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This is an Accep ed Manusc ip o an a icle published by Taylo & F ancis in
In e na ional Jou nal o P oduc ion Resea ch, Vol. 56, Issue 16, on Janua y
2018, a ailable a :
h ps://doi.o g/10.1080/00207543.2018.1430908
© 2018 In o ma UK Limi ed, ading as Taylo & F ancis G oup.
En idUS Licencia C ea i e Commons CC BY-NC-ND
Job shop managemen o p oduc s unde in e nal li espan
and ex e nal due da e
Ped oL. Gonzalez-Ra*, Ma cos Callea and Jose L. And ade-Pinedaa
aIndus ial Managemen , School o Enginee ing, Uni e si y o Se ille, Se ille, Spain
*Co esponding au ho . Email: [email p o ec ed]
P ep in submi ed o INTERNATIONAL JOURNAL OF PRODUCTION RESEARCH Janua y 3, 2018
DOI: 10.1080/00207543.2018.1430908
Job shop managemen o p oduc s unde in e nal li espan
and ex e nal due da e
De e io a ing i ems a e ound in a wide a ie y o p oduc i e en i onmen s and
ha e been ex ensi ely epo ed in he li e a u e. Howe e , he e olu ion o
ma ke s demand he de elopmen o new p oduc s and new o ms o wo k a e
made necessa y o adap p oduc ion sys ems o hose changes. The p esen wo k
ocuses on he p oduc ion con ol o pe ishable p oduc s in a job-shop
en i onmen . Speci ically, in hose p oduc s ha ha e an expi a ion da e wi hin
he p oduc ion in e al (in e nal caduci y) ha mus be deli e ed be o e a ce ain
da e. As a as we know, he e a e no p e ious wo ks ha ocus on he in e nal
caduci y o p oduc s a he p oduc ion-con ol le el. Two sys ems o di e en
na u e ha e been compa ed: Wo kload Con ol (WLC) and Kanban. WLC is
usually a benchma k in job-shop and made o o de en i onmen s. Recen s udies
show ha Kanban, adi ionally used in JIT (Jus in Time) en i onmen s,
pe o ms simila ly o e en be e han WLC. The s udy was pe o med by disc e e
e en s simula ion using Py hon© language, SimPy© and DEAP© modules, and
conside ing se e al esponses o he sys ems. The esul s show ha bo h sys ems
ha e a good pe o mance in a a ie y o scena ios, wi h o e all pe o mance o
Kanban in e ms o in e nal caduci y and a dy deli e ies.
Keywo ds: p oduc li espan; pe ishable p oduc ; job-shop; pull sys ems; wo k
load con ol; kanban sys em; p oduc ion con ol
1. In oduc ion
A common hypo hesis in esea ch s udies abou p oduc ion planning and con ol is o
conside ha he p ope ies and physical-chemical cha ac e is ics o p ocessed p oduc s
emain unchanged h oughou he en i e p ocess, o he changes a e a con olled phase
wi hin he p oduc p oduc ion li ecycle. In his case, he modi ica ions in he p oduc s
a e no impo an enough o be conside ed as some hing special in he pe o mance o
he p oduc i e sys em, and he e o e in managemen decisions.
In o he cases, he p ope ies o he p oduc s a e al e ed. One o he mos well-
known e ec s is he change in p ope ies o he p oduc s o e ime. As ime passes, he
p oduc deg ades, so he due da es equi ed by cus ome s a e usually qui e impo an in
p oduc ion managemen decisions, in o de o each he ma ke on ime and sell he
p oduc wi h he quali y cha ac e is ics es ablished by cus ome s. This is usually he
case in which he p oduc o be manu ac u ed is pe ishable. Examples o such p oblems
a e ound in lo icul u e, ag i- ood, ood manu ac u ing, medicine and pha macy, blood
banks, o in eady-mix conc e e pas e companies. Al hough hey a e o ally di e en
p oduc s, hey keep he ela ion as a as li ecycle is conce ned. In some cases, he
p oduc s ha e a ce ain li espan, while in o he s he quali y o he p oduc s dec eases
wi h ime be o e he end o he li ecycle.
Fo example, p oduc s ha es ed by ho icul u al companies begin o de e io a e
once he p oduc is collec ed, as i begins o lose mois u e. See 𝑡0 in Figu e 1 (a). The
p oduc li espan (𝐿𝑆) ends a he Expi a ion Da e (𝐸𝐷) a e he ime equi ed o
manu ac u e he p oduc o Lead Time (𝐿𝑇) a ins an FD (Finish Da e). Unde no mal
condi ions he p oduc is al eady in he hands o he cus ome be o e he Due Da e (𝐷𝐷)
equi ed by he cus ome . We say in his case ha he p oduc ion sys em has an "Ex e nal
Caduci y", since he caduci y o he p oduc occu s ou side he manu ac u ing sys em.
A lis o ac onyms and no a ions is p o ided in he Appendix o acili a e unde s anding
and eadabili y o he documen .
