Molinè, Joan Ignasi; Co es, Anna Ma ia
A icle
O de alloca ion in a mul i-supplie en i onmen : Re iew
o he li e a u e since 2007
Jou nal o Indus ial Enginee ing and Managemen (JIEM)
P o ided in Coope a ion wi h:
The School o Indus ial, Ae ospace and Audio isual Enginee ing o Te assa (ESEIAAT), Uni e si a
Poli ècnica de Ca alunya (UPC)
Sugges ed Ci a ion: Molinè, Joan Ignasi; Co es, Anna Ma ia (2013) : O de alloca ion in a mul i-
supplie en i onmen : Re iew o he li e a u e since 2007, Jou nal o Indus ial Enginee ing and
Managemen (JIEM), ISSN 2013-0953, OmniaScience, Ba celona, Vol. 6, Iss. 3, pp. 751-760,
h ps://doi.o g/10.3926/jiem.556
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Jou nal o Indus ial Enginee ing and Managemen
JIEM, 2013 – 6(3): 751-760 – Online ISSN: 2013-0953 – P in ISSN: 2013-8423
h p://dx.doi.o g/10.3926/jiem.556
O de alloca ion in a mul i-supplie en i onmen : Re iew o he
li e a u e since 2007
Joan Ignasi Molinè, Anna Ma ia Co es
Uni e si a Poli ècnica de Ca alunya (Spain)
[email p o ec ed], ann[email p o ec ed]
Recei ed: Sep embe 2012
Accep ed: Ma ch 2013
Abs ac :
Pu pose:
Op imal o de alloca ion on he pa o he buye in a mul i-supplie en i onmen has
become a majo conce n in supply chains. The e a e nume ous a icles ha analyze and p esen
models o op imizing o de alloca ion om a gi en panel o supplie s. The pu pose o his
pape is o p o ide an analysis on his opic which conside s: (i) aims, (ii) esul s, (iii) model
complexi y, and (i ) esolu ion p ocedu es.
Design/me hodology/app oach:
The pape e iews wen y-eigh a icles, wen y-one o hem
published since 2007 in jou nals indexed by Jou nal Ci a ion Repo s (in ISI Web o
Knowledge) on his opic.
Findings:
This e iew e eals ou main aspec s men ioned as de e minan in gene a ing
ma hema ical models. The analysis o hese ou poin s does no allow o a single, o e a ching
model. Ra he , all analyzed solu ions e lec and espond o a speci ic company en i onmen .
O iginali y/ alue:
A global analysis on se e al ecen pape s, desc ibing main aspec s wich
de e mines op imal o de alloca ion in mul i-supplie en i onmen .
Keywo ds:
o de alloca ion, supplie s, ma hema ical models
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1. In oduc ion
Op imal o de alloca ion by a pu chase in a mul i-supplie en i onmen has become ex emely
impo an in cu en supply chains. In gene al, o de pu chasing managemen has h ee
p incipal aims: educe acquisi ion cos s, insu e deli e y punc uali y and ensu e quali y
equi emen s on he pa o he supplie s. These aims mus be aligned wi h and insc ibed
wi hin a company’s s a egic amewo k, as well as inco po a ing and de eloping pu chasing
capabili ies (Gonzalez-Beni o, 2007). Pu chasing managemen aims a e especially impo an in
indus ial goods p oduc ion se ings in ol ing on-going p oduc o de alloca ion, whe e p ope
managemen con ibu es o dec ease company cos s.
The in luence o acqui ed p oduc s and se ices (pu chases) on manu ac u ing companies’ cos
s uc u e is highly a iable, and all cases, signi ican . In au omobile manu ac u e s,
p ocu emen cons i u es 68-79% (ICEX, 2009; Palla és, 1997) o manu ac u ing cos s, while in
he chemicals indus y, depending on he sec o , p ocu emen ep esen s be ween 42% and
71% o p oduc ion cos s (FEIQUE, 2008). Gi en his cos s uc u e con igu a ion, de ining
ac ions ha educe pu chasing cos s is s a egically signi ican as such ac ions will ha e a
di ec impac on inc easing p o i s.
Fo hese easons, pu chasing managemen has a di ec e ec on company esul s, such as
one o i s p incipal aims will be minimiza ion o p ocu emen cos s (acqui ed
p oduc s/se ices). To achie e his, di e en s a egies may be de eloped, one o he mos
impo an being op imal o de alloca ion om he panel o supplie s. Op imal o de alloca ion
will be condi ioned by (among o he ac o s) exis ing supplie s panel p e iously chosen
h ough assessmen and homologa ion by he pu chasing company.
