Chalida Donjuk; Ji aja Se asuk; Po-nga m Somkun
A icle
Regula and u gen o de ing wi h la e al ansshipmen
in a dis ibu ion ne wo k wi h s ochas ic p e-o de ed and
peddling demands
Asian Jou nal o Shipping and Logis ics (AJSL)
P o ided in Coope a ion wi h:
Ko ean Associa ion o Shipping and Logis ics, Seoul
Sugges ed Ci a ion: Chalida Donjuk; Ji aja Se asuk; Po-nga m Somkun (2025) : Regula and u gen
o de ing wi h la e al ansshipmen in a dis ibu ion ne wo k wi h s ochas ic p e-o de ed and
peddling demands, Asian Jou nal o Shipping and Logis ics (AJSL), ISSN 2352-4871, Else ie ,
Ams e dam, Vol. 41, Iss. 1, pp. 61-74,
h ps://doi.o g/10.1016/j.ajsl.2025.01.004
This Ve sion is a ailable a :
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Regula and u gen o de ing wi h la e al ansshipmen in a dis ibu ion
ne wo k wi h s ochas ic p e-o de ed and peddling demands
Chalida Donjuk
a
, Ji aja Se asuk
b
, Po-nga m Somkun
a,*
a
Depa men o Indus ial Enginee ing, Facul y o Enginee ing, Na esuan Uni e si y, Phi sanulok, Thailand
b
Thi apa D ink Company Limi ed, Thailand
ARTICLE INFO
Keywo ds:
In en o y eplenishmen policy
(R, s, S) policy
Demand classes
Ma hema ical model
Sp eadshee model
Logis ics
ABSTRACT
We p opose in en o y eplenishmen and la e al ansshipmen policies o a dis ibu ion ne wo k. The dis i-
bu ion cen e s place weekly egula o de s and daily u gen o de s o he ac o y. Two classes o s ochas ic
demands, p e-o de ed and peddling, cause ei he backlogging o los sales when hey a e no sa is ied. The policy
was simula ed using da a om a case s udy. The esul s showed ha he p oposed policies educed he o al cos ,
which includes anspo a ion cos s o sa is ied demands and la e al ansshipmen , back o de and los sale
cos s o unsa is ied demands, and in en o y holding cos s. The bes policy educed long- un o al cos and was
p o ed obus om sensi i i y analysis. Finally, implemen ing he policy wi h he case s udy con i med 9.97 %
o al cos educ ion and i s p ac ical applica ion.
1. In oduc ion
In en o y eplenishmen policies a e c i ical o main aining sa e in-
en o y le els o mee cus ome demand and p e en o e s ocking o
s ock sho ages. A ading business’s dis ibu ion ne wo k managing
a ious p oduc s equi es e icien in en o y eplenishmen policies ha
ensu e high cus ome sa is ac ion while keeping cos s low. In a con-
en ional supply chain, dis ibu ion cen e s (DCs) place o de s wi h
ac o ies o eplenish hei s ocks. Howe e , when dis ibu ion cen e s
can pe o m la e al ansshipmen , a p ocess whe e in en o y is mo ed
be ween neighbo ing loca ions o mee demand, he p ac ice becomes
mo e complex, equi ing ca e ul coo dina ion o in en o y eplenish-
men policies and inbound/ou bound ansshipmen decisions (Pa e son
e al., 2011).
The o de ing decision o he dis ibu ion ne wo k can be e en mo e
sophis ica ed when he DCs can place u gen o de s du ing he egula
o de ing cycle. U gen o de s a e placed o he uppe echelon o he
supply chain when he in en o y le el is c i ically low, and he egula
o de s ha ha e al eady been placed a e no a i ing soon enough. An
u gen o de has a sho e lead ime and ypically cos s mo e han a
egula one (Chiang, 2010; Johansen, 2019; Taga as and Vlachos,
2001). The e o e, hese expedi ed shipmen s a e expec ed o sa is y
incoming demand and a oid s ockou . P e ious s udies ha e shown ha
he combina ion o egula and u gen o de ing o in en o y
eplenishmen can educe he cos and imp o e he se ice le el in pe-
iodic (Johansen, 2019; Taga as and Vlachos, 2001) and con inuous
(Chiang, 2002; Chiang, 2010) sys ems.
Demand classes in he in en o y sys em gene ally ep esen he le el
o impo ance o demand sou ces. Howe e , in some s udies, he classes
only de ine he sou ces o demands, such as online o o line demands
(Qu e al., 2022) and local o swi ched demands (Liao e al., 2020). Thus,
he unme demands om di e en sou ces a e conside ed he same. Fo
example, hey could all be conside ed as los sales. Howe e , in some
s udies, he unsa is ied demands o di e en classes esul in di e en
ea men s and cos s. Some unme demands a e ega ded as los sales,
while o he s a e backlogged based on hei p io i ies (Malliga junan,
2016; Zhou and Zhao, 2010). This a angemen , necessa y o eal sys-
em implemen a ion, ele a es he di icul y o in en o y eplenishmen
decisions, unde sco ing he impo ance o unde s anding hese
complexi ies.
Ou s udy amewo k is based on all he abo e decisions ha he
dis ibu ion ne wo k ound in p ac ice mus make, including egula ,
u gen , and la e al o de ing. Addi ionally, he demands aced by he DCs
in his s udy can be sepa a ed in o p e-o de ed and peddling demands.