Ano he di e en case o he de e io a ion phenomenon occu s e.g. in he
manu ac u ing o ib e- ein o ced plas ic s uc u es whe e a ma e ial called p ep eg
(con ac ion o 'p e-imp egna ed') has become he s anda d echnology. The li e ime o
a p ep eg is limi ed, due o he sel - eac ing na u e o he esin (see Pansa 2013). The
composi e ma e ial mus be kep cold a e y low empe a u es un il i is used.
Subsequen ly, when he ma e ial lea es such condi ions, a ime 𝑡𝑜 in Figu e 1 (b), i has
a ime slo o be used, he e o e a ixed li espan. Tha is, he pieces should be p epa ed
in a ce ain ime limi and aken o he cu ing p ocess, in o de o s abilize he piece in
an au ocla e and o gi e i he physical p ope ies o which i has been designed. The
a ailable ime window o s abilize he p oduc is ep esen ed in he g aph as 𝑆𝑇, which
coincides in his case wi h he 𝐿𝑆 in e al. Once s abilized, he p oduc con inues he
p ocess un il i s comple ion ime in 𝐹𝐷. The e is also a commi men o he cus ome o
inish he o de be o e a ce ain da e, 𝐷𝐷. In his case he e ec o he de e io a ion o
he p oduc is amed wi hin he p oduc ion p ocess, so we deno e his case as "In e nal
Caduci y".
Figu e 1. (a) Ex e nal caduci y imeline (b) In e nal caduci y imeline
As is a gued la e in he li e a u e e iew, he managemen o de e io a ing
p oduc s wi hin he p oduc ion p ocess has been app oached e y b ie ly and ne e om
he poin o iew o p oduc ion con ol. Classically, p oduc ion con ol sys ems play a
e y impo an ole in sho - e m decisions and hei co ec ope a ion will p oduce
𝑡
In e nal P ocess
𝐿𝑆
𝑡𝑜
𝐸𝐷
𝐷𝐷
𝑆𝑇
𝐹𝐷
Ex e nal P ocess
𝐿𝑇
𝑡
In e nal P ocess
𝐿𝑆
𝑡𝑜
𝐸𝐷
𝐷𝐷
𝐹𝐷
Ex e nal P ocess
𝐿𝑇
𝑆𝑇
(a)
(b)

di e en esponses o he sys em in e ms o : Wo k in P ocess (WIP), lead ime and
o de delays. In addi ion o he abo e, and in he con ex o in e nal caduci y, i is also
necessa y o co ec ly manage he de e io a ion o p oduc s wi hin he p oduc ion
sys em.
We could hen o mula e he Resea ch Ques ion as ollows: How does he join
phenomenon o caduci y and due da e a ec he managemen o p oduc ion con ol
sys ems? To add ess his ques ion, we compa e he wo al e na i es ha a e mos
sui able o his ype o en i onmen s: The WLC sys em and he Kanban sys em. WLC
has p o en o be a benchma k in made- o-o de (MTO) p oduc s in job shops. A
di e en app oach is gi en by a ecen e sion o Kanban ha has p o en o achie e a
simila o e en be e pe o mance han he mos ad anced implemen a ion o he WLC.
The e a e se e al no el aspec s in his pape : i) he p oduc has an in e nal
li espan, ha mus be managed by he p oduc ion con ol sys em, ii) he WLC sys em is
compa ed o a ecen and uns udied e sion o he Kanban sys em in job-shop
en i onmen s, and iii) p io i y ules a e adap ed o mee li espan and ex e nal due da es.
The es o he chap e is o ganised as ollows: Sec ion 2 p esen s he e iew o
he li e a u e on he p oduc s de e io a ion conce ns in p oduc ion, as well as e iewing
he p oduc ion con ol sys ems in job-shop en i onmen s. Sec ion 3 desc ibes he
implemen a ions o he WLC and Kanban used in his wo k. Sec ion 4 p o ides a
de ailed desc ip ion o he shop loo unde s udy, as well as he compu a ional
expe ience. Sec ion 5 desc ibes he simula ion analyses, and discusses he esul s.
Finally, he las sec ion is de o ed o d awing conclusions and poin ing ou possible
esea ch di ec ions.
2. Li e a u e e iew
2.1 De e io a ing p oduc s: de ini ion and p e ious wo ks
Usually companies wo k wi h p oduc s ha do no always main ain he physical-
chemical cha ac e is ics o which hey ha e been concei ed and which mus emain
s able o e ime. I is said in his case ha he p oduc s a e de e io a ing i ems (Mi zaei
and Sei i 2015). De e io a ing i ems e e o i ems ha become decayed, damaged,
e apo a i e, o expi ed h ough ime (Li, Lan, and Mawhinney 2010). P oduc s ha
ha e a maximum usable li e ime a e known as pe ishable p oduc s (e.g. mea , g een
ege ables, human blood, medicine, lowe s, and ilms). Commodi ies such as alcohol
and gasoline which ha e no shel -li e a e known as decaying p oduc s (Goyal and Gi i
2001).
