Fab in, B una H. P.; Fe a i, Denise B.; A au , Edua do M.; Neumann, Simone
A icle
Towa ds balancing e iciency and cus ome sa is ac ion in
ai plane boa ding: An agen -based app oach
Ope a ions Resea ch Pe spec i es
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(2024) : Towa ds balancing e iciency and cus ome sa is ac ion in ai plane boa ding: An agen -
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Towa ds balancing e iciency and cus ome sa is ac ion in ai plane boa ding:
An agen -based app oach
B una H.P. Fab in a, Denise B. Fe a ia, Edua do M. A au a, Simone Neumann b,∗
aAe onau ics Ins i u e o Technology, P aça Ma echal Edua do Gomes 50, São José dos Campos, 12228-900, São Paulo, B azil
bUni e si ä Hambu g, Moo weidens asse 18, Hambu g, 20148, Ge many
ARTICLE INFO
Keywo ds:
Ai plane boa ding
Agen -based modeling
Simula ion
ABSTRACT
The ai plane boa ding p ocess, which can ha e a signi ican impac on a ligh ’s u na ound ime, is o en
iewed by esea che s and ai lines p ima ily in e ms o minimizing o al boa ding ime (TBT). Ai plane
capaci y, numbe o passenge s on boa d, amoun o luggage, and boa ding s a egy a e common ac o s ha
a ec TBT. Howe e , besides ope a ional e iciency, ai lines a e also conce ned wi h cus ome sa is ac ion,
which a ec s cus ome loyal y and inancial e u n. One ac o ha in luences passenge expe ience is he
indi idual boa ding ime (IBT), he e de ined by he ime passenge s s and inside he cabin. Conside ing hese
wo aspec s, an agen -based model is p esen ed ha compa es he pe o mance o h ee al e na i e mains eam
boa ding s a egies in a 132-sea and a 160-sea single-aisle comme cial ai plane. An impo an cha ac e is ic
o he model ha di e en ia es i om p e ious wo k is ha o e head bins ha e a physical limi a ion, which
could lead o an inc ease in aisle in e e ences on ull ligh s as passenge s ake longe o ind a place o
hei ca y-on luggage. Ano he impo an con ibu ion is he analysis o how passenge sea loca ion a ec s
IBT. Ou esul s show ha ou side-in (OI) p oduces sho e TBT han andom and back- o- on boa ding, and
also sho e IBT and much sho e maximum IBT han BTF, pa icula ly o passenge s sea ed in he middle
o he ai plane. This sugges s ha among he h ee mos popula boa ding s a egies used by ai lines ac oss
he wo ld, OI is he bes when i comes o balancing ai plane boa ding e iciency wi h indi idual cus ome
sa is ac ion.
1. In oduc ion
In 2022, ai lines e enue eached US$ 727 billion, ep esen ing 87%
o p e-pandemic le els [1]. As he indus y con inues i s eco e y, he
a ia ion ma ke is expec ed o g ow annually by 3.3% and each nea ly
8 billion passenge ips pe yea by 2040 [2]. Wi h his an icipa ed
ma ke g ow h, ai po ope a ions a e expec ed o encoun e mo e
in as uc u e challenges, such as a ic con ol o ai po capaci y
cons ain s. Many ai po s a ound he wo ld al eady ace egula delays
and c owding, p ima ily caused by ai ca ie delays, ai plane la e
a i als, and eac iona y delays [3–5]. These delays no only con ibu e
o ai po conges ion bu also inc ease he wo kload o ai a ic
con olle s [6]. As a esul , ai lines a e unde inc easing p essu e
no only o imp o e ope a ional e iciency, bu also o main ain o
enhance cu en le els o cus ome sa is ac ion. F om he passenge ’s
pe spec i e, o e c owding and delays a e pe cei ed as signs o poo
se ice quali y, which may lead o nega i e eedback and in luence he
ai line choice [7].
∗Co esponding au ho .
E-mail add ess: [email p o ec ed] (S. Neumann).
A key pe o mance indica o used by ai lines ha is closely ied o
e enue and cus ome sa is ac ion is he u na ound ime. Tu na ound
ime is de ined as he ime in e al be ween he a i al o an ai plane
and i s depa u e om he ga e. Du ing his ime, se e al ope a ions
a e pe o med, such as ueling, ca e ing, boa ding and deboa ding o
passenge s and c ew, as well as he ai plane main enance [8]. Since
ai line companies gene a e e enue only while lying, he sho e he
u na ound ime, he mo e e enue he ai lines should be able o
gene a e. Mo eo e , ai lines mus adhe e o schedules se by ai a ic
con ol and he ai po . I is es ima ed ha each minu e on he g ound
cos s he ai line be ween US$ 30 and US$ 250, depending on he ype
o ai plane [9,10].
