* Co esponding au ho .
E-mail add ess: jaku[email p o ec ed] (J. Cíleček)
© 2024 by he au ho s; licensee G owing Science, Canada.
doi: 10.5267/j.jpm.2024.4.002
Jou nal o P ojec Managemen 9 (2024) 255–268
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Op imiza ion model o s a ing o ai c a g ound handling in he case o pe sonnel subs i u abili y
Jakub Cílečeka*, Dušan Teichmanna and S anisla Szabob
aIns i u e o T anspo , Facul y o Mechanical Enginee ing, VSB – Technical Uni e si y o Os a a, 708 33 Os a a – Po uba, Czech Republic
bSecu i y and De ense Indus y Associa ion o he Slo ak Republic, 911 01 T encin, Slo ak Republic
C H R O N I C L E A B S T R A C T
A icle his o y:
Recei ed: Janua y 25, 2024
Recei ed in e ised o ma :
Ma ch 15, 2024
Accep ed: Ap il 7, 2024
A ailable online:
Ap il 7, 2024
The p esen ed a icle deals wi h he ma hema ical modelling o ai c a g ound handling on he
se ice ap on o u ilize g ound pe sonnel mo e e icien ly in he case o exis ing subs i u abili y
o wo ke s. This a icle p oposes a suppo ing decision-making ool o e ec i e planning o he
ai c a g ound handling. This ool will be used o a selec ed ype o ai c a and using he
minimum numbe o pe sonnel pa icipa ing in he ai c a g ound handling p ocedu e. The
op imiza ion is based on he o iginal ma hema ical p og amming model and i s solu ion.
Compu a ional expe imen s e i ying he unc ionali y o he p oposed model we e pe o med
on cu en da a om he Os a a In e na ional Regional Ai po in he Czech Republic. The
o iginali y o he p oposed app oach (apa om he o iginal model) comes wi h in oducing he
subs i u abili y o wo ke s o indi idual quali ica ions and he decomposi ion o wo kg oups
composed o wo ke s o he same quali ica ion down o he le el o indi idual wo ke s. Abo e-
men ioned decomposi ion o wo kg oups enables he lexible and sepa a e ans e o indi idual
wo ke s included in he same g oups be ween ac i i ies in he e en o down ime o he gi en
g oup and he exis ence o an ac i i y ha is no co e ed by he equi ed numbe o wo ke s.
The subs i u abili y o wo ke s and he decomposi ion o indi idual g oups down o he le el o
indi idual wo ke s will make i possible o lowe he numbe o wo ke s o e i y ha he
numbe o wo ke s is op imal and elimina e po en ial s a down ime.
© 2024 G owing Science L d. All igh s ese ed.
Keywo ds:
Op imiza ion
Ma hema ical modelling
Ai c a
G ound handling
Subs i u abili y
1. In oduc ion
A cha ac e is ic ea u e o ai anspo is speed when co e ing medium and longe dis ances. The e o e, despi e he
empo a y slump caused by he Co id-19 pandemic, ai anspo is expec ed o e u n o p e-pandemic pe o mance in he
u u e. Howe e , he inc ease in ai a ic densi y also b ings wi h i he ac ha impo an ai po s a e o e c owded wi h
ai a ic, o en limi ing hei capaci y. A he same ime, he demands o ai ca ie s o sho en he ai c a g ound handling
imes a e g owing (Van Blokland e al., 2008; Kwasibo ska, 2010; S ako a & M a, 2011).
The whole ange o ac i i ies wi hin ai c a g ound handling is ela i ely physically demanding and, in many coun ies,
also no signi ican ly inancially alued. A ai po s wi h hea y a ic, he e is always he possibili y ha a sho age o
pe sonnel dealing wi h ai c a g ound handling will eme ge. The e o e, i is necessa y o add ess he issue o minimizing
he numbe o employees needed o ensu e ai c a g ound handling (E le e al., 2018; F icke & Schul z, 2008; Al-Bazi e
al., 2016).
The a icle's main goal is o p esen a possible app oach o suppo pe sonnel planning in ai c a g ound handling. The goal
is o de e mine he minimum numbe o wo ke s needed o pe o m ai c a g ound handling. Op imiza ion esul s can be
used in case o c ises, such as inc eased sickness o qua an ine o wo ke s (because o a pandemic) o poin s o sho - e m
256
inc eased in ensi y o he ai c a g ound handling when seasonal wo ke s canno co e his inc eased in ensi y (Schmid ,
2017; Maland i e al., 2019; Shen e al., 2019; Okwi e al., 2017; Weige e al., 2018).