The e ec o pe ishabili y on he p oduc s is a phenomenon al eady s udied
p e iously. In ac , as a as we know, he e a e 17 e iews on his phenomenon. In
addi ion o he e iews men ioned abo e he ollowing e isions s and ou : Nahmias
(1982), Ka aesmen, Schelle -Wol , and Deniz (2011), Bakke , Riezebos, and Teun e
(2012), Amo im e al. (2013), and Janssen, Claus, and Saue (2016). In he la e , he
main con ibu ions o each o he e isions, di e ences and e olu ion o e ime a e
assessed and explained.
2.2 Pe ishable p oduc s a p oduc ion and dis ibu ion
De e io a ing i ems impac on decisions a he p oduc ion le el, as much as on decisions
in long, medium and sho e m. I should be no ed ha he majo body o li e a u e on
pe ishabili y is conce ned wi h in en o y managemen , al hough he e has been a
g owing in e es in i s e ec on supply chain managemen p oblems (Amo im e al.
2013). Dis ibu ion ne wo ks and cen es a e esponsible o managing he complex
p oblem o dis ibu ion and s o age o p oduc s. In he case o pe ishables, he p oblem
is e en mo e complica ed, since he dis ibu ion and s o age o pe ishable i ems usually
equi es conside a ion o he limi ed li e ime o he i ems. See o example ecen s udies
by Mine and T anschel (2017) on he e ec o o de a iabili y in he supply chain o
pe ishable goods. Dis ibu ion plans ha need e ige a ion a e o pa icula in e es
wi hin he supply chain, since dis ibu ion planning asks a e one o he main ac i i ies
in cold supply chains (see Hsiao, Chen, and Chin 2017). In a ecen publica ion Keize
e al. (2017) add ess aspec s o ne wo k design when p oduc quali y can be ca ego ized
and hus spli lows. O he issues add essed in he con ex o he supply chain a e
localiza ion p oblems, including ILDN (In eg a ed Logis ic Dis ibu ion Ne wo k)
dis ibu ion p oblems in eg a ed wi h loca ion o acili ies and alloca ion o e aile o
he open acili ies. See in his ega d Wu, Shen, and Zhu (2015) whe e he backlogging
o a pe ishable p oduc is also conside ed.
The in eg a ion o in en o y con ol and ehicle ou ing p oduces a complex
op imiza ion p oblem called IRP (In en o y Rou ing P oblem) which aims o minimize
o al in en o y and anspo a ion cos s. Recen wo ks simul aneously s udy he
in en o y managemen p oblem associa ed wi h ou ing o e aile s. P og ess in his a ea
is also impo an in p oblems which simul aneously op imize in en o y managemen
wi h he associa ed anspo p oblem VRP (Vehicle Rou ing P oblem). See in his
ega d Mi zaei and Sei i (2015), which add esses an IRP wi h los sales. The IRP ha
also in eg a es he a iables ela ed o he quan i ies o be p oduced o each p oduc yield
he IPDS (In eg a ed P oduc ion and Dis ibu ion Scheduling P oblem) op imiza ion
p oblem. In a ecen pape (see De ap iya, Fe ell, and Geisma 2017), he au ho s s udy
an IPDS o de e mine lee size, uck ou es, p oduc ion schedule and dis ibu ion
sequence, ul illing a planning ho izon. Belo-Filho, Amo im, and Almada-Lobo (2015)
ca y ou new esea ch on he MILP (Mixed In ege Linea P og amming) model
in oduced in Amo im e al. (2013) using he lo sizing app oach. The au ho s p oposed
solu ion me hods based on he ALNS (Adap i e La ge Neighbou hood Sea ch) heu is ic
o add ess la ge ins ances o he p oblem.
2.3 In e nal Caduci y
To ou knowledge, he e a e e y ew jobs which conside ha he end o he li espan
occu s in e nally du ing he p oduc ion p ocess. The wo ks by Cai e al. (2008) and
Billau , Della C oce, and G osso (2015) belong o his ca ego y in he con ex o lo
sizing and scheduling p oblems. Cai e al. (2008) pe o m a scheduling o pe ishable
p oduc s a a sea ood manu ac u ing plan . The p oduc s a e made om aw ma e ial
which, o easons o eshness, mus be used be o e a ixed deadline. The decisions a e
ela i e o wha ype o p oduc is p oduced, he quan i y and he sequence o be
p ocessed a manu ac u ing. Billau , Della C oce, and G osso (2015) in oduce an
in e es ing p oblem inspi ed by he p oduc ion o chemo he apy d ugs o cance
ea men by in a enous injec ion (an ea ly desc ip ion o he same p oblem can also
be ound in Billau 2011). The au ho s add ess a scheduling p oblem om he
pha maceu ical indus y whe e aw ma e ials ha e a limi ed li e ime once hey ha e le
he en i onmen al condi ions o s o age, and he e o e, hey mus be used be o e a
ce ain deadline.