Boa ding is a c ucial ac i i y ha akes place du ing he u na ound
ime because i is one o he leng hies p ocedu es [11] and alls on
he c i ical pa h o he u na ound [12], which means ha a delay
in boa ding usually leads o a delay in he whole p ocess. Addi ion-
ally, boa ding is highly a iable, since i is e y much in luenced by
h ps://doi.o g/10.1016/j.o p.2024.100301
Recei ed 9 No embe 2023; Recei ed in e ised o m 5 Ap il 2024; Accep ed 6 Ap il 2024
Ope a ions Resea ch Pe spec i es 12 (2024) 100301
2
B.H.P. Fab in e al.
he human ac o s in ol ed. I signi ican ly a ec s passenge s’ expe i-
ences [13], which in u n in luences hei pe cep ion o he ai line’s
se ice quali y [14]. Consequen ly, i is a key de e minan o cus ome
sa is ac ion o dissa is ac ion [15].
The boa ding p ocess consis s o passenge s en e ing he ai plane
one a a ime. They may o may no ha e luggage. Upon en e ing,
he passenge p oceeds o hei assigned ow, s o es hei luggage (i
applicable) in he o e head bin, and hen akes hei assigned sea . In
he p ocess, he passenge may need o wai while o he s s and in he
aisle o s o e luggage o esol e a sea in e e ence. Sea in e e ence
occu s when a passenge canno ake hei window o middle sea
immedia ely because ano he passenge al eady sea ed in he same ow
(in he middle o aisle sea ) mus ge up i s [16]. Due o limi ed
s o age capaci y, nea by o e head bins may be ull by he ime a
passenge a i es a hei assigned sea . As a esul , hey may ha e o
mo e a ound o ind an a ailable space o s ow hei ca y-on bag.
Key ac o s ha a ec he ai plane boa ding p ocess include he
numbe o passenge s on boa d, he ai plane model (cabin layou ),
he ype o ligh (business o leisu e), he p esence o g oups o
amilies a eling oge he , he numbe o ca y-on i ems on boa d, as
well as passenge ’s cha ac e is ics [17–22]. Va ia ions in hese ac o s
can ha e a signi ican impac on o al boa ding ime [23], which is
conside ed he mos c i ical measu e o an ai line’s boa ding success.
While in as uc u e changes o he in oduc ion o new echnology –
o en expensi e and ime-consuming – a e op ions o educing o al
boa ding ime, a mo e immedia e solu ion is o adop mo e e icien
boa ding s a egies.
To da e, he scien i ic li e a u e on ai plane boa ding has ocused
p ima ily on educing o al boa ding ime by e alua ing al e na i e
boa ding s a egies. Se e al s a egies ha e been p oposed [17,24–29]
ha ake in o accoun ac o s such as passenge di e si y [19,20,30,31],
amoun o luggage on boa d [32–36], g oups a eling oge he [17,
26,33,35,37], and COVID-19- ela ed social dis ancing [38,39]. The
me hodologies used in hese s udies ha e been di e se, including in e-
ge p og amming [36,40–42], pedes ian dynamics [43], disc e e e en
simula ion [44,45], machine lea ning [46], expe imen a ion [47,48],
physics and op ics [31,49], cellula au oma a [50,51], and agen -based
modeling [28,52–54].
Resul s so a ha e shown ha no s a egy is uni e sally he mos
e ec i e in e ms o o al boa ding ime ac oss all possible boa ding
scena ios, al hough g oup boa ding has consis en ly been shown o be
slowe han o he s [28,44,53,55,56], while some au ho s emphasize
ha andom boa ding pe o ms poo ly [57,58]. F om an ai line pe -
spec i e, ou side-in boa ding is gene ally conside ed he mos e icien
s a egy due o ewe in e e ence e en s [55,57,58], despi e being
conside ed a g oup boa ding s a egy. As p e iously men ioned, ewe
s udies ha e ocused on indi idual passenge me ics. Ne e heless,
hese s udies ha e indica ed ha back- o- on boa ding esul s in he
longes indi idual boa ding imes (IBT) [20,28,44].
In p ac ice, when an ai line is selec ing a boa ding s a egy o adop ,
i mus conside no only ope a ional e iciency bu also cus ome sa is-
ac ion. This aspec has so a ecei ed li le a en ion om he scien i ic
li e a u e. A ecen online su ey o 1500 passenge s ound ha while
passenge s alue as o e all boa ding imes, ge ing o hei sea s
quickly is e en mo e impo an o hem [59]. The modeling s udies so
a which conside ed indi idual passenge in e es ha e indica ed ha
back- o- on boa ding s a egy is he wo s op ion because i esul s in
he longes indi idual boa ding imes [20,28,44].
The p esen wo k p oposes a spa ially-explici agen -based model
(ABM) o compa e he pe o mance in a comme cial ai plane o al e na-
i e boa ding s a egies wi h espec o balancing ai line e enue wi h
cus ome sa is ac ion. He e h ee main-s eam boa ding s a egies a e
compa ed: ou side-in, back- o- on and andom. The model ep esen s
single-aisle ai planes, like he B737 o A320, which may accommoda e
a ying passenge capaci ies. Such ai planes a e ypically u ilized o
sho - and medium-haul ligh s, in which boa ding ime is pa icula ly
c i ical compa ed o long-haul ligh s [16]. He e, he ai line’s in e es
is assessed ia measu emen s o he o al boa ding ime (TBT), de ined
as he ime in e al om he i s passenge en e ing he ai plane o he
las passenge si ing. Passenge p e e ence o as e sea ing is assessed
wi h wo measu es: indi idual boa ding ime (IBT), he e de ined as he
ime in e al be ween a passenge en e ing he ai plane and si ing,
i.e., he o al ime walking o s anding inside he ai plane, and he
maximum indi idual boa ding ime (MAXIBT) pe boa ding p ocess.
