Gö ges, Michael; F ei ag, Michael
Con e ence Pape
Modeling au onomously con olled au omobile e minal
p ocesses
P o ided in Coope a ion wi h:
Hambu g Uni e si y o Technology (TUHH), Ins i u e o Business Logis ics and Gene al
Managemen
Sugges ed Ci a ion: Gö ges, Michael; F ei ag, Michael (2019) : Modeling au onomously con olled
au omobile e minal p ocesses, In: Jahn, Ca los Ke s en, Wol gang Ringle, Ch is ian M. (Ed.): Digi al
T ans o ma ion in Ma i ime and Ci y Logis ics: Sma Solu ions o Logis ics. P oceedings o he
Hambu g In e na ional Con e ence o Logis ics (HICL), Vol. 28, ISBN 978-3-7502-4949-3, epubli
GmbH, Be lin, pp. 186-214,
h ps://doi.o g/10.15480/882.2497
This Ve sion is a ailable a :
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P oceedings o he Hambu g In e na ional Con e ence o Logis ics (HICL) – 28
Michael Gö ges and Michael F ei ag
Modeling Au onomously Con olled
Au omobile Te minal P ocesses
Published in: Digi al T ans o ma ion in Ma i ime and Ci y Logis ics
Ca los Jahn, Wol gang Ke s en and Ch is ian M. Ringle (Eds.)
Sep embe 2019,epubli
CC-BY-SA4.0
Modeling Au onomously Con olled Au omobile
Te minal P ocesses
Michael Gö ges1 and Michael F ei ag2
1 – BLG LOGISTICS GROUP AG & Co. KG
2 – BIBA – B eme Ins i u ü P oduk ion und Logis ik GmbH
Pu pose: Au omobile e minals play an essen ial ole in au omo i e supply chains.
Due o sho planning cycles and ola ile planning in o ma ion, he ya d assignmen
de e mines e minals pe o mance. Exis ing planning app oaches a e no able o
cope wi h hese dynamics. This con ibu ion p oposes a no el bio-analogue au ono-
mous con ol me hod o ace hese dynamics, i s e ec s and o imp o e he e mi-
nals pe o mance.
Me hodology: Causes o in e nal and ex e nal e minals dynamics will be discussed
and an au onomous con ol me hod will be de i ed. A gene ic 185a ame e izable au-
omobile e minal model and i s implemen a ion o a disc e e e en simula ion will
be in oduced in his pape . This simula ion is used o compa e he new app oach o
classical ya d assignmen .
Findings: This pape con ibu es o he heo e ical unde s anding o causes and e -
ec s o dynamics in he con ex o au omobile e minals. I will show ha au ono-
mous con ol ou pe o ms classical app oaches unde highly dynamic condi ions.
O iginali y: The gene ic modelling app oach is a no el desc ip ion o au omobile
e minals. I allows in es iga ions o a b oad spec um o use cases. Mo eo e , he
bio-analogue au onomous con ol o au omobile e minals is an inno a i e ap-
p oach.
Keywo ds: Au omobile Logis ics, Po Te minal, Au onomous Con ol, Disc e e
E en Simula ion
Fi s ecei ed: 08.May.2019 Re ised: 27.May.2019 Accep ed: 11.June.2019
186 Michael Gö ges and Michael F ei ag
1 In oduc ion
Du ing he ecen yea s, he shipmen olume o inished ca s inc eased
cons an ly, due o an eme ging global in e connec ion be ween p oduc ion
and dis ibu ion ne wo ks. In his con ex , au omobile e minals a e cen al
elemen s in in e na ional au omo i e supply chains. Au omobile e minals
allow he ansshipmen om he p oduc ion plan o he a ge ma ke s.