2.4 P oduc ion con ol sys ems in job-shop en i onmen s
In o de o selec which ypes o p oduc ion con ol sys ems can achie e a be e
pe o mance in he managemen o pe ishable p oduc s, we ha e aken he WLC sys em
as a e e ence. WLC is he mos widely used me hod o p oduc ion con ol in MTO and
job-shop en i onmen s (S e enson, Hend y, and Kingsman 2005), and i is conside ed
𝑂𝑐𝑐𝑢𝑝𝑎𝑡𝑖𝑜𝑛 = 𝑚𝑒𝑎𝑛 𝑝𝑟𝑜𝑐𝑒𝑠𝑠𝑖𝑛𝑔 𝑡𝑖𝑚𝑒 · 𝑚𝑒𝑎𝑛 𝑟𝑜𝑢𝑡𝑖𝑛𝑔 𝑙𝑒𝑛𝑔𝑡ℎ
𝑖𝑛𝑡𝑒𝑟−𝑎𝑟𝑟𝑖𝑣𝑎𝑙 𝑡𝑖𝑚𝑒 · 𝑐𝑎𝑝𝑎𝑐𝑖𝑡𝑦 𝑜𝑓 𝑡ℎ𝑒 𝑠ℎ𝑜𝑝 𝑓𝑙𝑜𝑜𝑟 (1)
The due da es a e se exogenously by adding o he job en y ime, a andom
allowance ac o which is uni o mly dis ibu ed o e he ange 40 o 50 ime uni s. As
in Thü e and S e enson (2016), he minimum alue will be su ficien o co e a
minimum shop loo h oughpu ime co esponding o he maximum p ocessing ime
(4 ime uni s) o he maximum numbe o possible ope a ions (8) plus an a bi a ily se
allowance o he wai ing o queuing imes o 8 ime uni s. The alue o he maximum
wai ing ime allowance is chosen in o de ha he basic se o expe imen s esul in a
pe cen age a dy be ween 5 and 20%, see González-R and Calle (2017).
The maximum caduci y window is se o 18 ime uni s, in o de ha he se o
basic expe imen s achie es a pe cen age o expi ed p oduc s less han 10%. Fo all
o de s, he li espan s a s a he beginning o he p ocess in he ac i a ion s a ion, which
is a ixed wo k cen e (numbe 5), independen ly o he posi ion in he ou e. These
se ings acili a e compa ison wi h ea lie s udies on bo h Wo kload Con ol (e.g.
Oos e man, Land, and Gaalman 2000, Thü e e al. 2012, Thü e e al. 2014) and
Kanban (González-R and Calle 2017). Table 1 shows a summa y o simula ed shop and
job cha ac e is ics.
Table 1. Summa y o simula ed shop and job cha ac e is ics.
Shop Cha ac e is ics
Rou ing a iabili y
Random ou ing; no e-en an lows
No. o wo k cen es
8
In e change-abili y o wo k cen es
No in e change-abili y
Wo k cen e capaci ies
All equal
Wo k cen e u iliza ion a e
80%
Job Cha ac e is ics
No. o ope a ions pe job
Disc e e uni o m [1, 8]
Ope a ion p ocessing imes
T unca ed 2-E lang (mean=1; max=4)
Planned h oughpu ime pe ope a ion
5 ime uni s
Due da e allowance
Uni o mly dis ibu ed [40, 50]
In e -a i al imes
Exp. dis ibu ion; mean=0.703125

4.2 O de elease
As in p e ious simula ion s udies on wo kload con ol (e.g. Land and Gaalman 1998,
F edendall, Ojha, and Pa e son 2010, Thü e e al. 2012, and Thü e , S e enson, and
Qu 2016), i is assumed ha all jobs a e accep ed, ma e ials a e a ailable and all
necessa y in o ma ion ega ding shop loo ou ings, p ocessing imes, e c. is known.
Jobs low in o a p e-shop pool o awai elease acco ding o LUMS COR, as Land,
S e enson, and Thü e (2014). The ime in e al be ween eleases o he pe iodic
elemen o LUMS COR is se o 5 ime uni s, as Thü e e al (2014).