MAXIBT was included o allow o he assessmen o he disp opo ion-
a ely la ge nega i e e ec on an ai line ha a ew ex emely dissa is ied
cus ome s migh impose, in e ms o example o judicial p oblems o
nega i e social media campaigning.
In a eal ligh si ua ion, he passenge demog aphics may change
depending on he ou e. Fo example, ai shu le ligh s a e ypically
lown by indi iduals who a el equen ly and alone, and a e he e o e
amilia wi h he boa ding p ocedu e. In con as , ou is ligh s a e
la gely made up o amilies o elde ly passenge s who may ake longe
o si down. This s udy does no conside any pa icula ype o ligh
and assumes ha indi iduals a el alone, ca ying o no a s anda d-
sized piece o luggage. Based on inpu om ai line execu i es and
in o ma ion ob ained om Boeing’s websi e [60], he o e head bins
in he p esen simula ion a e modeled wi h limi ed capaci y. In o he
wo ds, he e is insu icien space o e e y passenge o b ing and
s o e a piece o luggage on boa d. To he bes o ou knowledge, his
aspec has no been add essed in scien i ic li e a u e be o e. The usual
app oach in ol es inc easing s o age ime in o de o accoun o he
numbe o bags passenge s ca y [18,33,44,61,62]. This makes he
p oposed model mo e ealis ic, as limi ed s o age space may o ce some
passenge s o s ow hei luggage a he om hei sea s, causing aisle
conges ion.
The main con ibu ion o his wo k lies in he de elopmen and
analysis o an agen -based model ha di e s om p e ious models
in ha i akes in o accoun he physical limi a ion o o e head bins,
and enables he compa ison o he pe o mance o al e na i e boa ding
s a egies in e ms o measu es ha e lec he in e es s o bo h ai lines
and passenge s. In addi ion, his s udy examines how passenge sea
loca ions a ec indi idual boa ding imes, which is an impo an ac o
in cus ome sa is ac ion.
The emainde o he pape is o ganized as ollows: Fi s , we de-
sc ibe he esea ch p oblem and ou model. In Sec ion 3we p esen ou
simula ion scena ios and he esul s. These a e discussed in Sec ion 4
be o e we conclude he pape in Sec ion 5.
2. Resea ch ques ion and me hodology
This s udy add esses a undamen al ques ion o a ia ion: among he
mos common boa ding s a egies employed oday, which one should
an ai line adop o a gi en speci ic ligh in o de o imp o e ope a-
ional e iciency and cus ome sa is ac ion? This ques ion is add essed
o wo la ge comme cial ai planes, 132 and 160 passenge s, aking in o
accoun cons ain s such as limi ed space o ca y-on luggage along
wi h ac o s such as he ai plane’s passenge capaci y, he quan i y o
ca y-on i ems on boa d, passenge walking speed, as well as he ime
equi ed o s o e luggage and esol e sea in e e ences.
The agen -based modeling (ABM) app oach was selec ed o in es-
iga ing his ques ion because i allows o he quan i ica ion o ai line
pe o mance and cus ome sa is ac ion om obse a ions o i ual
passenge s beha ing simila ly o eal passenge s boa ding a i ual ai -
plane o scale. The ABM app oach o e s nume ous ad an ages ele an
o he p esen s udy, including: (i) a high le el o in e ac ion be ween
en i ies and hei en i onmen [63], (ii) some deg ee o unp edic abil-
i y and unce ain y [64], and (iii) he abili y o en i ies o adap hei
beha io and decision-making p ocesses [65]. These ea u es allow o
he isualiza ion o eme ging beha io s and pa e ns, enabling a mo e
ho ough in es iga ion o complex eal-wo ld sys ems [66].
Ope a ions Resea ch Pe spec i es 12 (2024) 100301
3
B.H.P. Fab in e al.
Fig. 1. Example o a boa ding simula ion un. A ows indica e he passenge s and hei acing di ec ions; whi e cells ep esen open spaces whe e passenge s can walk eely,
such as aisles and leg oom; b own cells ep esen sea s in he economy class; g ay cells ep esen sea s in he business class; blue cells ep esen ai plane in e nal s uc u es; he
g een cell ep esen s he doo . (Fo in e p e a ion o he e e ences o colo in his igu e legend, he eade is e e ed o he web e sion o his a icle.)
2.1. The agen -based model
The me hodology adop ed o build he simula ion model ollows he
O e iew, Design concep s and De ails (ODD) p o ocol [67], which is
equen ly used o desc ibing agen -based models (ABMs). The de ails
a e gi en nex . The model was de eloped using Ne logo [68], an open-
sou ce p og amming so wa e. Fo u he in o ma ion on he model,
please e e o [69]. In he supplemen a y ma e ial, ideos o he
simula ion a e a ailable.