Besides handling o inished ca s om di e en anspo modes (e.g., ship
o uck), hese e minals usually o e a b oad spec um o addi ional ech-
nical se ices in o de o mee cus ome s’ demands in he po o des ina-
ion. In gene al, he main asks o au omobile e minals can be de ined as
handling, echnical ea men and s o age o inished ehicles (Ma eld,
2006; Böse and Pio owski, 2009). All ela ed p ocesses a e igge ed di-
ec ly by he ca manu ac u e s (OEM). Acco dingly, au omobile e minals
can be in e p e ed as a classical decoupling poin in he au omo i e supply
chain, which allows o eac lexibly o demand luc ua ions (Dias, Calado
and Mendonça, 2010). Hence, planning o p ocesses au omobile e minals
is aced wi h o ecas -d i en and cus ome -o de d i en p ocesses a he
same ime. This s ongly a ec s he ya d mas e planning, which aims a
minimizing he dis ance be ween he poin o ca en ance, s o age a ea
and i s exi poin (Gö ges and F ei ag, 2019). Classical mas e planning ap-
p oaches sol e his ask by assigning p ede ined pa king a eas o he di e -
en ehicle ypes (e.g. so ed by manu ac u e , model and des ina ion). This
leads o good planning esul s o si ua ions wi h high o ecas quali y and
less dynamics. Howe e , due o i s long e m o ien a ion, his ype o ya d
Modeling Au onomously Con olled Au omobile Te minal P ocesses 187
mas e planning is p one o o ecas de ia ions, ola ile pa ame e a ia-
ions and un o eseen e en s, which may a ec he e minals pe o mance
nega i ely (Co deau e al., 2011; Ma eld and O h, 2006).
Au onomous con ol o logis ics p ocesses add ess hese sho comings by
ans e ing decision making capabili ies om a cen alized planning in-
s ance o he logis ics objec i sel . Due o in e ac ions and decision making
o in elligen logis ics objec s, au onomous con ol aims a c ea ing sel -o -
ganizing sys ems beha io , which inc eases he sys ems pe o mance
(Wind and Hülsmann, 2007). This sel -o ganiza ion can be seen as eme -
gen beha io o a complex dynamic sys em, which is no a cha ac e is ic o
he sys ems elemen s bu o he o al sys em (Vaa io and Ueda, 1998). Fo
p oduc ion logis ics, di e en au onomous con ol s a egies showed al-
eady hei ope a ional po en ial. In he con ex o au omobile e minals,
i s implemen a ions indica ed p omising esul s conce ning he assign-
men o ca s in impo p ocesses o echnical se ice s a ions (Böse and Pi-
o owski, 2009). Howe e , comp ehensi e au onomous con ol s a egies
co e ing all inbound and ou bound ma e ial lows o an au omobile e mi-
nal a e s ill missing. Thus, his pape will ocus a b oade use case. I will
de i e an au onomous con ol s a egy, which allows he in eg a ion all
lows o ca s (impo , expo and in e e minal) a an au omobile e minal.
In o de o analyze he pe o mance o he au onomous con ol s a egy,
his pape will p esen a gene ic modeling app oach o in es iga ing a
b oad ange o ela ed scena ios. Fu he mo e, i will in oduce a disc e e
e en simula ion model implemen a ion o analyzing hese scena ios. This
simula ion model will be used o in es iga e he pe o mance o he de i ed
au onomous con ol me hod compa ed o a classical ya d mas e plan.
188 Michael Gö ges and Michael F ei ag
2 Au onomous Con ol o Au omobile Te minals
2.1 Te minal Planning
Ma e ial lows in au omobile e minals can be cha ac e ized as a sequence
o se e al gene ic sub p ocesses (e.g. loading o s o age ope a ions). Basi-
cally, e e y p ocess s a s wi h unloading ope a ions om di e en
anspo ca ie s ( uck, ail, ship) ollowed by he s o age o he ehicle.