4.3 Expe imen al design and pe o mance measu es
The expe imen al ac o s a e: i) he wo p oduc ion con ol sys ems (WLC LUMS COR
y Kanban), and ii) ou dispa ching ules a in e media e bu e s, which a e he FIFO
ule (Fi s -In-Fi s -Ou ule), he EDD ule (Ea lies Due Da e), he SRPT ule (Sho es -
Remaining-P ocessing-Time) and he CR ule (C i ical Ra io). In he ela ed li e a u e
on he WLC sys em i is usual o implemen he FIFO ule as an in e nal dispa ching
ule. Howe e , none o hese s udies add essed he e ec o in e nal caduci y o
p oduc s. The e o e, we conside necessa y o s udy he pe o mance o di e en
p io i y ules in his wo k. The FIFO ule gi es p io i y o he nex job in he queue. This
ule eme ges as he bes in minimizing he makespan objec i e in all cases ega dless o
changing he lexibili y o he p oblem ins ances. The SRPT ule, whe e he job wi h he
leas slack pe emaining p ocess ime is chosen o loading, yields he sho es mean
low ime, and i is ex ensi ely implemen ed in indus y and o en used as a benchma k
o e alua ing a diness- ela ed measu emen s. To include he e ec o he in e nal
caduci y and deli e y da e we p opose wo p io i y ules (EDD and CR) adap ed o his
p oblem, and, as a as we know, ne e p oposed be o e. The EDD ule gi es p io i y o
he job wi h he ea lies due da e. This ule pe o ms well ega ding he mean low ime,
being he mos popula due da e based ule, and is equen ly used as a benchma k o
educing maximum a diness and a iance o a diness. A e he ac i a ion s a ion he
p oposed EDD ule selec he minimum alue be ween he due da e and he expi a ion
da e. Finally, he CR ule ends o p io i ise jobs ha ha e less ime a ailable,
sequencing jobs in non-dec easing o de o a a io de ined as he emaining allowance
( he ime ill i is due) o he job di ided by i s emaining p ocessing ime. The CR ule
has been es ed in a numbe o s udies, mainly o job shops and pe o ms well o
objec i es based on he due da e. In he p oposed CR ule, he alue o he emaining
allowance, used in he e alua ion o he c i ical a io, is assessed by wo al e na i e
p ocedu es: i) be o e caduci y ac i a ion, he emaining allowance, o each job 𝑗
wai ing in he in e media e bu e , is he emaining ime om now o he due da e, and
ii) a e caduci y ac i a ion, he emaining allowance is gi en by he minimum alue
be ween he emaining ime om now o he expi a ion da e, and he emaining ime
om now o he due da e.
E olu iona y algo i hm oolki DEAP (Fo in e al. 2012), an abb e ia ion o
“Dis ibu ed E olu iona y Algo i hms in Py hon”, is used in he adjus men p ocess o
WLC and Kanban sys ems o ind i) he op imum alues o he wo kload no m o each
s a ion, in he WLC model, and ii) he op imum numbe o ca ds o each s a ion, in he
Kanban model. To educe he a ea o sea ch, only disc e e a iables a e de ined, i.e., he
sea ch o he load no ms is es ic ed o in ege alues. DEAP is an e olu iona y
compu a ion amewo k ha allows apid p o o yping o di e se gene ic algo i hms,
including gene ic algo i hms (Mi chell 1998), gene ic p og amming (Banzha e al.
1998), e olu ion s a egies (Beye and Schwe el 2002), co a iance ma ix adap a ion
e olu ion s a egy (Hansen and Os e meie 2001), pa icle swa m op imiza ion
(Kennedy and Ebe ha 2001), and many mo e. In his s udy, wo objec i e unc ions
ha e been used, which aim a i) educing he amoun o jobs wi h de ec s due o he
ma e ial expi a ion, and ii) educing he amoun o jobs deli e ed a dy o he cus ome .
As in Thü e , Sil a, and S e enson (2010 and 2011), he simula ion so wa e
calcula es he mean alues o he objec i e unc ions om 100 eplica es (Law and
Kel on 2000). DEAP hen e alua es his alue and de ines new pa ame e s o he
simula ion which hen epea s he calcula ion o he objec i e unc ion wi hin he newly
de ined pa ame e s. This op imisa ion p ocess can be epea ed o e a limi ed ime pe iod
o un il he op imum solu ion has been ound. Resul s we e collec ed o e 10,000 ime
uni s ollowing a wa m-up pe iod o 3,000 ime uni s. These pa ame e s allowed us o
ob ain s able esul s while keeping he simula ion un ime o a easonable le el.
Below a e lis ed he pe o mance indica o s measu ed in his s udy, which
co espond o he mos common pe o mance indica o s used in he s udies o
p oduc ion con ol sys ems:
 Pe cen age expi ed: he pe cen age o jobs comple ed a e he maximum ime
allowed o emain uncu ed. This indica es he p opo ion o jobs wi h de ec s
on i s inal deg ee o cu e.
 Pe cen age a dy: he pe cen age o jobs comple ed a e he due da e. This
indica es he p opo ion o jobs ha a e deli e ed a dy o he cus ome .
 Mean a diness: he mean o he a diness 𝑇𝑗=𝑚𝑎𝑥(0,𝐿𝑗), wi h 𝐿𝑗 being he
la eness o job 𝑗 (i.e., i s ac ual deli e y ime minus i s due da e). This indica es
he ex en o which jobs a e a dy.
 G oss h oughpu ime: he mean o he comple ion ime minus he a i al ime
ac oss jobs. This measu e e lec s he ime ha a cus ome has o wai o he
p oduc .
 P e-shop ime: he mean o he elease ime ac oss jobs. This indica es he
mean ime ha a job spends wai ing in he pool be o e elease.
5. Resul s and discussion
Fi s , his sec ion analyses he ob ained esul s ela ed o he o de s deli e y, ocusing
on h ee indica o s: he deli e y o i) expi ed p oduc s, ii) delayed o de s, and iii) he
a e age o he delays du a ion. Secondly, we ha e s udied he deg ee o u ilisa ion o
he shop by wo indica o s: i) he P e-shop Time, consis ing o he ime ha he o de s
emain in he p e-shop pool wai ing o be eleased, and ii) he G oss Th oughpu Time,
consis ing o he o al h oughpu ime including pool wai ing ime.