The p e-o de ed demand is known a he beginning o each pe iod
be o e he la e al ansshipmen occu s. These demands a e om s eady
cus ome s. I he s ock is ou , hese cus ome s will wai , and he new
s ock will be sen o hem i s . The e o e, he unme p e-o de ed
* Co esponding au ho .
E-mail add ess: [email p o ec ed] (P.-n. Somkun).
Con en s lis s a ailable a ScienceDi ec
The Asian Jou nal o Shipping and Logis ics
jou nal homepage: www.else ie .com/loca e/ajsl
h ps://doi.o g/10.1016/j.ajsl.2025.01.004
Recei ed 21 Oc obe 2024; Accep ed 27 Janua y 2025
The Asian Jou nal o Shipping and Logis ics 41 (2025) 61–74
A ailable online 12 Feb ua y 2025
2092-5212/© 2025 The Au ho (s). Published by Else ie B.V. on behal o The Ko ean Associa ion o Shipping and Logis ics, Inc. This is an open access a icle unde
he CC BY-NC-ND license ( h p://c ea i ecommons.o g/licenses/by-nc-nd/4.0/ ).
demand is backlogged and applied o he back o de cos . The DC also
has ano he selling app oach, he ein called peddling. The ac o peddling
is de ined as he mo emen o a company’s ehicle ha ca ies he DC’s
p oduc s on a ou o o e a sale o i s cus ome s ha a e local e ail and
wholesale s o es (adap ed om Ruan e al. 2012 and Me iam-Webs e
2024). The demand om hese cus ome s is called peddling demand,
which has ye o be known in ad ance. The peddling demand is ealized
a e he la e al ansshipmen is ope a ed. These demands a e o he
e ail and wholesale s o es he company’s ehicles isi along i s ou in
he locali y. Because hese peddling cus ome s a e conside ed less
impo an and he ehicle’s ou e migh some imes di e each day,
unsa is ied peddling demand is conside ed a los sale and associa ed wi h
he los sale cos .
In his pape , we simula e a case s udy o a dis ibu ion ne wo k o
dis ibu ion cen e s (DCs) ha deli e mul iple p oduc s o hei cus-
ome s: local wholesale and e ail s o es. The DCs a e non-iden ical
based on uni cos s, shipping lead imes, and capaci ies. The cos com-
ponen s conside ed in his s udy included in en o y holding cos s,
shipping cos s om he DCs o cus ome s and be ween DCs, and op-
po uni y cos s om unsa is ied demands. We desc ibe he ela ionship
be ween en i ies o he sys em using ma hema ical modeling. Ou main
objec i e is de e mining he in en o y eplenishmen policy he DC
placed on he ac o y ha wo ks wi h he la e al ansshipmen policy.
The sp eadshee model compa es se s o p oposed policies wi h he
cu en ule applied by he case s udy. Ou p oposed policies conside
he sys em’s complexi y unique om p e ious s udies, as depic ed in
Fig. 1.
Fi s , wo ypes o pe iodic o de ing ha he DCs send o he ac o y
a e conside ed. Each DC places a egula o de e e y week, while an
u gen o de wi h a sho e lead ime can be placed daily. Ou in en o y
policy adap s a well-known (R, s, S) con ol o bo h egula and u gen
o de ing. In his (R, s, S) in en o y policy, e e y R in e al, i he in-
en o y le el alls below he e-o de le el, s, an o de is placed o ill up
he o de -up- o le el, S (Visen in e al., 2023). This con ol has p o en o
be e icien in e ms o cos s and p ac ical in ac ual si ua ions (Cab e a
e al., 2013; Esmaili e al., 2019; Johansson e al., 2020; Visen in e al.,
2021). The simplici y o he (R, s, S) policy allows p ac i ione s o apply
i o any a ailable so wa e. Ou p oposed policies include he Basic (R,
s, S) policy and PIP (R, s, S) policy, whe e he la e conside s he
pipeline deli e y in o a eo de decision. Weekly and daily demand da a
a e u ilized wi h hese policies o egula and u gen o de ing.
Second, he DCs con on wo classes o s ochas ic cus ome de-
mands: p e-o de ed and peddling demands. When he demands a e un-
sa is ied, he e will be backlog and los sale cases in he same sys em.
Mos s udies conside each case sepa a ely, while some simila ly handle
he unsa is ied demand om di e en classes. Also, li e a u e ha
conside s peddling demands is sca ce, while his ype o demand exis s in
he business en i onmen . The e o e, ou wo k can ul ill hese esea ch
gaps.
Thi d, we conside bidi ec ional la e al ansshipmen be ween he
DCs. Each pai o dis ibu ion cen e s could eques o be eques ed o
ans e p oduc s based on a decen alized decision scheme. This
ans e is a comple e pooling (Pa e son e al., 2011), whe e he DC i s
akes ca e o hei p e-o de ed demands o he cu en pe iod, and hen
he es o he in en o y can be ans e ed. Ou h ee p oposed la e al
ansshipmen policies a e s aigh o wa d and designed based on he
p esence o he wo s ochas ic demand classes: p e-o de ed and peddling.
In conclusion, his s udy con ibu es o in en o y policy esea ch by
add essing a unique p oblem scope ha occu s in p ac ice. Addi ionally,
he p oposed in en o y policy is simple and can be implemen ed using
sp eadshee so wa e, which is ypically a ailable in mos o ganiza ions.
Mo eo e , he bes se o p oposed egula , u gen , and la e al ans-
shipmen policies was applied o he case s udy o alida e he model
esul s.