The desc ibed scena io mo i a es his a icle, which e iews wen y-one a icles published in
jou nals indexed by Jou nal Ci a ion Repo s (in ISI Web o Knowledge), be ween 2007 and he
p esen . The a icles analysed he e look a op imal o de alloca ion om a panel o supplie s in
which he e is a single pu chase and N supplie s. This s a e o he a does no include a
p e ious assessmen and homologa ion o supplie .
The ollowing sec ion includes an analysis o hose aspec s ha his e iew has e ealed as
de e minan in gene a ing ma hema ical models. Finally, in sec ion 3, on he basis o his
e iew o he s a e o he a , conclusions a e d awn.
2. Analysis o S a e o he A (since 2007)
In his p esen s a e o he a , we analyze ou main aspec s; (a) Aims, (b) esul s ( a iables),
(c) model complexi y and (d) ype o esolu ion p ocedu e u ilized.
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2.1. Aims
The mos common objec i e unc ion is cos minimiza ion (9 cases, 42.9%). The e a e also
models ha conside p o i maximiza ion (4 cases, 19%) and o he eigh cases (38.1%) whe e
a mul i-objec i e model has been de eloped.
Mul i-objec i e models oscilla e be ween wo and ou objec i e unc ions. In gene al, one o
hese unc ions is pu chasing cos minimiza ion. The o he unc ions a y, wi h he mos
no ewo hy being maximiza ion o pu chasing alue and minimiza ion o : de ec s, and la e
deli e ies.
Despi e he ac his s a e o he a only co e s o de alloca ion, i wo h men ioning ha six
(28.6%) o he a icles in eg a e he assessmen and supplie selec ion phases wi h o de
alloca ion.
2.2. Resul s
In gene al, he pu chase has a need (demand) o Q uni s, and assigns o he supplie s a
quan i y qi ( o each supplie i), such ha ∑ qi = Q.
The common decision o all he a icles (21 cases, 100%) a e he quan i ies pu chased om
each supplie ha may be accompanied by o he a iables: ime be ween o de s, p ocu emen
poin , s ock le els, quan i y o inal p oduc o be p oduced, e c. I mus be s essed ha a
he same ime ha o de alloca ion o panel supplie s is being unde aken, some a icles
conside ha supplie selec ion is also aking place, as he e may be supplie s ha will ill ze o
o de s.
2.3. Model Complexi y
Ma hema ical models a e made up o one o se e al objec i e unc ions and a se o
es ic ions. The g ea e he numbe o pa ame e s inco po a ed in he objec i e unc ions, and
he mo e aspec s o he pu chase ’s en i onmen e lec ed in he es ic ions, he mo e
comple e and complica ed (complex). Complexi y is mainly de e mined by wo axes (Table 1):
•Dep h: his axis shows he numbe o s ages in he supply chain p esen ed in he
model. The mo e s ages included in he supply chain, he mo e comple e and complex
he model.
•Cha ac e is ics: Range o cos s and company en i onmen pa ame e s in oduced.
These depend on he pa icula cha ac e is ics o he company, he sec o i belongs o,
and he decisions made by he pu chasing depa men (single-pe iod s. Mul i-pe iod,
andomness…). The model will be mo e o less complex depending on he deg ee o
which hese ac o s a e inco po a ed in o i .
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Table 1 syn hesizes he wo abo e men ioned axes, such ha he uppe ow designa es he
s ages o he supply chain, and o each o he s ages in he co esponding column, he
cha ac e is ics ha can be inco po a ed a e desc ibed. Cha ac e is ics a e subdi ided in o wo
ca ego ies: Cos s and Company en i onmen , in which all he cos s and ac o s speci ic o each
s age (in he supply chain) a e de ailed, as well as hose ac o s ha a ec all s ages in he
supply chain.
The dep h axis is designed o e lec he a icles analysed in he s udy. Fo his eason he
s ages in he supply chain a e no enume a ed. S ages such as ecep ion logis ics, s o age
o wa ding, and shipping logis ics a e no speci ied, and whose company en i onmen ac o s
and/o cos s ha e been included in columns: Pu chases and Demand. In he same way, wi h
igo , he concep “Quali y” should be gene al o all s ages and include a wide ange o
ac o s in each s age, which one can obse e how quali y has been inco po a ed as a
p e ious s age o ha o P oduc ion. This is because in he analysed a icles, quali y is linked
o echnical use ulness (o no ) o he pu chased p oduc s. Aspec s ha a e a quali y
pa ame e , such as deli e y ime, a e included in o he s ages, such as Pu chases. Finally, i
is impo an o s ess ha he P oduc ion s age is complex, in ol ing many company
en i onmen ac o s and cos s. The analysed a icles ha include he p oduc ion s age
g ea ly simpli y i . Fo his eason, he P oduc ion s age only e lec s ac o s and cos s
desc ibed in hose analysed a icles.