2.1.1. Model pu pose and pa e ns
The gene al pu pose o he spa ially-explici agen -based model
(ABM) p esen ed he e is o compa e he pe o mance o al e na i e
ai plane boa ding s a egies in e ms o balancing ai line e enue and
cus ome sa is ac ion. I s speci ic pu pose is o compa e he pe o -
mance o andom, back- o- on and ou side-in boa ding s a egies in
132-passenge and 160-passenge ai planes wi h espec o (i) o al
boa ding ime (TBT), (ii) indi idual boa ding ime (IBT) and (iii)
maximum indi idual boa ding ime (MAXIBT).
2.1.2. En i ies, s a e a iables and scales
The e a e wo ypes o en i ies in he model: (i) passenge s, ep e-
sen ed by mobile agen s, and (ii) ai plane s uc u es, ep esen ed by
s a iona y pa ches.
The s a e a iables o he passenge s a e: (i) he passenge ’s walking
speed (SPEED), (ii) he ime needed o s o e hei luggage in he
o e head bin (TIMELUG), and (iii) he ime needed o esol e a sea
in e e ence, also known as sea shu le ime (SHUFFLE). These a i-
ables ha e iden ical alues o all passenge s. The e a e wo addi ional
cha ac e is ics ha a y o each agen : (i) sea loca ion (SEATPATCH),
and (ii) luggage possession upon en e ing he ai plane (LUGGAGE?);
hese a iables a e bo h andomly assigned acco ding o a Be noulli
p ocess, and desc ibe ha each passenge has a inal des ina ion in he
cabin, and may o may no ha e exac ly one piece o ca y-on luggage.
The ai plane model is based on a A320/B737 ai plane cabin, which
co esponds o a single-aisle layou o 3-3 sea con igu a ion. A ep e-
sen a ion o he Ne Logo in e ace is shown in Fig. 1. Some pa ame e s
de ined by he use a e: he maximum sea capaci y (CAP), he numbe
o ows ese ed o business class passenge s (BUSROWS), and he
o e head bin capaci y (BINCAPAC), de ined as he maximum numbe
o luggage pieces ha a bin could hold pe hal - ow. The ime s ep in
Ne logo is e e ed o as a ‘ ick’ and is de ined as 1/10 o a second
(1 s = 10 icks). Addi ionally, a pa ch in Ne logo, which co esponds
o he uni a ea, is equi alen o 0.5 m ×0.5 m.
Table 1 lis s he main a iables used in he simula ion, as well as
hei desc ip ions and uni s.
The low a e (FLOWRATE) is de ined he e as a cons an num-
be o passenge s en e ing he ai plane doo pe minu e, measu ed
in pax/min. Ou app oxima ion o his a e is based on da a om
he li e a u e [23]. Using he numbe o passenge s and he imes
a which he i s and las passenge s boa ded he ai plane o each
ligh obse a ion, i was possible o es ima e an a e age low a e o
each occu ence. Wi h he calcula ed low a es, a eg ession cu e
Table 1
En i ies and s a e a iables used in he boa ding p ocess simula ion.
En i y S a e a iable Uni Desc ip ion
Global CAP passenge Maximum sea capaci y in
he ai plane
PAX passenge Numbe o passenge s
OCC – Fligh ’s occupancy le el
LUGPERC % Pe cen age o passenge s
ca ying luggage a he
beginning o boa ding
p ocess
BUSROWS ow Numbe o ows
designa ed o business
class
SPEEDREDUCT – Walking speed educ ion
ac o o passenge s
walking in coun e low
BINCAPAC piece Numbe o luggage pieces
ha an o e head bin can
hold pe hal - ow
STRATEGY – En e ing o de o
passenge s
FLOWRATE pax/min Numbe o passenge
en e ing he ai plane doo
pe minu e based on
occupancy le el
Passenge SPEED m/s Maximum passenge ’s
walking speed
TIMELUG s Time needed o s o e
luggage in he o e head
bin by a passenge
SHUFFLE s Time needed o sol e a
sea in e e ence by a
passenge
LUGGAGE? boolean De ines i passenge
ca ies luggage
SEATPATCH pa ch Pa ch e e ing o sea
loca ion
Ai plane BINCUR pieces Cu en numbe o
luggage pieces in a
o e head bin abo e a sea
o he low a e e sus expec ed ligh ’s occupancy le el (OCC) was
cons uc ed (Fig. 2). The ixed alue o low a e used h oughou he
en i e simula ion is calcula ed a he beginning o each simula ion un.
Howe e , and impo an ly, i he e a e passenge s queuing close o
he en ance doo , o example because one o mo e a e s owing hei
luggage, no new passenge s will en e un il he e is ee space. Thus,
du ing he model un, he ac ual low a e a ies depending on local
condi ions. In eal li e, his a e is con olled a he boa ding ga e,
whe e he agen s check passenge s’ icke s and IDs. Occupancy le el is
de ined as he expec ed o al numbe o passenge s on he ligh (PAX)
o e he sea capaci y (CAP). Fo mo e in o ma ion, please see [69].