2. Li e a u e e iew
The dis ibu ion ne wo k wi h la e al ansshipmen , a unique a ea
o s udy, is cha ac e ized by he numbe o i ems, echelons, and s ock
poin s being conside ed, he iden icalness o he dis ibu ion cen e s,
and he in en o y eplenishmen iming (Pa e son e al., 2011). Apa
om ha , exis ing wo ks ha ela e o he scope o ou s udy can be
iden i ied by he h ee subjec s, which include u iliza ion o la e al
ansshipmen , p ac ice o egula and u gen o de ing, and conside -
a ion o demand classes.
La e al ansshipmen wi hin a dis ibu ion ne wo k in ol es
Demand classes
P e-o de ed demand
La e al ansshipmen
eques
Peddling demand
Cos s associa ed o he
sa is ied demands
T anspo a ion cos
La e al
ansshipmen cos
Peddling
anspo a ion cos
Cos s associa ed o he
unsa is ied demands
Back o de cos
Los sale cos
P opose policies o
Regula o de ing
U gen o de ing
La e al ansshipmen
O de ing ypes Placed o Re iew pe iod Lead ime
Regula Fac o y Weekly L1
U gen Fac o y Daily L
2
La e al Neighbo ing Daily L3
ansshipmen DCs
L1> L2> L3
In en o y holding
cos
Fig. 1. P oblem amewo k.
C. Donjuk e al. The Asian Jou nal o Shipping and Logis ics 41 (2025) 61–74
62
ans e ing in en o y be ween s ock poin s a he same le el o educe
in en o y cos s and imp o e lexibili y and cus ome se ice (Pa e son
e al., 2011). This ans e is made o inc ease in en o y le els in o de o
p e en sho ages. I he ans e occu s be o e demand a i es, i is
conside ed p oac i e la e al ansshipmen . I he ans e is done a e
he demand is known, i is classi ied as eac i e la e al ansshipmen .
These op ions depend on he ansshipmen cos (Pa e son e al., 2011).
S ock poin s in ol ed in he ansshipmen ypically ope a e unde wo
ypes o in en o y pooling: comple e pooling, whe e hey ul ill he
eques based on a ailabili y, and pa ial pooling, whe e hey alloca e
in en o y based on u u e usage. Se e al esea ch s udies ha e p oposed
di e en la e al ansshipmen models. Fo example, Chen and Lu
(2010) compa ed h ee la e al ansshipmen scena ios: non-la e al,
unidi ec ional, and bidi ec ional ansshipmen . Pa ial pooling la e al
ansshipmen occu s when one e aile lacks su icien in en o y and
he o he only ans e s he excess amoun . A pe iodic o de -up- o policy
was applied in egula eplenishmen wi h he ups eam playe . The
esul s indica ed ha bo h unidi ec ional and bidi ec ional ans-
shipmen could educe o al in en o y and inc ease cus ome sa is ac-
ion a es compa ed o he non-la e al ansshipmen scena io, bu only
when he demand a bo h ends is he same. Dhah i e al. (2022) p oposed
a join p oduc ion- ansshipmen con ol policy o a wo-loca ion sys-
em. This sys em allows ansshipmen be ween wo ailu e-p one p o-
duc ion acili ies wi h di e en capaci ies. Kundu and Rossini (2023)
also s udied in en o y eplenishmen policy in a dis ibu ion ne wo k o
mul iple p oduc s. They ound ha la e al ansshipmen combined wi h
a pe iodic deli e y-con inuous eo de policy could educe logis ics
cos s, inc ease deli e y uck sa u a ion, and main ain se ice le els.
Mos esea ch wo ks omi ed u gen o de ing in hei s udies,
al hough in en o y sys ems wi h combina ion o egula and u gen
o de ing a e o en ound in p ac ice (Chiang, 2010). Taga as and Vla-
chos (2001) in oduced a simple ule ha combined an u gen o de ing
wi hin he amilia base s ock policy. The base s ock’s a ge le el was
used o he egula o de o aise he in en o y le el when i is a he
ime o o de , and he in en o y le el is a o below he eo de poin . A
a p e-speci ied poin du ing he egula o de ’s lead ime, i he in-
en o y le el alls below he base s ock’s eo de poin , an u gen o de
is placed a he quan i y ha aises he in en o y le el o he eo de
poin . This ule, which ope a es wi hin he amewo k o he base s ock
policy, does no need any new pa ame e s o he con ol. The ad an-
ages om he base s ock con ol know-how can e icien ly ope a e his
addi ional u gen o de ing in p ac ice. Johansen (2019) also examined a
combina ion o well-known policies. The eo de poin and ixed o de
quan i y we e applied o he egula o de s, while he eo de poin and
a ge s ock le el we e used o he u gen o de s. Ma ko decision
model and neighbo hood sea ch we e used o compu e he combined
policies. Chiang (2010) p oposed a p ac ical me hod by inco po a ing an
u gen o de ea u e in o a s anda d con inuous eo de poin and
ixed-o de quan i y policy. This was achie ed h ough he use o a new
pa ame e , he expedi e-up- o le el. A egula o de is placed once he
in en o y le el eaches he eo de poin . Subsequen ly, he in en o y
le el is checked a a ixed ime. I he in en o y le el is lowe han he
expedi e-up- o le el, an u gen o de is placed o aise he s ock o he
expedi e-up- o le el. Impo an ly, a po ion o he egula o de is
ea ed as an u gen o de . The emaining, which is no expedi ed, a -
i es a a la e ime. This me hod ensu es ha he o al p oduc om
egula and u gen shipmen s emains equal o he ixed o de quan i y,
he eby main aining a s eady supply o in en o y. In ou s udy, we
modi y a amilia (R, s, S) policy o p opose a combined egula and
u gen o de ing policy ha is unique om p e ious a icles. A ci (2019)
in es iga es he e ec o la e al ansshipmen and expedi ed shipping
on dis up ion managemen . A simula ion model and a di e en ial e o-
lu ion algo i hm a e applied o achie e he op imal pa ame e s o e-
aile s’in en o y policies wi h cen alized decision-making.