Dep h
Pu chasing
Wa ehouse
ecep ion Quali y P oduc ion Demand
Cha ac e is ics
Cos s
•P ocu emen cos s.
•A ailable discoun s.
•O de ing cos s.
•T anspo a ion cos s.
•Managemen cos s.
•Raw
ma e ial
holding
cos s.
•Recep ion
cos s.
•Selec ion
cos s 100%.
•Raw
ma e ial
ans o ma i
on cos s.
•Finished p oduc
holding cos s.
•Sho age cos s.
•Sales p ice o pieces.
•Sales p ice o
de ec i e pieces
Company en i onmen
•N supplie s.
•Single p oduc s mul iple
p oduc s.
•Supplie p oduc ion capaci y.
•P io i iza ion o supplie s
(mínimum o de , weigh
assignemen , maximum o
minimum numbe o
supplie s.
•Budge a ailable.
•Supplie deli e y ime.
•Reo de poin .
•Supplie unce ain y
(quan i y and deli e y ime).
•P esence o 3PL.
•S o age
space o
each a icle.
•Maximum
s ock
capaci y.
•Raw Ma e ial
s ock.
•Pe cen age
o co ec
pieces (o
de ec i e).
•Minimal
accep able
quali y.
•Selec ion
a e.
•P oduc ion
a e.
•One inished
p oduc s
mul iple
inished
p oduc s.
•Cons an and
andom demand.
•Numbe o
shipmen s pe cycle.
•Finished p oduc
s ock.
•Single s. mul iple pe iods.
•Single buye .
•Push/pull sys em.
•Type o chosen modelling.
•Cos a ia ion pe pe iod s ixed cos s pe pe iod.
•O he s a egies: possibili y o ou sou cing, isk inclusion, wa ehouse loca ion decisions,...
Table 1. Desc ip ion o axes (dep h and cha ac e is ics) de e mining model complexi y
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The con en o each o he columns (s ages) is no exhaus i e, since depending on he in e es
o he buye , mo e ac o s could be added. The able shows hose ac o s mos equen ly ci ed
in he a icles analysed. Addi ionally, hose cos s and company en i onmen ac o s included
wi hin one o he supply chain s ages a e no necessa ily p esen in all models including ha
s age. E e y model includes he cha ac e is ics co esponding o he sec o /company unde
analysis o o he academic model being de eloped. The analysed models will be classi ied
acco ding o he wo indica ed axes. To assu e he objec i eness o his classi ica ion, he
calcula ing key indica o s o each o he wo axes is de ined;
•Dep h indica o , supply chain s ages, is a in ege numbe de e mined by he numbe o
s ages (de ined in Table 1) included in he model.
•Cha ac e is ics indica o is measu ed using he ollowing o mula:
Cha ac e is ics Indica o = Cos s * 0.5 + En i onmen * 0.5 (1)
The e o e cha ac e is ics indica o is de e mined 50% by cos s, and 50% by he company
en i onmen desc ibed in he model. In o de o measu e bo h alues Table 2 is de ined.
Whe e o each s age in he supply chain bo h cos s and company en i onmen ac o s ha e
been de ailed, in case o be included in he model, a alue o 1 is assigned. I no , he alue
will be 0. Rega ding ac o s ha a e ans e sal, a all s ages, mul ipe iodici y is assigned a
alue o 1. I he model is single-pe iod, he alue assigned is 0.3, and he same c i e ia is
used ega ding single o mul iple p oduc o de alloca ion o single o mul i objec i e unc ions.
By so doing, he g ea e complexi y o models including mul i a ian s is shown.
Suppy Chain Cos s Company en i onmen
Pu chases
RM acquisi ion cos s Supplie capaci y
O de ing cos s P io iza ion o supplie s
T anspo a ion cos s Discoun s
Deli e y deadline
Wa ehouse Recep ion
RM s o age cos s S o age capaci y
RM s ock
Quali y 100 % selec ion cos s Pe cen age o co ec pieces
Selec ion a e
P oduc ion P oduc ion Cos s P oduc ion a e
S o age Fo wa ding S o age cos s FP FP S ock
Final Clien Sho age cos s Final cus ome demand
Sales p ice
Single s mul iple pe iods
Single o mul iple p oduc s
Single o mul iple objec i es
Table 2. Fo ma o calcula ing cha ac e is ics indica o included in model
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Using he co esponding calcula ion, each o he a icles has been plo ed along he o e
men ioned axes (Figu e 1). Resul s allow o an app oach o s udy he dispe sion o he scope
co e ed by he analyzed models. Table 3 desc ibes co espondence be ween codes and
a icles.