Subsequen ly, ca s a e loaded o ou bound anspo ca ie s o ecei e
one o mo e echnical se ices. Au omobile e minals o e a b oad spec-
um o echnical se ices wi h highly a ying p ocess imes (Ho -Ho -
meye -Zlo nik e al., 2017). Figu e 1 depic s his physical ma e ial low o
ehicles a an au omobile e minal. Fu he mo e, i shows he ela ed plan-
ning asks in espec o hei empo al occu ence (planning ho izon). The
o e all objec i e o all planning asks is he e icien ope a ion o all physi-
cal ehicle mo emen s om he sou ce (i.e. unloading poin a he e mi-
nal) o he sink (i.e. loading poin )(Özkan, Nas and Güle , 2016). On a s a-
egic le el, planning ocuses on long e m decisions like he planning o in-
as uc u e (e.g. addi ional be h o ya d ex ensions). Fo ecas ing o ex-
pec ed ehicle olumes and ela ed long- e m planning o esou ces be-
long o his s a egic ime ho izon as well. Based on hese o ecas s, a long
e m o ien a ed a ea mas e planning de i es equi ed pa king a eas
(Ma eld, 2006). A esul o his planning s ep is a ough assignmen o es i-
ma ed ehicle olumes o pa king a eas. This i s assignmen is he s a -
ing poin o he asks on he ac ical planning ho izon. In his planning
phase, o ecas ed ehicle olumes a e used o plan be hs and he u iliza-
ions o be hs (Dias, Calado and Mendonça, 2010). Usually, o ecas s be-
Modeling Au onomously Con olled Au omobile Te minal P ocesses 189
come mo e p ecise and ge a highe le el o de ail wi h mo e speci ic in o -
ma ion (e.g. model-des ina ion spli o olume ela ed model-spli ). The e-
sul s o he s a egic planning is used in he ac ical planning o gene a e
and adjus he ya d plan. The ya d plan comp ises he assignmen o ehi-
cle olumes o speci ic a eas o he ya d. In o de o gene a e sho ou es
be ween he loading and unloading loca ions, he ya d planning o en in-
cludes he localiza ion o loading and unloading ope a ions (be h alloca-
ion planning, s o age space pa i ioning and s o age a ea design)
(Ma eld, 2006; Ma eld and O h, 2006). The pe sonnel equi emen can
be de i ed wi h he esul s o localiza ion and ehicle assignmen . In gen-
e al, he ope a ional planning is cha ac e ized by inc easing le el o ele-
an in o ma ion (e.g. ETA o ships o he assignmen o ca s o ships). On
his ope a ional planning le el, he esul s o ac ical planning a e e ined
in p ede ined u ns o wi h a olling ime ho izon (Ma eld and Kop e ,
2003). This app oach allows o eac o changes and ex e nal dis u bances
(e.g. delay o ships o changes in ships anspo quan i ies).
190 Michael Gö ges and Michael F ei ag
Figu e 1: e minals planning ask – based on (Gö ges and F ei ag, 2019)
These plan adjus men s may lead o changes o ou es leng h be ween in-
bound loca ions, s o age a eas and ou bound loca ions and a ec he o e -
all e minals p oduc i i y and he pe sonal equi emen s. The p ocess con-
ol ocuses on he execu ion o pa icula d i ing o de s esul ing om he
p e ious planning asks. I assigns d i ing o de s o wo ke s and moni o s
he p og ess o o de p ocessing
Ya d planning plays a key ole in he desc ibed, cascaded planning p ocess.
I mainly de e mines d i ing dis ances be ween ca s’ a i al and depa u e
poin s and he ela ed p ocess p oduc i i y (i.e. ca s pe hou pe wo ke ).
Incoming ehicles a e so ed and assigned o pa king lo s acco ding o he
ya d mas e plan. A he a i al o a ehicle, usually he in o ma ion abou
i s ou going anspo ca ie is no a ailable. La e , he cus ome (e.g.