Eq. (1) shows he unc ion o he low a e used in he model.
𝐹 𝐿𝑂𝑊 𝑅𝐴𝑇 𝐸(𝑂𝐶𝐶) = {16.797 − 9.015 ∗ 𝑂𝐶𝐶, i 0≤𝑂𝐶𝐶 ≤1
0,o he wise. (1)
Ope a ions Resea ch Pe spec i es 12 (2024) 100301
4
B.H.P. Fab in e al.
Fig. 2. Flow a es in e ms o ligh ’s occupancy le el. The blue line ep esen s he app oxima ed eg ession unc ion ob ained and he black poin s a e da a om he obse a ional
s udy [12]. (Fo in e p e a ion o he e e ences o colo in his igu e legend, he eade is e e ed o he web e sion o his a icle.)
The simula ion p oduces he ollowing ou pu s: (i) o al boa ding
ime (TBT), (ii) indi idual boa ding ime (IBT), and (iii) maximum
indi idual boa ding ime (MAXIBT), as p e iously de ined. All h ee
a iables a e analyzed in his pape , bu we gi e special ocus o TBT
and MAXIBT because we belie e hey a e he mos p edominan when
compa ing ai line and passenge in e es s a ound he boa ding p ocess.
I is impo an o men ion ha in [59], IBT desc ibes he en i e
ime in e al aken by a passenge om he momen he o she passes
h ough he icke check un il he o she akes he assigned sea inside
he cabin. Howe e , since s anding in he aisle o he ai plane is he
pa o he boa ding p ocess ha mos bo he s passenge s [59], in he
p esen pape , IBT only conside s he ime passenge s wai s anding in
he cabin be o e aking hei sea s.
2.1.3. P ocess o e iew
The model’s high-le el algo i hm p oposed in his s udy is p esen ed
in Fig. 3.
The simula ion s a s wi h an emp y ai plane wi h he de ined
cha ac e is ics. Then, he ollowing ac ions ake place:
•A he beginning o he simula ion, all passenge s a e gene a ed,
each being assigned o a andom sea (SEATPATCH). Whe he
a passenge ca ies one piece o luggage o no is de e mined
andomly acco ding o a Be noulli p ocess. Then, all passenge s
a e ga he ed and awai hei u n o boa d.
•In acco dance wi h he selec ed boa ding s a egy and expec ed
ligh occupancy, he i s passenge boa ds he ai plane ollowing
he low a e (Eq. (1)). Each passenge p oceeds o hei sea
wi hou making any mis akes ( he passenge does no ge los
inside he cabin, o example).
•Upon eaching hei assigned ow, he passenge ca ying luggage
checks he o e head bin o he same ow and side whe e hei sea
is loca ed. I he e is space a ailable, he passenge s ands in he
aisle o a ce ain pe iod o ime (he ein TIMELUG) while s owing
hei luggage. Du ing his ime, o he passenge s canno pass and
mus wai behind he pe son s o ing hei luggage.
•I , con e sely, he passenge eaches hei assigned ow and e -
i ies he o e head bin abo e hei sea is ull, hey will imme-
dia ely disco e he loca ion o he nea es emp y o e head bin,
assuming pe ec in o ma ion abou i s loca ion, as i hey saw i
s aigh away o cabin c ew membe s we e assis ing hem. The
passenge walks owa ds his nea es emp y o e head bin, s o es
he luggage ollowing he usual p ocedu e, u ns back owa ds
hei assigned sea and e u ns o i .
•When a passenge wi hou luggage eaches hei assigned ow,
hey check o sea in e e ence; in posi i e case, he passenge
s ands in he aisle o ano he pe iod o ime (called SHUFFLE)
while he in e e ence is esol ed, meanwhile blocking he way
o o he s.
•A e esol ing luggage s o age and sea in e e ence, he passen-
ge is allowed o en e he ow and o ake hei sea .
•I all o e head bins in he cabin a e ull, a passenge ha is
ca ying a piece o luggage d ops i and mo es di ec ly owa ds
hei sea wi hou any ime penal y, as i ai line employees we e
a he en ance o he ai plane con olling he bin capaci y and
checking in bags be o e he passenge en e s he ai plane.
•By de aul , passenge s mo e along he cabin a maximum speed
(SPEED). Howe e , his speed can be adjus ed. Fo example, i a
passenge is s anding in he aisle, he o he s mus also s op and
wai un il his in e e ence is esol ed. I he e is coun e low,
i.e., wo passenge s passing each o he in opposi e di ec ions in
he aisle, SPEED is educed by a ac o gi en by SPEEDREDUCT
o bo h passenge s, un il bo h ha e comple ed he passage.
•The nex passenge is allowed inside he cabin acco ding o
FLOWRATE, which speci ies a uni o m a e o passenge s en e ing
he ai plane doo pe minu e, and ollows he same p ocess as he
p e ious passenge . This p ocess is epea ed i e a i ely un il all
passenge s ha e boa ded.