The impo ance o di e en sou ces o demand in an in en o y sys-
em can a y. Fo example, eques s o spa e pa s due o machine
b eakdowns o p e en i e main enance, as well as o de s om cus-
ome s wi h di e en le els o impo ance, all con ibu e o his classi-
ica ion (Fadılo˘
glu &Bulu , 2010). The e o e, he ea men o cos s o
unsa is ied demands may di e based on hei impo ance o demand
class. Fo ins ance, Malliga junan, (2016) s udy examines a con inuous
in en o y sys em wi h wo demand classes o he Poisson p ocess. In a
s ockou , he unme demand may be conside ed backlogs o los sales,
depending on i s class. Zhou and Zhao (2010) also add ess mul iple
demand classes, ca ego izing hem as ei he backlogs o losses o sales
du ing sho ages. They explain ha o line demand ends no o wai ,
esul ing in los sales, while online demand ends o wai , esul ing in
back o de . The op imal pe iodic eplenishmen o hese demands was a
s a e-dependen (R, s, S) policy. Qu e al. (2022) in es iga e hese ypes
o demands in omnichannel mul i-echelon dis ibu ion ne wo ks. Thei
model also allows eme gency la e al ansshipmen a he s o e le el.
They de eloped a join decision on in en o y eplenishmen and o de
alloca ion o mee online and o line demands by adop ing a gene ic
algo i hm. Howe e , he unme demands o he wo classes a e all
ea ed indi e en ly as los sales. Liao e al. (2020) ocus on he bene i
o eac i e la e al ansshipmen o a single-pe iod decen alized deci-
sion o wo e aile s wi h andom demand swi ching. Cus ome s acing
s ockou a a s o e ha e h ee op ions: wai o la e al ansshipmen
om ano he s o e, swi ch o buy a ano he s o e, o gi e up buying.
The demands could be classi ied as local and swi ched, whe eas he
unme demands a e ea ed simila ly. The la e al ansshipmen eques
om he sho age s o e is as much as a pe cen age o he lack amoun .
an Wijk e al. (2019) p oposed op imal spa e pa s managemen wi h
wo s ock poin s in echnical sys ems based on mul iple demand classes.
The classes a e de ined based on down ime cos s; hus, s ock a ioning is
equi ed when he demand o a spa e pa a i es. The ul illmen op-
ions include using one’s s ocks, eques ing la e al ansshipmen , o
epai ing o o de ing expedi ed shipmen om o he sou ces.
P e ious s udies ha e ye o explo e a dimension simila o ou s,
which includes a join conside a ion o he egula and u gen in en o y
eplenishmen and la e al ansshipmen policies o a dis ibu ion
ne wo k wi h mul iple p oduc s and demand classes as shown in Table 1.
3. Me hods
This esea ch me hodology consis s o ou pa s. In Sec ion 3.1, we
i s desc ibe he ma hema ical ela ionship o he in en o y sys em used
in ou sp eadshee model. Then, in Sec ion 3.2, we p opose ou egula
and u gen in en o y eplenishmen and la e al ansshipmen policies.
The case s udy and he model inpu a e in oduced in Sec ion 3.3 and he
nume ical expe imen se ing is explained in Sec ion 3.4.
3.1. Ma hema ical and sp eadshee modeling
3.1.1. Indices
i, j Dis ibu ion Cen e (DC)
Time
pP oduc
3.1.2. Se s
i* P ima y dis ibu ion cen e
* The e ec i e ime o egula o de ing
3.1.3. Pa ame e s
ω
j
T anspo a ion cos om DC j o he e ail s o es (Cu ency/Uni )
δjT anspo a ion cos o inbound la e al ansshipmen o DC J(Cu ency/
T ip)
(con inued on nex page)
C. Donjuk e al. The Asian Jou nal o Shipping and Logis ics 41 (2025) 61–74
63
Table 1
Li e a u e ela ed o he s udy scope.
A icles Dis ibu ion
ne wo k (Numbe o echelons) (Numbe
o s ock poin s)
Mul iple
p oduc s
/ I ems
Demand classes In en o y eplenishmen
policy
La e al ansshipmen Cos componen s
S udy De ails E ec s om
unme demands
Regula U gen P oac i e Reac i e Pa ial
pooling
Comple e
pooling
Vehicle
capaci y
A ci
(2019)
Yes (2) (N) No No - - Pe iodic Pe iodic ✓✓No Holding; Back
o de ; Pu chase;
La e al; Expedi ed
Bu on
and
Bane jee
(2005)
Yes (2) (N) No No - - Pe iodic No ✓ ✓ ✓ No La e al
Chen and
Lu
(2010)
Yes (2) (2) No No - - Pe iodic No ✓✓No -
Chiang
(2010)
Yes (1) (1) No No - - Con inuous Con inuous - - - - - Fixed o de ing;
Holding
Dhah i
e al.