OEM) sends ad ices o pa icula ca s, assigning hem, o example, o a
speci ic ship. Dias e al. (2010) desc ibe his cha ac e is ic as pa allel push
ail
ship
uck
ail
ship
uck
Te minal
ma e ial low
ou bound p ocesses
s o age and echnical ea men
Vehicle
ake-o e
ehicle
s oa age
echnical
se ices
ehicle
ake-o
physical ma e ial
low
inbound p ocesses
p ocess planning and con ol
p ocess
con ol
sequencing o d i ing
o de s
assignmen o d i ing
o de s
ca ie assignmen ca ie assignmen
Planning ask
ope a ional
planning
ac ical
planning
s a egic
planning
ya d assignmen
pe sonal and esou ce planning
planning o a ea and echnical esou ces
be h planning
be h
assigmen
pe sonal
and
esou ce
planning
o ecas ing and olume planning
ya d mas e planning
planning o in as uc u e
capaci y planning
ya d planning
unloading
localiza ion
be h
assigmen
pe sonal
and
esou ce
planning
be h planning
unloading
localiza ion
Modeling Au onomously Con olled Au omobile Te minal P ocesses 191
and pull p ocesses occu ing a he same ime a an au omobile e minal
(Dias, Calado and Mendonça, 2010). These pa allel push and pull p ocesses
allow e minals o eac quickly o changing demands in he supply chain.
Howe e , his also leads o complex in e nal dynamics in he e minals p o-
cesses and sho planning ime ho izons. Classical ya d planning add esses
he o de s’ neu al ( o ecas -d i en) aspec . Volumes o ehicles a e as-
signed o speci ic pa king a eas o he e minal based on o ecas s. A e
cus ome o de s a e a ailable, he ope a ional planning (e.g., be h plan-
ning) aims a inc easing he e minals p oduc i i y by educing dis ances
be ween s o age a ea o he ca s and he ou going anspo ca ie (e.g.,
by assigning ships o quay posi ions). Figu e 2 depic s bo h push and pull
p ocesses o au omobile e minals and ela es hem o he planning asks.
In his con ex , e minals o e a highe deg ee o lexibili y o he en i e sup-
ply chain a expense o an inc easing complexi y o he e minals’ planning
and i s ope a i e p ocess execu ion. In his con ex , he ya d planning is a
key ins umen o cope wi h o ecas ed ehicle olumes and o alloca e i
o pa king a eas.
Acco dingly, i de e mines ou es o ehicles om he sou ce o he sink on
he e minal. Due o he o de -na u al na u e o he a i al p ocess, he ya d
planning canno eac o nea - e m changes (e.g., inc easing o dec easing
ehicle olumes). An inc easing deg ee o lexibili y and dynamical adjus -
men o ya d assignmen s may inc ease he e minals’ pe o mance
(Gö ges and F ei ag, 2019).
198 Michael Gö ges and Michael F ei ag
Figu e 4: a i als o OEM 1 & OEM2 ( op); o al a i als (bo om)
Table 2: in en o y imes
OEM 1 - M1 OEM 1 - M2 OEM 2 - M3 OEM 2 - M4
a g. in en o y ime [d] 10 20 10 20
a iance [d] 2 2 2 2
The depa u e o ehicles is modelled in wo di e en a ian s. The i s a -
ian uses simple cons an in en o y imes modelled by adding a no mal dis-
ibu ed delay o he a i al ime o each ehicle. Acco dingly, ca s lea e he
e minal a e a p ede ined ime. Table 2 summa izes he unde lying depa -
u e a es.
Modeling Au onomously Con olled Au omobile Te minal P ocesses 199
The second a ian models he depa u e o ca s in a mo e ealis ic way. In
his a ian ships sailing o des ina ion D1 and D2 a e gene a ed as a ime
se ies wi h a no mal dis ibu ed shipmen olume pe essel.