Visual analysis o Figu e 1, allow app ecia ing a cloud o poin s, wi hin which one obse es;
di e en ia ed poin s and a o al o i e clus e s o poin s. The i e clus e s o poin s a e o med
by a icles: [12][17], [7][26], [18][23][2], [1][24], and [21][16][4]. Each clus e includes
a icles con aining he same numbe o s ages and simila o equal deg ee o cha ac e is ics
indica o . Wi h he suppo o in o ma ion included in he a icles, one obse es ha in gene al
hese a icles pa ially coincide wi h espec o he s ages included, bu di e in he es o he
s ages. Despi e he ac ha he cha ac e is ics indica o a e is simila , in he a icles in each
clus e , cos s and company en i onmen ac o s a e di e en . Consequen ly he models e lec
di e en si ua ions.
Fo his eason, a isual analysis o he di e en ia ed poin s, and a mo e de ailed analysis o
he clus e s allow us o a i m ha all wen y-one a icles (100%) analyse di e en cases,
whe he o he dep h o company en i onmen included. Likewise, one obse es ha 9
(42.85%) models include wo s ages and 5 (23.8%) include 3 s ages. In 14 models (66.7%),
cha ac e is ics indica o is g ea e han 50%.
Code A icles/Au ho s
1 Abginehchi and Fa ahani (2010)
2 Bidhandi, Yusu , Ahmad and Baka (2009)
3 Bu ke, Ca illo and Vakha ia (2008)
4 Bu ke, Ca illo and Vakha ia (2009)
7 Ce e a and Co es (2009)
10 Hajji, Gha bi, Kenne and Pelle in (2011)
11 Haleh and Hamidi (2011)
12 Hassini (2008)
14 Ki y opoulos, Leopoulos, Ma o as and Voulga idou (2010)
15 Kokangul and Susuz (2009)
16 Lin (2010)
17 Lin (2009)
18 Ma akhe i, B e on and Ghoniem (2011)
19 Mendoza and Ven u a (2010)
21 Rezaei and Da oodi (2008)
22 Sawik (2010)
23 Tsai and Wang (2010)
24 Us un and Demi as (2008)
26 Woo and Saghi i (2011)
27 Wu, Sukoco, Li and Chen (2009)
28 Zhang and Ma (2009)
Table 3. Co espondence be ween codes and a icles
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Figu e 1. G aph measu ing dep h and cha ac e is ics indica o o analyzed a icles
2.4. Resolu ion P ocedu es
Model classi ica ion is ca ied ou using wo main p ocedu es: exac p ocedu es and heu is ics
p ocedu es (heu is ics). Wi hin he i s s; 4 a icles (19%) use dynamic p og amming, 2
a icles (9.5%) linea p og amming, 4 (19%) mixed in ege linea p og amming, and 1 (4.8%)
nonlinea in ege p og amming. The heu is ics a e subdi ided in o hose based on exac
p ocedu es and hose ha a e no . In heu is ics one obse es ha ; 3 a icles (14.3%) a e
based on mixed in ege linea p og amming; 1 (4.8%) nonlinea p og amming; 3 (14.3%) non
lineal in ege p og amming; 2 (9.5%) dynamic p og amming; and 1 a icle (4.8%) based on
heu is ic p ocedu es.
3. Conclusions
Va ious conclusions may be d awn om his o e iew o he s a e o he a . The mos
signi ican conclusion is he absence o an o e all o de alloca ion model in a mul i-supplie
en i onmen . Pa ial solu ions exis depending on he dep h o he supply chain, as well as he
cos s and company en i onmen ac o s conside ed, including pa icula aspec s o he
company and sec o in ques ion. Thus he e a e a wide ange o app oaches, and each model
add esses speci ic cha ac e is ics, and ies o e lec he eali y o he company unde s udy.
In o he cases, a icles y o model speci ic academic hypo heses. The e a e also a a ie y o
esolu ion p ocedu es u ilized.
While no wi hin he scope o his s a e o he a , ou s udy ound a numbe o a icles ha
conside echniques o c ea ing a supplie panel.
On he basis o he s a e o he a analysis, new esea ch lines ha e been ini ia ed aimed a
designing a comp ehensi e model ha inco po a es he en i e managemen o he supply
chain, as well as pa ame e s ha go beyond he speci ic a ea o pu chasing.
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Acknowledgemen s
The au ho s g a e ully acknowledge he pa ial suppo o g an DPI2010-15614 (Minis e io de
Economia y Compe i i idad, Spain).
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