47
0
7.47
0.15
24.71
0
8.99
7.47
0
7.47
0.16
24.71
0
8.74
7.47
0
7.47
0.17
24.71
0
8.48
7.47
0.18
7.65
0.18
24.71
0
8.23
7.47
0.63
7.95
0.19
24.71
0
7.99
7.47
0.79
7.88
0.20
24.71
0
7.77
7.47
0.88
7.74
0.21
24.71
0
7.51
7.47
0.95
7.50
0.22
2.75
21.96
7.47
7.47
1.00
7.47
25
Figu e 14- Leade expec ed P o i s s. P obabili y o accep ance
I is wo h o emphasize he impo ance o he G id ene gy p ice-quan i y cons ain s.
Fo example, he Local G id is o e ing he leade 0.20 €/kWh jus when he ene gy demand
exceeds 4GWh each planning ime pe iod, bu i migh be wo h o he Leade o main ain i s
con ac wi h he ollowe , as i is mo e e iden om Table 8, whe e he schedule o ene gy
pu chase le els om he ollowe (in case i accep s) along he planning ime ho izon is
explici . Then, pu chasing 24.71 GWh om he ollowe a he p ice o 0.21€/kWh cos s he
leade 5.19 M€, bu i he leade pu chases hese amoun s om he Local G id, his will imply
a cos o 5.38 M€.
Table 8- In e nal ene gy pu chase le els a p ice 0.21 €/kWh
1
2
3
4
5
6
P1
1.47
1.47
1.59
1.47
0.75
1.47
P2
2.56
1.53
2.56
1.53
0.95
1.31
P3
1.53
0.67
1.53
0.67
0.67
0.98
I is wo h no icing ha he coo dina ion con ac o e ed by he leade esul s om
he an icipa ion o he ollowe ’s esponse, which in u n depends on he quali y o he
knowledge he/she has abou he o he pa icipan s, 3 d pa ies included, and he way how
she/he p edic s he ma ke p ices. Wi hin he con ex o he p esen ed case-s udy, he leade ’s
expec ed p o i (whe e he ollowe 's unce ain eac ion is p ojec ed) is conside ed as he key
e e ence o selec ing he coo dina ion con ac . The leade 's decision-making may ha e
di e en c i e ia ha can lead o di e en decisions. He e, we will analyze h ee op ions
acco ding o he SBDN c i e ia, which depend on he isk-beha iou o he decision-make .
F om Table 7 i esul s ha , i he leade o e s he lowes p ices 0.14-0.16 €/kWh,
she/he would ace a 0 % p obabili y o accep ance esul ing om he high equency o
nega i e p o i scena ios. This means ha he leade should no choose hese p ices al hough
he po en ial bene i s a e highe .
Howe e , an op ion wi h a e y high p obabili y o accep ance by he ollowe is no
always he sma es decision o he leade , since he coo dina ion migh be e en unp o i able
as he p ice o be paid o he ollowe is e y high, e en highe han he one o e ed by he
local elec ici y g id (so leade SC should e u n o i s s andalone case). Fo example, o he
32
cases (3,450 ons) and he o al p oduc ion is also he same (3,380 ons), as he leade
decision is o ul ill he o al polys y ene ma ke demands. I is no iced ha using he isk-
neu al nCNS coo dina ion con ac esul s in 7% imp o emen s in he o al in en o y, in
compa ison wi h he SS case, while leading o 5 % inc ease in he o al dis ibu ion le els, o
he same easons explained be o e.
Table 12- Leade ac ical decisions-b eakdown ( isk-neu al)
nCNS
SS
RM pu chase ( ons)
3,449.75
3,449.75
Ene gy om G id (GWh)
0
24.71
In e nal Ene gy (GWh)
24.71
0
P oduc ion ( ons)
3,380.40
3,380.40
Dis ibu ion (k. ons.km)
1,332.07
1,271.50
In en o y ( ons.h)
495.00
530.18
Figu e 21 illus a es he economic decisions b eakdown o he leade in case o using he isk-
neu al s a egy. Using he nCNS isk-neu al s a egy leads o 17% imp o emen s in he o al
ene gy pu chase cos (0.75 M€ sa ings); 1 % imp o emen s in he RM pu chase cos (25.72
k€ sa ings); and 2 % imp o emen s in he o al polys y ene p oduc ion cos (42.24 k€), when
compa ed wi h i s S andalone SS case.