Figu e 5: in en o y o e ime: a g. 600 ca s pe ship ( op); a g. 2000 ca s
pe ship (bo om) o bulked depa u es
The ships a i ing a he e minal ha e an a e age capaci y based on a no -
mal dis ibu ion. This leads o a bulked depa u e o ca s o e ime. In his
scena io, he a e age ships' capaci y 𝑠 will be a ied om 500 o 2000 wi h
a s anda d de ia ion o 10% o he mean alue. Figu e 5 shows he es i-
ma ed in en o y o e ime o di e en mean ships capaci ies. I shows ha
he mean ships pa ame e 𝑠 has an impac on he dynamic o he in en o y
ime se ies. Compa able in en o y cu es can be obse ed in eal au omo-
bile e minals. This scena io comp ises acco ding o he sinusoidal inpu s,
he ini ial e minals in en o y and he ou pu a es (see Table 1 and Table
0
500
1000
1500
2000
2500
3000
50 100 150 200 250 300 350
in en o y [ca s]
ime [d]
OEM 1 - M 1
OEM 2 - M 3
0
500
1000
1500
2000
2500
3000
3500
4000
50 100 150 200 250 300 350
in en o y [ca s]
ime [d]
OEM 1 - M 1
OEM 2 - M 3
200 Michael Gö ges and Michael F ei ag
2) app oxima ely 127.000 ehicles unning h ough his scena io in 365
days.
In he 4x4 scaled scena io he e a e h ee sou ces and h ee sinks. The lo-
ca ions o sou ces and sinks will be add essed in de ail in sec ion 4.1 (Figu e
6 summa izes hei loca ions). The spli o ou going olumes o bo h OEMs
is modelled as ollows: A sou ce 1 75% o OEM 1's olume a i e. A sou ce
2 25% o OEM 1's and 25 % o OEM 2's olumes a i e and a sou ce 3 75%
o OEM 2's olume a i es. 75% o all ships sailing o des ina ion 1 lea e
om sink 1, 20% om sink 2 and 5% om sink 3. Fo des ina ion 2 75% lea e
om sink 3, 20% om sink 2 and 5% om sink 1.
4 Ya d Assignmen Me hods
4.1 Con en ional Ya d Assignmen
Based on hese in o ma ion a simple planning and assignmen o ca s o
pa king a eas has been done. Figu e 6 shows hese assignmen s. The main
conce n o his assignmen is o gene a e sho ou es be ween sou ces,
s o age a eas and sinks. Fo example mos ca s o OEM 1 will a i e a
sou ce 1 and lea e a all sinks. Thus, he assignmen s a e close o sou ce 1.
Usually, di e en models om one OEM may be mixed when he e minals
u iliza ion is high. Thus, Figu e 6 shows he p ima y assignmen o ca s and
a seconda y assignmen in b acke s. The seconda y assignmen can only
be used i no ee ow o he p ima y assignmen is a ailable. These assign-
men s a e conside ed as esul s o a classical planning p ocess in he ol-
lowing e alua ion.
Modeling Au onomously Con olled Au omobile Te minal P ocesses 201
Figu e 6: classical ya d assignmen
Fo he pu pose o benchma king a andomized assignmen will also be
used. In his case a i ing ca s a e assigned o a andomly chosen ow on
he e minal. Only capaci y es ic ions o a ow ha e o be me .
4.2 Phe omone Based Au onomous Con ol App oach
The au onomous con ol me hod p esen ed in his sec ion allows ca s o
e alua e, o compa e and o choose a pa king ow by a phe omone based
app oach, which is inspi ed by an 's na u al o aging beha io . As depic ed
ea lie , bounded a ional s a egies like his o e he possibili y o conside
many di e en decision pa ame e s. The me hod a hand can be seen as a
combined me hod, using bounded a ional aspec s and a ional measu es.