The i s analysis consis s o he s udy o he sys ems pe o mance, which has
been measu ed by 2 indica o s, he deli e y o expi ed p oduc s and he deli e y o
delayed o de s. This analysis con ains wo opposing objec i es: minimizing expi ed
deli e ies, and minimizing delayed deli e ies. The pe o mance achie ed o each
con igu a ion o maximum pe missible wo kload is ep esen ed by he coo dina es o a
poin (𝑥,𝑦), whe e he i s coo dina e ep esen s he ‘pe cen age o a dy deli e ies’,
and he second coo dina e ep esen s he ‘pe cen age o expi ed deli e ies’.
The Table 2 summa izes, o each combina ion o s udied sys em (WLC and
Kanban) and p io i y ule (FIFO, SRPT, EDD and CR), he e icien poin s ha make
up he e iciency on ie o Pa e o on ie .
Figu es 2 o 5 show he pe cen age o expi ed deli e ies o e he pe cen age o
a dy deli e ies, ob ained o bo h sys ems (WLC and Kanban), and applying he ou
p io i y ules s udied in he p esen wo k. Each igu e ep esen s he esul s ob ained
om bo h he WLC sys em and he Kanban sys em, whe e each poin co esponds o
he a e age alue ob ained om all eplica es which ha e been pe o med o a gi en
maximum pe missible wo kload. These igu es also ep esen he poin s (o
con igu a ions o maximum pe missible wo kload) ha a e simul aneously e icien o
he wo objec i es o i) minimizing expi ed deli e ies and ii) minimizing delayed
deli e ies. Thus, he g oup o e icien poin s composes he e iciency on ie o Pa e o
on ie .

Table 2. Summa y o e icien poin s o each combina ion o sys em and p io i y ule.
Pa e o F on ie o he Kanban sys em
Pa e o F on ie o he WLC sys em
To al numbe o poin s
o he on ie
Endpoin s o he on ie
To al numbe o poin s
o he on ie
Endpoin s o he on ie
(𝑀𝑖𝑛𝑖𝑚𝑢𝑚
𝑃𝑒𝑟𝑐𝑒𝑛𝑡𝑎𝑔𝑒
𝑜𝑓 𝐸𝑥𝑝𝑖𝑟𝑒𝑑
𝑃𝑟𝑜𝑑𝑢𝑐𝑡𝑠 ; 𝑀𝑎𝑥𝑖𝑚𝑢𝑚
𝑃𝑒𝑟𝑐𝑒𝑛𝑡𝑎𝑔𝑒
𝑜𝑓 𝑇𝑎𝑟𝑑𝑦
𝐷𝑒𝑙𝑖𝑣𝑒𝑟𝑖𝑒𝑠)
(𝑀𝑎𝑥𝑖𝑚𝑢𝑚
𝑃𝑒𝑟𝑐𝑒𝑛𝑡𝑎𝑔𝑒
𝑜𝑓 𝐸𝑥𝑝𝑖𝑟𝑒𝑑
𝑃𝑟𝑜𝑑𝑢𝑐𝑡𝑠 ; 𝑀𝑖𝑛𝑖𝑚𝑢𝑚
𝑃𝑒𝑟𝑐𝑒𝑛𝑡𝑎𝑔𝑒
𝑜𝑓 𝑇𝑎𝑟𝑑𝑦
𝐷𝑒𝑙𝑖𝑣𝑒𝑟𝑖𝑒𝑠)
(𝑀𝑖𝑛𝑖𝑚𝑢𝑚
𝑃𝑒𝑟𝑐𝑒𝑛𝑡𝑎𝑔𝑒
𝑜𝑓 𝐸𝑥𝑝𝑖𝑟𝑒𝑑
𝑃𝑟𝑜𝑑𝑢𝑐𝑡𝑠 ; 𝑀𝑎𝑥𝑖𝑚𝑢𝑚
𝑃𝑒𝑟𝑐𝑒𝑛𝑡𝑎𝑔𝑒
𝑜𝑓 𝑇𝑎𝑟𝑑𝑦
𝐷𝑒𝑙𝑖𝑣𝑒𝑟𝑖𝑒𝑠)
(𝑀𝑎𝑥𝑖𝑚𝑢𝑚
𝑃𝑒𝑟𝑐𝑒𝑛𝑡𝑎𝑔𝑒
𝑜𝑓 𝐸𝑥𝑝𝑖𝑟𝑒𝑑
𝑃𝑟𝑜𝑑𝑢𝑐𝑡𝑠 ; 𝑀𝑖𝑛𝑖𝑚𝑢𝑚
𝑃𝑒𝑟𝑐𝑒𝑛𝑡𝑎𝑔𝑒
𝑜𝑓 𝑇𝑎𝑟𝑑𝑦
𝐷𝑒𝑙𝑖𝑣𝑒𝑟𝑖𝑒𝑠)
P io i y ule
FIFO
2
(1.535%, 8.583%)
(1.585%, 8.526%)
25
(0.829%, 6.344%)
(2.916%, 2.335%)
SRPT
2
(8.370%, 4.927%)
(8.409%, 4.906%)
2
(4.185%, 3.026%)
(4.213%, 3.017%)
EDD
4
(0.098%, 3.389%)
(0.124%, 3.352%)
20
(0.176%, 3.462%)
(1.938%, 2.076%)
CR
1
(0.065%, 0.085%)
7
(0.159%, 0.087%)
(0.282%, 0.073%)
(a)
(b)
Figu e 2. (a) Pe cen age o expi ed deli e ies o e he pe cen age o a dy deli e ies,
ob ained by WLC sys em when uses FIFO ule. (b) Pe cen age o expi ed deli e ies o e
he pe cen age o a dy deli e ies, ob ained by Kanban sys em when uses FIFO ule.