Figu e 21- Leade economic decisions ( isk-neu al)
Table 13 summa izes he inal economic decisions o he leade in case o using he
isk-neu al s a egy, in compa ison wi h i s SC s andalone case (SS). Conside ing ha he
decision in bo h cases is o ul ill he inal ma ke demands, i esul s in 18.59 M€ o al sales,
wi h 10 % imp o emen s in he leade SC bene i s.
Table 13- Leade SC economic summa y ( isk-neu al)
nCNS
SS
Cos (M€)
10.36
11.12
Sales (M€)
18.59
18.59
P o i (M€)
8.23
7.47
5.4.3 Leade isk-a e se s a egy

33
Table 14 summa izes he ac ical decisions o he leade in case o deciding o a oid
isk (coo dina ion con ac : 24.71 GWh a 0.19€/kWh), compa ed wi h i s SC s andalone case.
I is o be no iced ha using he isk-a e se nCNS coo dina ion con ac esul s in an
imp o emen o 13 % in he o al in en o y le els, while leading o 4.3 % inc ease in he o al
dis ibu ion le els, in compa ison wi h he SS case.
Table 14- Leade ac ical decisions-b eakdown ( isk-a e se)
nCNS
SS
RM pu chase ( ons)
3,449.75
3,449.75
Ene gy om G id (GWh)
0
24.71
In e nal Ene gy (GWh)
24.71
0
P oduc ion ( ons)
3,380.40
3,380.40
Dis ibu ion (k. ons.km)
1,328.19
1,271.50
In en o y ( ons.h)
468.90
530.18
Figu e 22 illus a es he economic decisions o he leade in case o using he isk-a e se
s a egy, leading o 11% imp o emen s in he o al ene gy pu chase cos (0.51 M€ sa ings); 1
% in he RM pu chase cos (26.79 k€ sa ings); and 2 % in he o al p oduc ion cos (40.71
k€), when compa ed wi h i s SC s andalone case.
Figu e 22- Leade ac ical decisions ( isk-a e se)
Table 15 summa izes he inal economic decisions o he leade in case o using he
isk-a e se s a egy, compa ed wi h i s SC s andalone case (SS), esul ing in 7 %
imp o emen s in he leade SC bene i s.
Table 15- Leade SC economic summa y ( isk-a e se)
nCNS
SS
Cos (M€)
10.61
11.12
Sales (M€)
18.59
18.59
P o i (M€)
7.99
7.47
5.5 Followe expec ed ac ical decisions
34
The expec ed ac ical decisions o he ollowe a e analyzed nex based on he 500
gene a ed scena ios a he nCNS, in compa ison wi h i s SC s andalone case. Figu e 23 shows
he expec ed ene gy lows a ound he ollowe SC a i s s andalone case.
Figu e 23- Expec ed ene gy lows (SS)
The ollowe expec ed ac ical decisions hen will be analyzed o each isk- esponse
he ollowe could make, compa ing wi h i s abo e-men ioned s andalone case.
5.5.1 Followe isk-seeking esponse
In case he ollowe accep s he leade isk-seeking s a egy (coo dina ion con ac :
24.71GWh a 0.17€/kWh), he ollowe SC is expec ed ha will gene a e 15 % mo e ene gy in
o de o be able o sell he 24.71 GWh o he leade SC (Figu e 24), leading o 18% educ ions
in he expec ed ene gy sales o Local G id, and 20 % educ ions in he expec ed o al sales o
he ex e nal ene gy ma ke s, in compa ison wi h i s expec ed s andalone case. He e, one may
say ha he ollowe should sell mo e ene gy o he G id in o de o compensa e, bu in ac ,
i s expec ed SC o al cos is also inc easing. Gene a ing hose 15 % ex a ene gy leads o 14 %
inc ease in i s expec ed SC o al cos , in compa ison wi h i s expec ed s andalone case
(di e ence o 2.21 M€), whe eas he con ac p ice is s ill low o compensa e he sales o he
ollowe .