Phe omone based app oaches ha e shown hei capabili y o eac on dy-
namical changes and o s abilize he sys ems beha io unde ola ile con-
di ions (Wind e al., 2010). Acco dingly, his app oach seems o be sui able
OEM 1 M2
OEM 1 –M1
OEM 1 M1
OEM 1 –M2
OEM 1 M1
OEM 1 –M2
OEM 1 M2
OEM 1 –M2
OEM 1 M2
OEM 1 –M1
OEM 1 M2
OEM 1 –M1
OEM 1 M1
OEM 1 –M2 OEM 1 M2
OEM 1 –M1
OEM 2 M3
OEM 2 –M4
OEM 2 M3
OEM 2 –M4
OEM 2 M3
OEM 2 –M4
OEM2 M3
OEM 2 – M4
OEM 2 M4
OEM 2 –M3
OEM 2 M4
OEM 2 –M3
OEM 2 M4
OEM 2 –M3
OEM 2 M4
OEM 2 –M3
sink 3 sin
k
2 sin
k
1
sou ce1 sou ce2 sou ce3
202 Michael Gö ges and Michael F ei ag
o he ehicles ya d assignmen a an au omobile e minal. In gene al phe-
nome based me hods imi a e communica ion p inciples o social insec s
(i.e. an s). While sea ching o ood, an s lea e e apo a ing phe omone
ails, ma king possible ou es o ood sou ces. O he an s a e a ac ed by
hese ails and ollow i . An s ollowing a ail inc ease he phe omone con-
cen a ion. The phe omone concen a ion dec eases in ime due o he na -
u al e apo a ion p ocess. By using his in e play be ween ma king ails
wi h phe omones on he one hand and na u al e apo a ion p ocess on he
o he hand, an s a e able o ind he sho es ou es o ood sou ces. Au on-
omous con ol me hods using his p inciple lea e ele an in o ma ion in
he sys em (e.g. h oughpu imes) as an a i icial phe omone. Subsequen
objec s a e able o ead his phe omone in o ma ion o make a local deci-
sion on his basis and o ollow he ail wi h he highes concen a ion. The
e apo a ion p ocess is o en modeled as a mo ing a e age o e a p ede-
ined se o objec s unning h ough he sys em (A mb us e e al., 2006).
This pape p oposes a simila app oach o assigning ehicles o pa king
ows. Vehicles belonging o a ca ego y 𝑘 calcula e o e e y ow 𝑖 a phe o-
mone alue 𝑃 and chose he ow wi h he bes 𝑃 alue. Equa ion (2) de-
sc ibes his phe omone alue. The o al numbe o ehicle ca ego ies is de-
ined as K. In his con ex c i e ia o ehicle ca ego ies a e OEM, model
ypes and he shipmen des ina ion (see also Table 1).
𝑃𝛾
𝛾
𝛾1
𝛾
(2)
The phe omone alue 𝑃 consis s o ou e ms. Each e m ocuses on a di -
e en a ge alue and can be weigh ed by a ac o 𝛾. Excep om e m 3
all emaining e ms use he mo ing a e age concep o emula e he phe o-
mone e apo a ion. All e ms and he e apo a ion p ocess will be desc ibed
in he ollowing. Fo each ca ego y 𝑘 a mo ing a e age o he las 𝛼 ehicles
Modeling Au onomously Con olled Au omobile Te minal P ocesses 203
is used o de e mine wo key pa ame e s. The i s pa ame e s a e he mos
equen ed sou ces and sinks o he speci ic ehicle ca ego y. These pa am-
e e s a e he basis o de i ing dis ance ela ed measu es like 𝑊. The 𝑊
is de ined as he dis ance be ween he mos equen ly used sou ce, he
s o age a ea o he pa king ow 𝑖 and he mos equen ly used sink. The
second pa ame e is he mo ing a e age o he in en o y ime (days a he
e minal) 𝐺 o he ehicles belonging o ca ego y 𝑘.
The i s e m o he phe omone alue equa ion (2) ocuses on balancing
he es ima ed dis ance 𝑊 and he a e age in en o y ime 𝐺 o a ca ego y
𝑘. The basic in en ion o his e m is o a e ows wi h longe es ima ed dis-
ance be e o ca ego ies wi h highe in en o y ime and ice e sa.