(2022)
Yes (2) (2): Manu ac u e and e aile s No No - - Pe iodic /
Con inuous
No ✓✓Yes Holding; Back
o de ; Fixed and
a iable la e al
Johansen
(2019)
Yes (1) (1) No No - - Pe iodic Pe iodic - - - - - Fixed and a iable
o de ing; Holding;
Back o de
Kundu and
Rossini
(2023)
Yes (2) (N) Yes No - - Pe iodic /
Con inuous
No ✓✓Yes Holding; La e al
Liao e al.
(2020)
Yes (1) (2) No Yes: 2 Local
demand;
Swi ched
demand
Same Pe iodic
(Single
pe iod)
No ✓ ✓ No P ocu emen ;
La e al
Olsson
(2010)
Yes (1) (N) No No - - Con inuous No ✓ ✓ No Holding; La e al;
Back o de ; Los
sale
Qu e al.
(2022)
Yes (3) (N) No Yes: 2 Online;
O line
Same: Los sale Pe iodic No ✓✓No Replenishmen ;
La e al; Holding;
S ock-ou
an Wijk
e al.
(2019)
No (1) (2): Ad anced echnical sys em No Yes:
Mul iple
High o low
p io i y
Di e en : High o
low cos s o
la e al
ansshipmen
and eme gency
p ocedu e
Con inuous Con inuous ✓ ✓ ✓ No La e al; Eme gency
p ocedu es;
Down imes o he
sys ems
Wei e al.
(2022)
Yes (1) (N) No No - - Pe iodic No ✓✓ ✓ No Holding;
Replenishmen ;
La e al; Penal y o
unsold i ems
This s udy Yes (2) (7) Yes Yes: 3 P e-
o de ing;
Peddling;
La e al
eques
Di e en : Back
o de ; Los sale;
No penal y
Pe iodic:
Weekly
Pe iodic:
Daily
✓ ✓ ✓Yes T anspo a ion o
p e-o de ed and
peddling; Holding;
Back o de ; Los
sale; La e al
C. Donjuk e al. The Asian Jou nal o Shipping and Logis ics 41 (2025) 61–74
64
(con inued)
βpBack o de cos o p oduc p(Cu ency/Uni )
γpLos sale cos o p oduc p(Cu ency/Uni )
α
pIn en o y holding cos o p oduc p(Cu ency /Uni /Uni o ime)
Lj
RRegula deli e y lead ime o DC j(Uni o ime)
Lj
UU gen deli e y lead ime o DC j(Uni o ime)
VCap Maximum capaci y o a ehicle used o deli e y la e al ansshipmen
(Uni /T ip)
3.1.4. In e media y a iables o each p oduc p a DC j a ime
All a iables a e in uni s.
Ej
(p, )Incoming egula deli e y om he ac o y
Fj
(p, )Incoming u gen deli e y om he ac o y
Gj
(p, )A ailabili y a e ecei ing he deli e y om he ac o y
Dj
(p, )Cus ome s’p e-o de s
Tij
(p, )Inbound deli e y o la e al ansshipmen o p oduc p om DC j o he
p ima y DC ia ime
Wj
(p, )A ailabili y a e ecei ing incoming la e al ansshipmen
Jj
(p, )Ou going deli e y o cus ome s’p e-o de s
Bj
(p, )Back o de o p e-o de ed demand
Aj
(p, )A ailabili y a e ou going deli e y o cus ome s’p e-o de s
Mj
(p, )Cus ome peddling demands
Hj
(p, )A ailabili y a e ou going deli e y o peddling demands
Vij
(p, )Ou bound deli e y o la e al ansshipmen o p oduc p om p ima y DC i o
DC ja ime
Nj
(p, )Sa is ied peddling demand
Lj
(p, )Los sales o he peddling demand
Ij
(p, )In en o y le el a he end o pe iod
Rj
Numbe o la e al ansshipmen ips (T ip)
3.1.5. Decision a iables o he in en o y eplenishmen policy o each
p oduc p a DC j a ime
All a iables a e in uni s.
Sj
(p, )Regula o de placed o he ac o y
Uj
(p, )U gen o de placed o he ac o y
Kij
(p, )O de placed by a p ima y DC i o la e al ansshipmen o p oduc p o DC j
a ime
Oij
(p, )O de placed by a mino DC j o la e al ansshipmen o p oduc p o DC ia
ime
3.1.6. The o al cos o he dis ibu ion ne wo k
TC Annual o al cos o he dis ibu ion ne wo k in mone a y uni s includes six
cos e ms:
TRC T anspo a ion cos s o deli e y o p e-o de ed p oduc s om he DCs o he
e aile s;
PC Peddling cos s o deli e y o p oduc s om he DCs o he e aile s o se e
peddling demands;
LTC La e al ansshipmen cos s o deli e y be ween DCs;
BC Back o de cos s o he unme p e-o de ed demands;
LC Los sale cos s o he unme peddling demands;
IC In en o y cos s o holding p oduc s in s ock,
as desc ibed in Eq. (1) and Eq. (2) .
TC =TRC+PC+LTC +BC +LC +IC (1)
TC =∑p∑j
ω
j(∑
Jj
(p, ))+∑p∑j
ω
j(∑
Nj
(p, ))+∑jδj(∑
Rj
)
+∑p∑jβp(∑
Bj
(p, ))+∑p∑jγp(∑
Lj
(p, ))
+∑p∑j
α
p(∑
Ij
(p, ))
(2)
We ema k ha he DCs ha e decen alized decisions and he la e al
ansshipmen cos s a e o ecei ing pa y o pay.