35
Figu e 24- Expec ed ene gy lows ( isk-seeking)
Figu e 25 shows he expec ed ene gy gene a ion le els along he planning ime
ho izon esul ing om accep ing he leade isk-seeking s a egy (Figu e 25a), compa ed wi h
ejec ing i (Figu e 25b). I is no iced ha he expec ed ene gy gene a ion is dis ibu ed
equally be ween he ene gy gene a ion plan s (g4, g5, and g6) wi h 15 GWh ene gy
gene a ion pe ime pe iod using he isk-seeking s a egy (nCNS); 15 % highe han he
s andalone case (Figu e 25b), in o de o sell he high amoun o ene gy needed by he leade
(24.71 GWh). The es is o be educed om he ene gy sales o he G id and o he ex e nal
ene gy ma ke s. I is wo h men ioning ha each ene gy gene a ion plan has a capaci y o
6GWh, bu in his case, he expec ed cos o ope a ing up o hei ull capaci y does no
compensa e he ollowe . This akes in o conside a ion ha gene a ing he ene gy plan s (g1,
g2, and g3) is expensi e o he ollowe , due o hei lowe e iciency (see Table 3). This
s a egy leads o an 18 % highe o he expec ed RM pu chase amoun s, in compa ison wi h
he expec ed s andalone case.
Figu e 25- Expec ed ene gy gene a ion le els ( isk-seeking)
a) nCNS b) SS
Figu e 26 summa izes he ollowe expec ed economic decisions acco ding o he
leade isk-seeking s a egy, in compa ison wi h i s expec ed s andalone decisions. I is
no iced ha he coo dina ion con ac (24.71GWh a 0.17 €/kWh) leads o 14 % inc ease in
36
he expec ed ene gy gene a ion cos , esul ing in 16 % inc ease in he expec ed RM pu chase
cos , and consequen ly o 17% dec ease in he expec ed ene gy sales o he G id; and 17 %
dec ease in he expec ed ene gy sales o he ex e nal ma ke s, compa ed wi h i s expec ed
s andalone case.
Figu e 26- Followe expec ed ac ical decisions ( isk-seeking)
Table 16 summa izes he ollowe inal expec ed economic decisions in case o
accep ing he leade isk-seeking s a egy, in compa ison wi h i s expec ed s andalone case
(SS). Conside ing all he expec ed bene i s esul ed om he 500 isk scena ios (posi i e and
nega i e cases), he p oposed coo dina ion con ac esul s in 10 % educ ions in he ollowe
o al expec ed p o i . Howe e , as we men ioned be o e, he ollowe would isk and accep
based on he 22 % expec ed p o i s imp o emen s esul ing om he 18 % imp o ed
p obabili ies.
Table 16- Followe expec ed economic summa y ( isk-seeking)
NCNS
SS
Cos (M€)
15.38
13.16
Sales (M€)
17.83
15.90
P o i (M€)
2.46
2.74
5.5.2 Followe isk-neu al esponse
I is expec ed ha he ollowe SC will gene a e 15 % mo e ene gy han he SS (Figu e
29) in o de o sell he 24.71 GWh o he leade . 63 % o he o al ene gy gene a ion is
expec ed o be sold o he Local G id, while he es is expec ed o be sold o he leade SC (27
%) and o he ex e nal ene gy ma ke s (10 %). This leads o 15 % inc ease in he expec ed SC
cos (Figu e 27 and Figu e 28), in compa ison wi h s andalone case.
37
Figu e 27- Expec ed ene gy lows ( isk-neu al)
Figu e 28 summa izes he ollowe 's expec ed economic decisions acco ding o he
leade 's isk-neu al s a egy, compa ed wi h he s andalone case. The coo dina ion con ac ,
esul s in a 14 % inc ease in he expec ed ene gy gene a ion cos , ensuing in a 16 % inc ease
in he expec ed RM pu chase cos , and 16 % dec ease in he expec ed ene gy sales o he G id,
as well an 18 % dec ease in he expec ed ene gy sales o he ex e nal ma ke s, compa ed wi h
i s expec ed s andalone decisions.
Figu e 28- Followe expec ed economic decisions ( isk-neu al)
Table 17 summa izes he inal expec ed economic decisions o he ollowe in case o
accep ing he leade isk-neu al s a egy, in compa ison wi h i s expec ed s andalone case.
Conside ing all isk scena ios ( he imp o ed 63% and he 37% nega i e cases), he p oposed
coo dina ion con ac gi es simila o al expec ed p o i s as he expec ed s andalone case.
Ne e heless, as we men ioned be o e, he ollowe would accep , based on he 12 % expec ed
p o i imp o emen esul ing om he 63 % imp o ed p obabili y.
Table 17- Followe expec ed economic summa y ( isk-neu al)
NCNS
SS
Cos (M€)
15.42
13.16

38
Sales (M€)
18.13
15.90
P o i (M€)
2.71
2.74
5.5.3 Followe isk-a e se esponse
In his case, he ollowe SC is expec ed o gene a e 15% mo e ene gy han he SS
(Figu e 29), 62 % o he o al ene gy gene a ion is expec ed o be sold o he Local G id, while
he es is expec ed o be sold o he leade SC (28 %) and o he ex e nal ene gy ma ke s (10
%).