The e o e, his e m calcula es he anking posi ion o he es ima ed dis-
ance ac o 𝑊 di ided by he amoun o pa king A eas 𝐹 and ela es i
wi h he anking o in en o y day o emaining ca ego ies.
Mos o e minal inbound and ou bound p ocesses ope a e in a FIFO mode.
Thus, ehicles wi h same in en o y imes should s and closely oge he .
The second e m add esses he FIFO p inciple, by ela ing he in en o y
ime o he la es ehicle in a s o age a ea wi h he in en o y ime o he
oldes ehicle o ca ego y 𝑘.
The hi d e m add esses he spli o ehicles on he e minal. An ob ious
cons ain coming om he basic ya d planning is o minimize he geo-
g aphical dispe sion o ehicles belonging o he same ca ego y. The num-
be o di e en sepa a ed s o age a eas pe ca ego y should be as less as
possible. The e o e, his e m ela es he olume o ehicles o ca ego y 𝑣
in he pa king a ea o ow 𝑖 o he o e all olume o ehicles 𝑉 belonging
o ca ego y 𝑘.
204 Michael Gö ges and Michael F ei ag
The ou h e m ocuses on he es ima ed dis ance o a ehicle s o ed on
he pa king a ea o ow 𝑖. I ies o a oid an assignmen , which lead o long
d i ing dis ances. This e m is de ined as he a io be ween he es ima ed
dis ance 𝑊 based on he mo ing a e age and he maximal possible dis-
ance o ca ego y 𝑘 ega ding all sou ces, s o age a eas and sinks.
The phe omone alue o each ow can be de i ed wi h equa ion (1). By
con as o na u al p ocess, ehicles choose he ow wi h he lowes alue
o 𝑃 as he highes concen a ion o phe omones.
5 Simula ion Resul s
5.1 Impac o Ex e nal Dynamics
An disc e e e en simula ion model has been se up acco ding o sec ion 4.
This model will be used o in es iga e he impac o ex e nal dynamics on
he con en ional ya d assignmen and he au onomous con ol me hod o
he cons an and he bulked depa u e a ian . The pa ame e 𝜇 (ampli-
ude o he a i al unc ion) will be a ied as a sou ce o ex e nal dynamics
(e.g., s onge seasonal e ec s by a ying o de olumes o cus ome s).
Highe alues o 𝜇 lead o s onge a ia ions and a mo e dynamic si ua-
ion. In his expe imen 𝜇 is he same o e e y ca ego y k in one simula-
ion un.
Modeling Au onomously Con olled Au omobile Te minal P ocesses 205
Figu e 7: Simula ion esul s o a ying ampli udes
Figu e 7 shows he a e age d i ing dis ance o all ca s in a simula ion un
o he con en ional planning, he phe omone based au onomous con ol
me hod and he andom assignmen . The alues o 𝛾 ha e been se o
(𝛾0.1 and 𝛾0.4). The ole o his pa ame e s will be discussed
la e in sec ion 5.2. As expec ed, he andom assignmen pe o ms wo s .
Due o he andom assignmen possible sho ou es be ween sou ce, s o -
age a ea and sink a e neglec ed. This leads o long d i ing dis ances. Figu e
7 shows ha his me hod is no a ec ed by an inc easing ampli ude. By
con as , Figu e 7 depic s a s ong dependency be ween he con en ional
planning and he ampli ude o he a i al unc ion. A highe ampli ude
causes s onge peak pe iods wi h highe amoun o a i ing ca s. In his
si ua ion ca s a e assigned o he pa e n shown in Figu e 6. The highe he
incoming olume in a peak pe iod, he mo e o en seconda y assignmen s
(peak ese e) a e used and occupy pa king a eas o o he models (p ima y
assignmen ) wi h po en ially sho e ou es. This leads o longe ou es un-
400
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500
550
600
0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75
a g. dis ance [m]
Ampli ude (
k
) [ca s/d]
con . planning
PHE-Meh od
and assignmen
206 Michael Gö ges and Michael F ei ag
de dynamic a i al condi ions. Compa ed o he con en ional planned si -
ua ion he au onomous con ol me hod beha es di e en . Al hough, he
a e age d i ing dis ance inc eases wi h highe alues o 𝜇, his e ec is
sligh ly lowe compa ed o he con en ional planning. The au onomous
con ol me hod is able o cope wi h he ex e nal dynamics mo e obus ly.