(a)
(b)
Figu e 3. (a) Pe cen age o expi ed deli e ies o e he pe cen age o a dy deli e ies,
ob ained by WLC sys em when uses SRPT ule. (b) Pe cen age o expi ed deli e ies o e
he pe cen age o a dy deli e ies, ob ained by Kanban sys em when uses SRPT ule.
(a)
(b)
Figu e 4. (a) Pe cen age o expi ed deli e ies o e he pe cen age o a dy deli e ies,
ob ained by WLC sys em when uses EDD ule. (b) Pe cen age o expi ed deli e ies o e
he pe cen age o a dy deli e ies, ob ained by Kanban sys em when uses EDD ule.
(a)
(b)
Figu e 5. (a) Pe cen age o expi ed deli e ies o e he pe cen age o a dy deli e ies,
ob ained by WLC sys em when uses CR ule. (b) Pe cen age o expi ed deli e ies o e
he pe cen age o a dy deli e ies, ob ained by Kanban sys em when uses CR ule.
Fi s , he deg ee o concen a ion o he e icien poin s o ming he e iciency
on ie is analysed. Table 2 de ails he numbe o e icien poin s ha make up each
e iciency on ie . In addi ion, his able con ains he endpoin s o each e iciency
on ie . Rega ding he simul aneous esponse owa ds he wo objec i es, i is necessa y
o emphasize ha achie ing a high deg ee o concen a ion o e icien poin s allows
simul aneously he minimizing o he quan i y o expi ed p oduc s and delayed
deli e ies. As o he Kanban sys em, Figu es 2(b), 3(b), 4(b) and 5(b), and Table 2
show a high deg ee o concen a ion o he e icien poin s o all he p io i y ules
s udied, since he e a e ew e icien poin s which a e close o each o he . As o he
WLC sys em, Figu es 2(a), 3(a), 4(a) and 5(a), and Table 2 show how he applied
p io i y ule a ec s he deg ee o concen a ion o he e icien poin s. Thus, highe
le els o concen a ion a e achie ed by wo p io i y ules, co esponding o he SRPT
and CR. Rega ding he p oduc ion o expi ed i ems, he WLC sys em exceeds he
Kanban sys em in he scena ios s udied, excep in he case whe e he Kanban sys em
applies he CR as p io i y ule in which bo h sys ems achie e e y simila pe o mance
le els. Wi h ega d o he delayed deli e ies, he sys em ha pe o ms bes a ies
acco ding o he p io i y ule ha has been applied. Thus, he WLC sys em o e comes
he Kanban sys em when he FIFO o SRPT p io i y ules a e applied. Howe e , in
scena ios applying he EDD and CR, he Kanban sys em su passes he WLC sys em.
Table 3 and Figu e 6 ga he o each p io i y ule he esul s ob ained by bo h
sys ems (WLC and Kanban). The objec i e o his analysis is o cons uc he join
e iciency on ie based on he bes esul s belonging o each sys em. The Table 3
de ails sepa a ely o each p io i y ule he expe imen al esul s co esponding o i) he
p ocessing o he mos u gen wo ks on i s due da e, since hey a e di ec ly eleased o
he shop and do no ha e o wai o he nex elease pe iod.
Con a y o wha was es ablished by S e enson, Hend y, and Kingsman (2005),
bu in ag eemen wi h he indings o González-R and Calle (2017), i has been shown
ha he pe o mance o he Kanban sys em is compe i i e o ha ob ained by he WLC
sys em which is usually implemen ed in his kind o en i onmen .
The scena io in oduced is, as a as we know, new in he ield o p oduc ion
con ol. This e ec is no only ound in eal p ac ise in he ae onau ical indus y, bu
also in he manu ac u e o pha maceu icals and, as has been epo ed in li e a u e in he
p oduc ion o pe ishable p oduc s, subjec o a ixed in e nal e mina ion da e and an
ex e nal due da e (see e.g. Billau , Della C oce, and G osso 2015 o Cai e al. 2008).