Figu e 29- Expec ed ene gy lows ( isk-a e se)
Figu e 30 summa izes he ollowe expec ed economic decisions acco ding o he
leade 's isk-a e se s a egy, compa ed wi h he expec ed s andalone decisions. The
coo dina ion con ac esul s in 16 % inc ease in he expec ed RM pu chase cos , and
acco dingly o 14 % inc ease in he expec ed o al SC cos (Table 18).
Figu e 30- Followe expec ed economic decisions ( isk-a e se)
Table 18 summa izes he inal expec ed economic decisions o he ollowe in case o
accep ing he leade 's isk-a e se s a egy, in compa ison wi h he expec ed s andalone case.
Conside ing all isk scena ios ( he imp o ed 79% and he 21 % nega i e cases), he
coo dina ion con ac p oposed esul s in an 8 % p o i imp o emen (0.21 M€), compa ed
39
wi h he expec ed s andalone bene i s. Fu he mo e, he ollowe would accep based on he
19 % expec ed p o i imp o emen , esul ing om he 79 % imp o ed p obabili y.
Table 18- Followe expec ed economic summa y ( isk-a e se)
nCNS
SS
Cos (M€)
15.38
13.16
Sales (M€)
18.33
15.90
P o i (M€)
2.95
2.74
As a inal esul , unlike he cu en nego ia ion me hods, and o be able o cap u e high
compe i i e si ua ions (ex e nal supplie s/ma ke s), he p oposed SBDN app oach does no
gi e a ull dominance o he leade , indeed, he ollowe has some “embedded” leade ship,
esul ing in educ ions in he expec ed leade bene i s. Fu he mo e, he unce ain na u e o
he hi d pa ies a ec s he ollowe 's eac ion o he leade s a egies, and hus plays a
impo an ole in he decision-making o decen alized SC and in he nego ia ion ou come.
6. Conclusions
Due o he ola ili y o he ma ke , en e p ises seek o change hei way in managing hei SCs
by collabo a ing wi h o he pa ne SCs in o de o enhance hei bene i s. In his amewo k,
and in o de o a oid double ma ginaliza ion o he ma ke s, a con ac is a mus ; and since
any con ac is be ween wo o ganiza ions, he o he pa icipan s in he decen alized SC
sys ems mus be conside ed as hi d pa ies. So in his wo k, a no el Scena io-Based Dynamic
Nego ia ion (SBDN) app oach has been p oposed in his wo k aiming o help he SC manage s
o make e icien decisions o global decen alized mul i-si e, mul i-p oduc SCs subjec ed o
unce ain compe i i e condi ions in he p esence o hi d pa ne s.
The p oposed app oach is based on es ablishing he bes condi ions o he
coo dina ion/collabo a ion con ac s be ween pa ne s wi h con lic ing objec i es h ough
nego ia ions buil on expec ed win- o-win p inciples. The in e ac ion be ween he pa ne s
(clien and p o ide , bo h ep esen ed as ull SCs, and hi d pa ies) is cap u ed h ough non-
coope a i e dynamic SBDN nego ia ion wi h non-ze o-sum non-symme ic oles. The clien ,
“as leade ”, designs a se o o e s (coo dina ion/collabo a ion con ac s) aking in o accoun
he unce ain eac ion o he p o ide (“ ollowe ”) esul ing om he unce ain na u e o he
ollowe SC beha io and i s hi d pa ies, which is modeled as a p obabili y o accep ance.
He e, he p obabili y o accep ance is able o cap u e he a ia ions be ween he p o i s
scena ios esul ed om a Mon e-Ca lo simula ion me hod.
As a esul , di e en nego ia ion scena ios can be analyzed based on indi idual and global
objec i es: i) Coope a i e Nego ia ion Scena io (CNS), and ii) Non-Coope a i e Nego ia ion
Scena io (nCNS), and iii) S andalone Scena io (SS). Fu he mo e, a inal decision-making
me hodology is p oposed o help bo h he leade and he ollowe o e alua e he inal
coo dina ion con ac , based on di e en isk s a egies ( isk-seeking, isk-neu al, and isk-
a e se).