3.1.7. Ma hema ical and Sp eadshee model
The sequence o ac i i ies, decisions, and he low o o de s and
p oduc s a e se in ou model o each DC j o a pa icula p oduc pa
pe iod . These a e depic ed in Fig. 2. A he beginning o each pe iod,
he DC ecei ed incoming deli e ies (Ej
(p, )and/o Fj
(p, )) ha co espond
o o de s ha had been placed as ei he egula o de s (Sj
(p, )) in Eq. (3) o
as u gen o de s (Uj
(p, )) in Eq. (4). Then, he in en o y le els a e upda ed
by Eq. (5).
The p ima y DC has he p io i y in placing a la e al ansshipmen
eques wi h a neighbo ing DC. The eques will only be made when i s
s ock canno sa is y p e-o de demand. The ecei ing la e al deli e y
(Tij
(p, )), howe e , depends on he a ailabili y o he pa ne DC, as shown
in Eq. (6).
The p ima y DC upda es i s in en o y again (Eq. (7)) be o e dis-
pa ching i s deli e y o he e aile s. The p e-o de demand is se ed
i s (Eq. (8)). Then, he p ima y DC upda es i s s ock (Eq. (11)) and
se es he peddling demand (Eq. (13)).
Fo he mino DC, i s p e-o de demand is se ed be o e deciding he
ansshipmen o he p ima y DC’s eques (Eq. (9)). Subsequen ly, he
mino DC places a la e al eques o he p ima y DC a e all o he
p ima y DC’s demands ha e al eady been handled. This eques could be
esponded o i he p ima y DC did no place any la e al eques in his
pe iod. The incoming deli e y o he la e al ansshipmen o he mino
DC is calcula ed by Eq. (17). A e upda ing i s s ock (Eq. (12)), he
mino DC se es he peddling demands (Eq. (14)). We assume ha all
a ailable s ock om he DC se es he peddling demand.
The backlog o he p e-o de demand is calcula ed by Eq. (10), while
he los sale o he peddling demand ollows Eq. (15).
Finally, he in en o y le el a he end o each pe iod, igh be o e
placing any o de wi h he ac o y, is p esen ed by Eq. (16),Eq. (18), and
Eq. (19). I is assumed ha he ac o y will ully sa is y all o de s ha he
DC places.
All p oduc s sha e he ehicle. Each la e al ansshipmen ip canno
be la ge han he ehicle’s capaci y, and he numbe o ips equi ed is
calcula ed om Eq. (20).
Ej
(p, )=Sj
(p, −Lj
R),∀j,p, (3)
Fj
(p, )=Uj
(p, −Lj
U),∀j,p, (4)
Gj
(p, )=Ej
(p, )+Fj
(p, )+Ij
(p, −1),∀j,p, (5)
Tij
(p, )=⎧
⎨
⎩
Kij
(p, ),Kij
(p, )≤Gj
(p, )−Jj
(p, )
Gj
(p, )−Jj
(p, ),else ,∀i∈i∗,j,p, (6)
Wj
(p, )=Gj
(p, )+Tij
(p, ),∀j∈i∗,p, (7)
Jj
(p, )=⎧
⎨
⎩
Dj
(p, ),Dj
(p, )≤Wj
(p, )
Wj
(p, ),else ,∀j∈i∗,p, (8)
Jj
(p, )=⎧
⎨
⎩
Dj
(p, ),Dj
(p, )≤Gj
(p, )
Gj
(p, ),else ,∀j∕∈ i∗,p, (9)
Bj
(p, )=Dj
(p, )−Jj
(p, ),∀j,p, (10)
Aj
(p, )=Wj
(p, )−Jj
(p, ),∀j∈i∗,p, (11)
C. Donjuk e al. The Asian Jou nal o Shipping and Logis ics 41 (2025) 61–74
65
Aj
(p, )=Gj
(p, )−Jj
(p, ),∀j∕∈ i∗,p, (12)
Nj
(p, )=⎧
⎨
⎩
Mj
(p, ),Mj
(p, )≤Aj
(p, )
Aj
(p, ),else ,∀j∈i∗,p, (13)
Nj
(p, )=⎧
⎨
⎩
Mj
(p, ),Mj
(p, )≤Aj
(p, )−Tij
(p, )+Vij
(p, )
Aj
(p, )−Tij
(p, )+Vij
(p, ),else ,∀j∕∈ i∗,p,
(14)
Lj
(p, )=Mj
(p, )−Nj
(p, ),∀j,p, (15)
Hj
(p, )=Aj
(p, )−Nj
(p, ),∀j,p, (16)
Vij
(p, )=⎧
⎨
⎩
Oij
(p, ),Oij
(p, )≤Hi
(p, )
Hi
(p, ),else ,∀j∕∈ i∗,p, (17)
Ij
(p, )=Hj
(p, )−Vij
(p, ),∀j∈i∗,p, (18)
Fo each DC j, p oduc p, and ime
Recei e incoming egula (E
j
(p, )
)
and/o u gen (F
j
(p, )
) deli e y
om he ac o y
Requi e la e al
ansshipmen ?
Calcula e los sale
(L
j
(p, )
)
Yes
No
Calcula e back o de
(B
j
(p, )
)
Upda e s ock a ailabili y (G
j
(p, )
)
O de o la e al
ansshipmen (K
ij
(p, )
)
Inbound deli e y o
la e al ansshipmen
(T
ij
(p, )
)
Upda e s ock a ailabili y (W
j
(p, )
)
La e al eques om
ano he DC (O
ij
(p, )
)
Incoming la e al
ansshipmen eques ?