•I he aisle is conges ed up o he doo o he ai plane, i.e., pas-
senge s a e s anding a he doo and no mo ing o wa d, he
passenge ’s boa ding will be in e up ed un il he conges ion
is clea ed and space is a ailable inside he cabin. Passenge
boa ding will hen esume.
•When all passenge s a e sea ed, he simula ion ends.
2.1.4. Main model assump ions
The main assump ions a e: (i) passenge s en e he ai plane one
a a ime, so he e a e no amilies o g oups a eling oge he , (ii)
passenge s boa d o e he b idge and only h ough one doo a he
on o he ai plane, (iii) e e y passenge has an assigned sea , (i )
passenge s canno o e ake each o he when mo ing in he same
di ec ion, i.e., i he e is a slowe passenge ahead, he nex passenge
Ope a ions Resea ch Pe spec i es 12 (2024) 100301
5
B.H.P. Fab in e al.
Fig. 3. Model’s high-le el algo i hm. All passenge s mo e a a maximum speed (SPEED), which is educed by a ac o (SPEEDREDUCT) when wo passenge s a e in coun e low.
mus ollow behind, ( ) passenge s make no mis akes ega ding pa h
o sea loca ion; he e a e no delays ei he , which means ha all
passenge s ollow he ules and come on boa d a hei assigned ime
and wi h hei g oup, ( i) all ca y-on luggage ha e he same size and
o ma , and each passenge may o may no ha e one piece o luggage,
( ii) he space in he o e head bin is limi ed, meaning ha i may be
insu icien o all passenge s o s o e one luggage piece, ( iii) as long
as he e is space a ailable, ca y-on luggage is always s owed in he
o e head bins; as soon as all bins a e ull, he emaining passenge s
ca ying luggage lea e i a he ai plane doo so ha i is anspo ed
o he ai plane’s unk, (ix) passenge s ha e pe ec in o ma ion, i.e., i
looking o a ailable space, passenge s always know whe e he closes
emp y bin is, (x) business class is no conside ed and passenge s can
only ake a sea a economy class.
2.1.5. Ou pu e i ica ion
The model has been ho oughly e i ied o ensu e ha i wo ks
as concep ually designed. The exis ing p ocedu es in he code we e
e i ied by indi idually es ing code pa s o check unc ionali y and
o make i as simple as possible. Ve i ica ion was also done isually,
gi en he isual elemen o he coding so wa e, by checking whe he
he o e all beha io o he passenge s e lec ed wha was expec ed o
hem.
2.2. Ou pu alida ion
Simula ion p edic ions we e compa ed wi h esul s ob ained om
obse a ions o eal boa ding p ocesses in ai planes [23]. In his pape ,
he au ho s pe o med a s a is ical analysis o boa ding imes wi h
espec o ac o s such as ai plane capaci y and numbe o luggage
i ems on boa d. The da a we e collec ed by obse ing eal boa d-
ing p ocesses a a Eu opean ai po . A o al o 58 obse a ions we e
ob ained wi hin se e al di e en ai plane models and con igu a ions.
Conside ing only ligh s wi h occupancy abo e 50%, he e a e 13
obse a ions o he 132-sea passenge ai plane and six obse a ions
o he 160-sea passenge ai plane, which a e one o he la ges da a
Ope a ions Resea ch Pe spec i es 12 (2024) 100301
6
B.H.P. Fab in e al.
Fig. 4. To al boa ding ime o a 132-sea passenge ai plane a di e en le els o occupancy. Poin s in ed co espond o occupancy obse a ions in he li e a u e [23], and poin s
in black a e esul s ob ained in he p esen simula ion. Black ba s shows he in e al including 95% o simula ion poin s. (Fo in e p e a ion o he e e ences o colo in his igu e
legend, he eade is e e ed o he web e sion o his a icle.)
Table 2
Ai plane models used o alida ion o he boa ding p ocess simula ion [23].
Pa ame e A319 A320neo
Maximum sea capaci y 138 168
Maximum numbe o passenge s 132 160
Numbe o business ows 3 4
Maximum numbe o passenge s in economy class 120 144
Table 3
Nominal alues o pa ame e s used in he alida ion o he boa ding p ocess simula ion.
Pa ame e Value Sou ce
CAP 138 and 168 pax [23]
OCC Acco ding o Hu e e al. (2019) [23]
LUGPERC 75% [23]
BUSROWS 3 and 4 ows [23]
SPEED 0.5 m/s [70]
TIMELUG 13.9 s [71]
SPEEDREDUCT 0.1
SHUFFLE 10 s [71]
BINCAPAC 2 pieces/hal - ow [60]
STRATEGY andom [23]
se s a ailable. In o de o alida e he simula ion buil in his pape ,
wo ai planes wi h he same con igu a ion as hose conside ed in he
li e a u e we e examined, as shown in Table 2.
The da a included ligh s wi h di e en numbe s o passenge s. In
line wi h he adop ed Re . [23], business class sea s we e no con-
side ed in ou simula ion model because he boa ding p ocess only
conside ed egula passenge s, no including p io i y passenge s. All
obse ed boa ding e en s used he andom boa ding s a egy, which
means ha passenge s did no ollow any pa icula o de and boa ded
on a i s -come, i s -se ed basis.