Rega ding he absolu e alues, he au onomous con ol me hod ou pe -
o ms he con en ional planning o e e y 𝜇. This e ec is s onge o
highe alues o 𝜇. Despi e highe ex e nal dynamics he au onomous con-
ol me hod is able o ind sui able ow assignmen s wi h sho e ou es.
As desc ibed in sec ion 3, he implemen a ion o bulked depa u es can be
seen as a sou ce o addi ional dynamics. Figu e 8 depic s simula ion esul s
o he scena io wi h bulked depa u es. Fo Figu e 8, he mean essels' ca-
paci y has been inc eased in s eps o 100 ca s pe essel (s a ing om 500
ca up o 2000 ca s pe essel). E e y simula ion un had a ixed mean a i-
al 𝜆 (see Table 1) and an ampli ude o 𝜇 =50 ca s pe day in o de o p o-
ide compa abili y wi h Figu e 7. As al eady discussed, bigge ship capaci-
ies lead o longe in en o y imes. These longe in en o y imes a ec he
o e all pe o mance nega i ely. This can be con i med by Figu e 8. I shows
ha bigge essels' capaci y inc ease di e ence be ween con en ional
planning and he new au onomous con ol me hod. Like in he i s sce-
na io, he au onomous con ol me hod ou pe o ms he con en ional as-
signmen . Fo essels' capaci y o 500 ehicles, he a e age d i ing dis ance
is abou 3.8% highe o he con en ional planning. By con as , his gap is
o essels' capaci y o 2000 ca s 11.35% highe compa ed o he au ono-
mously con olled si ua ion. In o al, Figu e 7 and Figu e 8 con i m he hy-
po hesis ha au onomous con ol imp o e he e minals' pe o mance un-
de inc easing ex e nal dynamics condi ions induced by ola ile demand
Modeling Au onomously Con olled Au omobile Te minal P ocesses 207
luc ua ions (Figu e 7) and a ying bulked depa u es (Figu e 8). Compa ing
bo h ypes o dynamics, he impac o a ying ampli udes seems o be
s onge han he essels' capaci y. Bo h sou ces o dynamics lead o di e -
ences in he in e nal sys ems' beha io o he au onomous con ol me hod
and he con en ional planning.
Figu e 8: Simula ion esul s o essel capaci ies
Figu e 9 con i ms he impac o inc easing dynamics on he con en ional
ya d assignmen and on he au onomous con ol me hod.
I p esen s sca e plo s o he phe omone based me hod and o he con-
en ional planning. Each plo depic s he d i ing dis ance agains he e -
minals in en o y o di e en poin s in ime in a simula ion un. The e mi-
nals in en o y is an indica o o he ex e nally induced dynamics. In bo h
cases (au onomous con ol and con en ional planning) he sys ems in en-
o y le el is de ined by he a i al and he depa u e unc ion (see also
Figu e 4 and Figu e 5). The e is no in luence o he con ol me hods on he
in en o y o e ime. Thus, his measu e can be seen as an indica o o ex-
e nal dynamics. In addi ion, Figu e 9 p esen s he a e age d i ing dis ance
ela ed o he e minals in en o y a he same ime. The d i ing dis ance
300
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450
500
550
600
500 600 700 800 900 1000 1100 1200 1300 1400 1500 1600 1700 1800 1900 2000
a g. dis ance [m]
essel ca
p
aci
y
[
ca s/ essel
]
con . planning
PHE-Meh od
and assignmen
214 Michael Gö ges and Michael F ei ag
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