Ou bound la e al
ansshipmen (V
ij
(p, )
)
Place egula o de (S
j
(p, )
)
o U gen o de (U
j
(p, )
)
Yes
No
Deli e y p e-o de (J
j
(p, )
)
o cus ome
Upda e s ock a ailabili y (A
j
(p, )
)
Deli e y peddle (N
j
(p, )
)
deli e y o cus ome
Upda e s ock a ailabili y (H
j
(p, )
)
Upda e s ock a ailabili y (I
j
(p, )
)
Fac o y
S a
End
Fig. 2. Flow diag am o he sp eadshee model.
C. Donjuk e al. The Asian Jou nal o Shipping and Logis ics 41 (2025) 61–74
66
Ij
(p, )=Hj
(p, ),∀j∕∈ i∗,p, (19)
Rj
=⌈∑
p
Tij
(p, )
VCap ⌉,∀j, (20)
3.2. P oposed in en o y eplenishmen and la e al ansshipmen policies
3.2.1. Nomencla u e o he in en o y eplenishmen policy o each DC j
and p oduc p
Sj
(p,week)Ta ge in en o y le el o egula o de ing (uni )
sj
(p,week)Re-o de poin o egula o de ing (uni )
Dj
(p,week)A e age demand calcula ed om pas weekly da a (uni /week)
Sj
D(p,week)The s anda d de ia ion o he demand calcula ed om pas weekly da a
(uni /week)
R(p,week)Re iew pe iod o egula o de ing (week)
CSL Desi ed cycle se ice le el [0,1] (Chop a &Meindl, 2007)
F−1
s(.)The in e se o he s anda d no mal dis ibu ion
Sj
(p,day)Ta ge in en o y le el o u gen o de ing (uni )
sj
(p,day)Re-o de poin o u gen o de ing (uni )
Dj
(p,day)A e age demand calcula ed om pas daily da a (uni /day)
Sj
D(p,day)The s anda d de ia ion o he demand calcula ed om a se o pas daily
da a (uni /day)
R(p,day)Re iew pe iod o u gen o de ing (day)
π
Numbe o wo king days in a week (day)
3.2.2. P oposed policies
3.2.2.1. Regula o de ing (Sj
(p, ))
Basic (R, s, S) Policy. The Basic (R, s, S) Policy placed an o de o
aise he in en o y le el o he a ge le el (Sj
(p,week)). The egula o de
can be placed only a he speci ic ime ( ∗), and when he in en o y le el
is a o below he e-o de poin (sj
(p,week)), as in Eq. (21). The a ge le el
and e-o de poin a e calcula ed by Eq. (22) and Eq. (23), espec i ely.
Sj
(p, )={Sj
(p,week)−Ij
(p, ),Ij
(p, )≤sj
(p,week)
0,else ,∀j,p, ∈ ∗(21)
Sj
(p,week)=Dj
(p,week)•(Lj
R+R(p,week))+F−1
s(CSL) •
Lj
R
åSj
D(p,week),∀j,p
(22)
sj
(p,week)=Dj
(p,week)•(Lj
R)+F−1
s(CSL) •
Lj
R
åSj
D(p,week),∀j,p(23)
PIP (R, s, S) Policy. The PIP (R, s, S) Policy ope a es he same way as
he Basic (R, s, S); excep he condi ion o e-o de ing is adjus ed by
conside ing pipeline in en o y. The pipeline in en o y is he o de ha
has al eady been placed bu no ye ecei ed. In ou policy, we conside
he pipeline in en o y ha is expec ed o be ecei ed by he DC in he
nex pe iod and e e s o hem as PIP. Thus, i he cu en pe iod is , he
PIP will be a i ed a pe iod +1. In o he wo ds, his PIP is a egula
o de o he ac o y ha has been placed a ime −Lj
R+1 and/o an
u gen o de placed a ime −Lj
U+1. Fo Lj
Rand Lj
U ha a e less han
o equal o one, he PIP o he calcula ion is ze o. The PIP (R, s, S) Policy
is desc ibed by Eq. (24).
Sj
(p, )=⎧
⎨
⎩
Sj
(p,week)−Ij
(p, ),Ij
(p, )+Sj
(p, −Lj
R+1)+Uj
(p, −Lj
U+1)≤sj
(p,week)
0,else ,∀j,p, ∈ ∗
(24)
3.2.2.2. U gen o de ing (Uj
(p, )).U gen o de s can be placed daily.
Again, we applied he Basic (R, s, S) Policy and PIP (R, s, S) Policy ha
conside ed he daily da a o demands as shown in Eq. (25) and Eq. (28),
espec i ely. We ema k ha his u gen o de can only be placed i he
egula o de has no been placed wi hin ha pe iod.
Basic (R, s, S) Policy
Uj
(p, )={Sj
(p,day)−Ij
(p, ),Ij
(p, )≤sj
(p,day)and Sj
(p, )=0
0,else ,∀j,p, (25)
Sj
(p,day)=Dj
(p,day)•(Lj
U+R(p,day))+F−1
s(CSL) •
Lj
U
åSj
D(p,day),∀j,p(26)
sj
(p,day)=Dj
(p,day)•(Lj
U)+F−1
s(CSL) •
Lj
U
åSj
D(p,day),∀j,p(27)
PIP (R, s, S) Policy. Again o Lj
Rand Lj
U ha a e less han o equal o
one, he PIP o he calcula ion is ze o.
Fig. 3 depic s how he Basic (R, s, S) policy o egula and u gen
o de ing wo k. The u gen o de ing is e iewed daily; he aised
amoun s aand ca e o u gen o de s, Uj
(p, ). The egula o de ing is
e iewed weekly; bis he amoun o a egula o de , Sj
(p, ).