O he pa ame e alues used in ou simula ions a e gi en in Table 3.
Nominal alues we e aken om he li e a u e and ha e no been
calib a ed.
The simula ions we e un 1000 imes o each ins ance, gi ing a
o al o 12,000 uns o he 132-sea passenge ai plane and 5000 uns
o he 160-sea passenge ai plane o ensu e s a is ical ele ance, due
o he andomness in oduced by passenge s boa ding o de and sea
assignmen . Each da a poin used o alida ion was selec ed based on
he ligh da a wi h unique occupancy le els abo e 50%, esul ing in
12 da a poin s o he 132-sea passenge ai plane and i e da a poin s
o he 160-sea passenge ai plane. Compa ed o eal obse a ions, he
simula ion esul s showed a endency o speed up boa ding (Figs. 4 and
5). To assess he ag eemen be ween he simula ion esul s and he da a
poin s, we quan i ied how di e en he a e age o each analyzed case
was om i s espec i e obse a ion. On a e age, he esul s o he 132-
passenge ai plane di e ed by 17% and o he 160-passenge ai plane
by 16% om he obse ed da a. Al hough he simula ed esul s do no
ully ma ch he eal da a, a simila end can be obse ed. Al hough ou
simula ion esul s a e in good ag eemen wi h he eal da a, because
he sample is a he small we ecommend he esul s he ein o be
in e p e ed wi h cau ion.
Addi ional inpu da a a e a ailable in he li e a u e, such as low
a e [71,72] o walking speed [44,71,73]. Va ious alida ion scena ios
o di e en alues o walking speed (SPEED) we e conside ed in o de
o in es iga e he impac o di e en pa ame e alues on he esul s,
as well as o showcase ou model’s capabili y o p oduce esul s ha
a e close o eali y (Figs. 6 and 7).
None heless, we op ed o using as he nominal alues o he
simula ions inpu da a om sou ces ha p o ided a well-documen ed
desc ip ion o hei expe imen al da a collec ion p ocesses.
3. Simula ion scena ios and esul s
This sec ion p esen s he esul s ob ained om he simula ed sce-
na ios and he sensi i i y analysis. The esul s in he main ex e e o
a 132-sea passenge ai plane, while hose o he 160-sea passenge
ai plane a e p esen ed in Appendix A. Each scena io was un 1000
imes. The pa ame e s used o his assessmen a e shown in Table 4.
The da a pos -p ocessing was pe o med in RS udio, using he R
p og amming language. In o de o do ha , he ou pu ile gene a ed
by Ne logo was ead in o RS udio. Besides he s anda d RS udio buil -
in unc ions, he ollowing lib a ies we e used: (i) idy e se and dply ,
o da a manipula ion, (ii) ggplo 2 and ggpub o plo c ea ion, (iii)
colo Blindness and i idis, o plo colo manipula ion, and (i ) FSA, o
hypo hesis es ing. To compa e dis ibu ions, non-pa ame ic s a is i-
cal es s we e used, including: (i) he Wilcoxon es o compa e wo
dis ibu ions, (ii) he K uskal–Wallis es o de e mine i one o he
analyzed dis ibu ions di e ed om he o he s, and (iii) Dunn’s es ,
o de e mine which o he non-pa ame ic dis ibu ions di e ed om
Ope a ions Resea ch Pe spec i es 12 (2024) 100301
7
B.H.P. Fab in e al.
Fig. 5. To al boa ding ime o a 160-sea passenge ai plane a di e en le els o occupancy. Poin s in ed co espond o occupancy obse a ions in he li e a u e [23], and poin s
in black a e esul s ob ained in he p esen simula ion. Black ba s shows he in e al including 95% o simula ion poin s. (Fo in e p e a ion o he e e ences o colo in his igu e
legend, he eade is e e ed o he web e sion o his a icle.)
Fig. 6. To al boa ding ime o a 132-sea passenge ai plane a di e en le els o occupancy and walking speed. Poin s in black co espond o occupancy obse a ions in he
li e a u e [23]. (Fo in e p e a ion o he e e ences o colo in his igu e legend, he eade is e e ed o he web e sion o his a icle.)
Table 4
Nominal alues o pa ame e s used in he boa ding p ocess simula ion.
Pa ame e Value Sou ce
CAP 138 and 168 pax [23]
OCC 100% Wo s case scena io
LUGPERC 75% [23]
BUSROWS 3 and 4 ows [23]
SPEED 0.5 m/s [70]
TIMELUG 13.9 s [71]
SPEEDREDUCT 0.1
SHUFFLE 10 s [71]
BINCAPAC 2 pieces/hal - ow [60]
STRATEGY andom, back- o- on and ou side-in [23]
each o he . The signi icance le el was conside ed o be 5% (𝛼= 0.05).
Local Sensi i i y Analysis [74] was pe o med in o de o e alua e how
changes on a pa icula inpu a ec a gi en ou pu . I was ca ied
ou by applying small pe u ba ions a ound nominal alues o inpu s,
one- ac o -a -a- ime.