Se e al lines o esea ch can be de i ed om his wo k. In ou opinion, we
belie e i is impo an o s udy he in eg a ion o he planning me hods in he highe
hie a chical le els wi h he sho - e m decisions a p oduc ion con ol le el, in he case
o in e nal caduci y p oduc s. Fu he mo e, in his case only ino ganic p oduc s ha e
been conside ed, so ha hei alidi y o esul s may di e in he case ha p oduc s such
as esh oods a e p ocessed. In such cases, o he ypes o en i onmen al ac o s e.g.
humidi y, empe a u e, o mic o-o ganisms may a ec he pe o mance o he sys ems.
The e o e, mo e esea ch is needed in his a ea. Besides, in many cases in he p ocessing
o pe ishable p oduc s, he human ac o is o g ea impo ance, g ea ly a ec ing he
inal quali y o he p oduc , and in e ening di ec ly in he p ocessing ime. Finally,
al hough he Kanban sys em has shown i s compe i i eness in he case s udied, u he
s udies a e s ill needed o suppo i s gene al use, as well as i s compa ison wi h o he
al e na i e p oduc ion con ol sys ems.

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Appendix: Lis o no a ion and ac onyms used
The ac onyms used in he ex a e he ollowing:
ALNS
Adap i e La ge Neighbou hood Sea ch
CR
C i ical Ra io
DD
Due Da e
DEAP
Dis ibu ed E olu iona y Algo i hms in Py hon
ED
Expi a ion Da e
EDD
Ea lies Due Da e
FD
Finish Da e
FIFO
Fi s in Fi s Ou
ILDN
In eg a ed Logis ic Dis ibu ion Ne wo k
IPDS
In eg a ed P oduc ion and Dis ibu ion Scheduling P oblem
IRP
In en o y Rou ing P oblem
JIT
Jus in Time
LS
Li espan
LT
Lead ime
LUMS COR
Lancas e Uni e si y Managemen School O de Release
MILP
Mixed In ege Linea P og amming
MRP
Ma e ials Requi emen Planning
MTO
Made o O de
SRPT
Sho es -Remaining-P ocessing-Time
ST
Slack Time
VRP
Vehicle Rou ing P oblem
WIP
Wo k in P ocess
WLC
Wo kload Con ol
Nex a e shown he WLC and Kanban ope a ing pa ame e s:
𝐷𝐷𝑗
Due da e o job 𝑗
𝐽
Lis o jobs
𝐿𝑗
la eness o job 𝑗
𝑁𝑠𝐶.
Wo kload no m a s a ion 𝑠
𝑁𝐶𝑠
Numbe o ca ds a ailable in he con ol panel o s a ion 𝑠
𝑁𝐶𝑆𝑗0′
Numbe o ca ds a ailable in he con ol panel o s a ion 𝑠𝑗0′.
𝑝𝑗𝑠
P ocessing ime o job j a s a ion 𝑠
𝑆𝑗
Se o s a ions in he ou e o he job 𝑗
𝑡𝑗𝑅
Planned elease da e o job 𝑗
𝑡𝑜
Le espan s a ing ins an
𝑇
Release pe iod
𝑇𝑗
Ta diness o job 𝑗
𝑇𝑗𝑠
Planned h oughpu ime o job 𝑗 in s a ion 𝑠
𝑊𝑠
Cu en wo kload a s a ion 𝑠
Figu e cap ions
Figu e 1. (a) Ex e nal caduci y imeline (b) In e nal caduci y imeline
Figu e 2. (a) Pe cen age o expi ed deli e ies o e he pe cen age o a dy deli e ies,
ob ained by WLC sys em when uses FIFO ule. (b) Pe cen age o expi ed deli e ies
o e he pe cen age o a dy deli e ies, ob ained by Kanban sys em when uses FIFO
ule.
Figu e 3. (a) Pe cen age o expi ed deli e ies o e he pe cen age o a dy deli e ies,
ob ained by WLC sys em when uses SRPT ule. (b) Pe cen age o expi ed deli e ies
o e he pe cen age o a dy deli e ies, ob ained by Kanban sys em when uses SRPT
ule.
Figu e 4. (a) Pe cen age o expi ed deli e ies o e he pe cen age o a dy deli e ies,
ob ained by WLC sys em when uses EDD ule. (b) Pe cen age o expi ed deli e ies
o e he pe cen age o a dy deli e ies, ob ained by Kanban sys em when uses EDD
ule.
Figu e 5. (a) Pe cen age o expi ed deli e ies o e he pe cen age o a dy deli e ies,
ob ained by WLC sys em when uses CR ule. (b) Pe cen age o expi ed deli e ies o e
he pe cen age o a dy deli e ies, ob ained by Kanban sys em when uses CR ule.
Figu e 6. (a) Join E iciency F on ie when bo h sys ems use he FIFO ule. (b) Join
E iciency F on ie when bo h sys ems use he SRPT ule. (c) Join E iciency F on ie
when bo h sys ems use he EDD ule. (d) Join E iciency F on ie when bo h sys ems
use he CR ule.