Fig. 4 p esen s he applica ion o he PIP (R, s, S) policy o egula
and u gen o de ing. The u gen o de s, Uj
(p, ), a e aand c. The egula
o de , Sj
(p, ), is b. I he Basic (R, s, S) policy is applied he ein, he numbe
o o de s will be 5 imes ins ead o 3. Thus, he conside a ion o pipeline
in en o y in he PIP (R, s, S) policy educes he numbe o o de s and he
a e age in en o y le el.
3.2.2.3. La e al ansshipmen o de ing (Kij
(p, )and Oij
(p, )). The DC can
place a la e al ansshipmen o de o i s neighbo ing DCs daily. The
la e al ansshipmen o de will be esponded o acco ding o he
a ailabili y o he o he DCs. The e a e p ima y DCs ha ha e mo e
p io i y han he o he DCs and ha e a chance o place he la e al
ansshipmen o de i s .
The o de ing ules ha e been in en ionally designed o simplici y,
making hem easy o inco po a e in o a sp eadshee . This s aigh o -
wa d app oach empowe s small and medium en e p ises, gi ing hem
he con idence o apply hese ules o hei sp eadshee s easily.
We ocused on sa is ying p e-o de ed demands gene ally om he
company’s egula cus ome s. The e o e, he la e al o de would be
placed only when he a ailable amoun a he beginning o he pe iod is
Uj
(p, )=⎧
⎨
⎩
Sj
(p,day)−Ij
(p, ),Ij
(p, )+Sj
(p, −Lj
R+1)+Uj
(p, −Lj
U+1)≤sj
(p,day)and Sj
(p, )=0
0,else ,∀j,p, (28)
C. Donjuk e al. The Asian Jou nal o Shipping and Logis ics 41 (2025) 61–74
67
insu icien o he p e-o de ed demands, Di
(p, )>Gi
(p, ).
“As much”: The 1s la e al ansshipmen ule o de s he amoun o
ul ill he p e-o de ed demand, as in Eq. (29).
Kij
(p, )=Di
(p, )−Gi
(p, ),∀i∈i∗,p, (29)
“A e age p e-o de ed”: The 2nd la e al ule o de s he amoun equal
o he mo ing a e age o he daily p e-o de ed demand o he pas week,
as desc ibed in Eq. (30).
Kij
(p, )=∑
k=
π
k=1
Di
(p, −k)
π
,∀i∈i∗,p, (30)
“A e age all”: The 3 d la e al ule o de s an amoun equal o he
mo ing a e age o he daily o al demand o he pas week. This o al
demand consis s o p e-o de ed and peddling demands, as desc ibed in
Eq. (31).
Kij
(p, )=∑
k=
π
k=1(Di
(p, −k)+Mi
(p, −k))
π
,∀i∈i∗,p, (31)
The mino DCs apply he same ule o la e al o de ing, (Oij
(p, )), bu
his o de can be conside ed a e he p ima y DC la e al ansshipmen
decision.
3.3. Ou case s udy and pa ame e se ing
Ou simula ion se ing and inpu s a e based on a case s udy. This case
s udy is a dis ibu ion ne wo k o a bo led so d ink business
comp ising se en DCs se ing app oxima ely 8,000 local wholesale and
e ail s o es in se e al ci ies in he no h o Thailand.
All DCs place hei egula o de s o a ac o y e e y Wednesday. The
deli e y will be ecei ed a he DC in ou wo king days. The DCs
cu en ly use pas sale igu es o decide he o de amoun . Fo each
p oduc , he a e age sales in he las mon h o his yea and he p e ious
yea a e used o his mon h’s o de . The mon hly igu e is di ided by
ou o i e o ge he amoun o weekly egula o de s. An u gen o de
can be placed any day du ing he week. The company does no ha e a
ixed ule o his u gen o de . Based on ou in e iew wi h he manage
and in es iga ion o he eco d, ou model assumes ha an u gen o de
is placed acco ding o a eo de poin and ixed o de quan i y policy.
The pa ame e s we e se based on he company’s pas wo-yea sales
da a.
Eme gency la e al ansshipmen is allowed be ween DCs in a
neighbo ing a ea, as shown in Fig. 5. The eques ed amoun is gene ally
jus enough o ul ill he p e-o de equi ed o ha day. The e a e h ee
g oups o DCs. In each g oup, we lis he DC by i s p io i y o la e al
o de ing, which is based on hei maximum capaci y, i.e.:
1. Chiang Rai and Phayao.
2. U a adi , Ph ae, and Nan.
3. Phe chabun (Ci y b anch) and Phe chabun (Bueng Sampan b anch).
Two-yea sales da a o 64 p oduc s we e collec ed o p e-o de ed
and peddling demands. We anked he p oduc s by he o al alue,
esul ing in he op p oduc s wi h 80 % cumula i e alue while he
cumula i e olume eached 50 %. Thus, ou model ocused only on
hese p oduc s, p={1, 2, 3, 4, 5}. The uck capaci y (VCap) was
calcula ed o hese i e p oduc s by a pe cen age o he o al olume.
Pa ame e s se ing:
Lj
R=4 days o 4/6 week, o all DC j
Lj
U=1 day o Phe chabun (Ci y b anch) and Phe chabun (Bueng
Fig. 3. P oposed Basic (R, s, S) policy o egula and u gen o de ing.
C. Donjuk e al. The Asian Jou nal o Shipping and Logis ics 41 (2025) 61–74
68