3.1. Simula ed scena ios
Following he e i ica ion and he alida ion s ages o he simula-
ion model, we explo ed a ious scena ios in o de o in es iga e he
e ec o he boa ding s a egy on o al boa ding ime and indi idual
boa ding ime. Th ee di e en boa ding s a egies we e examined: (i)
andom, (ii) back- o- on , and (iii) ou side-in. These s a egies we e
selec ed because hey a e among he mos commonly used boa ding
s a egies used by ai lines oday.
Ope a ions Resea ch Pe spec i es 12 (2024) 100301
8
B.H.P. Fab in e al.
Fig. 7. To al boa ding ime o a 160-sea passenge ai plane a di e en le els o occupancy and walking speed. Poin s in black co espond o occupancy obse a ions in he
li e a u e [23]. (Fo in e p e a ion o he e e ences o colo in his igu e legend, he eade is e e ed o he web e sion o his a icle.)
Fig. 8. To al Boa ding Time (TBT) in e ms o boa ding s a egy on a 132-sea passenge ai plane (RAND = andom, BTF = back- o- on , OI = ou side-in).
Random boa ding means ha no speci ic o de is used and pas-
senge s en e on a i s -come- i s -se ed basis. When back- o- on
boa ding s a egy is adop ed, i means ha passenge s a e sepa a ed
in o h ee g oups, and come on boa d in an o de dependen on hei
sea loca ions: he passenge s on he g oup ha will boa d i s ha e
sea s assigned o he back o he cabin; he nex g oup o passenge s
ha e hei sea s in he middle o he cabin and, inally, he las g oup
o en e he ai plane a e hose passenge s assigned o sea s a he on
o he cabin. Wi hin each g oup, he o de is andom. When ou side-
in boa ding s a egy is used, passenge s a e also sepa a ed in o h ee
g oups based on hei sea loca ions; howe e , in his case, he g oups
a e sepa a ed acco ding o he sea loca ions ela i e o hei p oximi y
o he windows: he i s g oup o boa d is he window sea g oup; hen,
he g oup o passenge s assigned o middle sea s; and, inally, he las
g oup o come on boa d a e hose passenge s assigned o aisle sea s.
Again, wi hin each g oup, he o de o passenge s is andom. Fo all
hese h ee s a egies, passenge s always en e h ough he on doo
o he ai plane.
3.2. Simula ion esul s
Conce ning o al boa ding ime, andom boa ding was he slowes
s a egy, wi h he la ges median ime, ollowed by back- o- on and
hen ou side-in (Fig. 8). A Dunn’s hypo hesis es showed ha he medi-
ans o all dis ibu ions di e ed (p- alue <2.2e−16, 𝛼= 0.05), hough
by a small amoun . Random boa ding had a median o 978.85 s, while
back- o- on and ou side-in had p ac ically he same esul (960.07 s
o back- o- on and 958.40 s o ou side-in, wi h a di e ence o
abou 2 s be ween hem). The a e ages o TBT o each s a egy we e:
961.37 s o ou side-in, 972.25 s o back- o- on and 982.86 s o
andom. As he dis ibu ions a e highly skewed, we decided o e alua e
he esul s h ough he median because i is a cen ali y s a is ics, gi ing
a mo e accu a e in e p e a ion. Also, esul s sugges ed ha he ou side-
in s a egy p esen ed he smalles de ia ion (15.56 s in compa ison o
back- o- on ’s 33.52 s) and he sho es uppe ail among he h ee
s a egies.
Ope a ions Resea ch Pe spec i es 12 (2024) 100301
15
B.H.P. Fab in e al.
Fig. A.17. To al Boa ding Time (TBT) in e ms o boa ding s a egy (STRATEGY) o a 160-sea passenge ai plane (RAND = andom, BTF = back- o- on , OI = ou side-in).
Fig. A.18. Maximum Indi idual Boa ding Time (MAXIBT) in e ms o boa ding s a egy (STRATEGY) o a 160-sea passenge ai plane (RAND = andom, BTF = back- o- on ,
OI = ou side-in).
Ope a ions Resea ch Pe spec i es 12 (2024) 100301
16
B.H.P. Fab in e al.
Fig. A.19. Indi idual Boa ding Times (IBT) in e ms o boa ding s a egy (STRATEGY) o a 160-sea passenge ai plane (RAND = andom, BTF = back- o- on , OI = ou side-in).
Fig. A.20. Indi idual Boa ding Times (IBT) in seconds pe sea o andom boa ding on a 160-sea passenge ai plane.
Ope a ions Resea ch Pe spec i es 12 (2024) 100301
17
B.H.P. Fab in e al.
Fig. A.21. Indi idual Boa ding Times (IBT) in seconds pe sea o back- o- on boa ding on a 160-sea passenge ai plane.
Fig. A.22. Indi idual Boa ding Times (IBT) in seconds pe sea o ou side-in boa ding on a 160-sea passenge ai plane.
Ope a ions Resea ch Pe spec i es 12 (2024) 100301
18
B.H.P. Fab in e al.
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