40
The p oposed app oach has been implemen ed h ough he o mula ion and combina ion o
di e en ac ical MINLP lexible models, which ha e been applied o a case s udy o a
decen alized la ge-scale SC composed by di e en p o ide s’ SCs a ound an indus ial
p oduc ion/dis ibu ion SC (“leade ”). The esul s show how he unce ain na u e o he hi d
pa ies is expec ed o a ec he ollowe eac ion o he leade s a egies, and hus a ec s he
ac ical decisions o he leade as well as he expec ed ac ical eac ions o he ollowe . Using
he p oposed SBDN app oach, i is possible o manage non-Coope a i e Nego ia ion Scena ios
(nCNS) in o de o iden i y and manage high indi idual p o i expec a ions likely o be
accep ed by all pa ne s/playe s.
The hi d pa ies pa icipa e in he decision-making h ough hei p ice policies, in luencing
he managemen o he SC inancial lows and helping o s ay compe i i e. Fu he mo e, he
hi d pa ies (ex e nal p o ide s/clien s) a e compe ing wi h o he nego ia ing pa ne s
which migh be pa o a di e en SC unc ioning as s andalone case. This lexibili y o
accep / ejec he coo dina ion, which coun s as added alue o he p oposed app oach, is
based on he es ima ion o he p ice policies o he compe ing pa ies, which a e in eg a ed
in o he model o mula ion. By doing so, equilib ium si ua ions esul be ween he nego ia ing
pa ne s and he 3 d pa ies. The cha ac e is ics o his equilib ium will be u he
in es iga ed in he u u e wo ks.
The p oposed app oach iden i ies si ua ions whe e he coo dina ion may lead o highe
expec ed bene i s o all pa ne s, p oposing a lexible p ocedu e able o cope wi h he
di e en isk beha iou s o he decision make s, which can be applied o eal cases when
di e en en e p ises seek o collabo a e unde unce ain condi ions. Using he p oposed
SBDN sys ema ic, he decision-make s will be able o e alua e he e ec s o hei decisions
and he o he pa ne s’ decisions on hei choice. The use o Mon e-Ca lo sampling me hod
adds alue o he p oposed app oach, as bo h leade and ollowe a e able o assess hei
decisions based on me hodically gene a ed da a and, unlike o he PSE li e a u e app oaches,
aking in o conside a ion he a iabili y be ween gene a ed p o i s scena ios.
Finally, he p oposed decision suppo p ocedu es enable he decen alized SCs o ganiza ions
o modi y hei ela ionships du ing he op imiza ion p ocedu e, which can be used o
u he second-s age ag eemen s. Fu he mo e, he p oposed gene ic models a e lexible
enough o be applied in p ac ice o eal cases, including simple/global SCs
cen alized/decen alized, as illus a ed in he p esen ed case s udy.
Acknowledgemen
Financial suppo ecei ed om he “Agència de Ges ió d'Aju s Uni e si a is i de Rece ca
AGAUR”, he Spanish Minis y o Economy and Compe i i eness and he Eu opean Regional
De elopmen Fund, bo h unding he P ojec SIGERA (DPI2012-37154-C02-01), and om he
Gene ali a de Ca alunya (2014-SGR-1092-CEPEiMA), is ully app ecia ed.
41
Ac onyms
CNS
Coope a i e-Nego ia ion Scena io
CPU
Cen al P ocessing Uni
EWO
En e p ise-Wide Op imiza ion
GAMS
The Gene al Algeb aic Modeling Sys em
GHz
Gigahe z
GloMIQO
Global Mixed-In ege Quad a ic Op imize
GT
Game Theo y
LP
Linea P og amming
MINLP
Mixed In ege Non-Linea P og amming
MILP
Mixed In ege Linea P og amming
MW
Megawa
nCNS
Non-Coope a i e-Nego ia ion Scena io
NE
Nash Equilib ium
NLP
Non-Linea P og amming
PMAGA
Pinch Mul i-Agen Gene ic Algo i hm
PSE
P ocess Sys em Enginee ing
RM
Raw Ma e ial
SBDN
Scena io-Based Dynamic Nego ia ions
SC
Supply Chain
SCM
Supply Chain Managemen
SS
S andalone Scena io
µ
Mean
σ
S anda d de ia ion
Nomencla u e
Indexes
D
3
d
pa y
M
Final cus ome s
N
numbe o Piecewise p ice and quan i y zones o 3
d
pa ies
PL
P oduc ion plan
R
esou ce ( aw ma e ials, in e media e/ inal p oduc s, ene gy,…)
SC
supply chain
T
ime pe iod
W
wa ehouse
Se s
F
ollowe SC
L
leade SC
m
inal consume s
n
piecewise p icing zone o 3
d
pa ies