The main con ibu ions o he p esen ed a icle a e h ee. The i s main bene i is he inco po a ion o subs i u abili y o
wo ke s o indi idual quali ica ions in ol ed in ai c a g ound handling. The second main bene i is he decomposi ion o
indi idual g oups o ai c a g ound handling wo ke s down o he le el o indi idual wo ke s, enabling hei mo e lexible
use du ing i . The hi d main con ibu ion is he ex ension o he applicabili y o he me hods o mixed in ege linea
p og amming (mixed in ege linea p og amming) o o he op imiza ion p oblems o ai anspo .
1.1 Analysis o he cu en s a e
The Co id-19 pandemic had a high impac on a ia ion causing a 65% d op in ai a el wo ldwide a i s s a in June 2020
(A ena & Ap ea, 2021). This d op was he esponse o ai a ic o he es ic ions applied a ound he wo ld. The en i e
ai line indus y had o adjus o sh inking p o i s and mass layo s o keep ai lines and se ice companies om going
bank up . The Co id-19 pandemic also esul ed in he modi ica ion o he ai c a g ound handling p ocess a ai po s as
demons a ed Schul z e al. (2020). A new way o assigning sea s o passenge s was in eg a ed in o he p ocess, and he
p ocess o cleaning he ai c a deck was also modi ied wi h new, abo e-s anda d ac i i ies ha educed he isk o passenge
in ec ion. The passenge sea alloca ion p ocess was modi ied by educing he ai c a 's ca ying capaci y by 1/3 and lea ing
e e y middle sea on he ai c a unoccupied o ensu e minimum spacing be ween passenge s. The deck cleaning p ocess
was expanded o include deck disin ec ion, which inc eased he du a ion o his ac i i y and he o e all du a ion o ai c a
g ound handling a he ai po . The au ho s pe o med an analysis o he gi en si ua ion and ound ha he o al ime o
ai c a g ound handling is inc eased by 20% and only by 10% when mo e wo ke s a e used.
The p ocess o checking in an ai c a a he ai po , which also includes ai c a g ound handling, is a ime-consuming,
complex p ocess du ing which he ai c a and passenge s a e p o ided wi h he equi ed se ices as demons a ed by Kazda
and Ca es (2010) and Ash o d e al. (2015). The o al du a ion o he ai c a g ound handling depends on se e al ac o s,
including:
1. ype o ai c a handled (na ow-body, wide-body) and i s ope a ional and echnical cha ac e is ics;
2. he ange o se ices equi ed by he ai ca ie du ing ai c a g ound handling ( he weigh o he ca e ing depends on
he ange o on-boa d se ices o he ai ca ie and he leng h o he ligh , he possibili y o a equi emen o clean he
ai c a );
3. e uelling equi emen (mass and olume o uel);
4. he numbe o passenge s disemba king/boa ding om/ o he gi en ai c a ;
5. me hod o he boa ding and exi o passenge s (use o boa ding b idges, anspo a ion o passenge s om he e minal
o he s and-by bus);
6. amoun o checked baggage, goods, and mail;
7. he possibili y o a equi emen o e ill d inking wa e and emp y he onboa d sep ic ank;
8. echnical equipmen o he ai po wi h handling equipmen (quan i y and pe o mance pa ame e s o handling
equipmen );
9. me hod o placing checked baggage on he plane ( ee checked baggage, placemen o checked baggage in con aine s);
10. numbe o g ound handling wo ke s;
11. he possibili y o subs i u abili y o wo ke s o indi idual quali ica ions pa icipa ing in ai c a g ound handling;
12. con igu a ion o s ands a he ai po and ansi imes o handling equipmen be ween s ands;
13. me eo ological condi ions (applica ion o an i-icing sp ays o he ai c a in win e );
14. he possibili y o ex ao dina y ope a ional ci cums ances (e.g., Bulky Load, Leg o Loading Equipmen , De ueling,
La e Documen a ion, e c.) (Vidosa lje ic & Tosic, 2010; And ea a e al., 2014; Wu & Ca es, 2004a; Wu & Ca es,
2004b).
The complexi y and o e all ime-consuming na u e o he en i e ai c a g ound handling gene a e he equi emen o he
maximum elimina ion o ime ese es occu ing du ing i . Remo ing ese es can educe o e all handling ime and a
subsequen inc ease in ai po handling capaci y du ing peak imes, as he check-in p ocess can be a bo leneck o ai po
capaci y du ing peak imes (Me edi h & Man el, 2003; Basse e al., 2000).
J. Cíleček e al. / Jou nal o P ojec Managemen 9 (2024)
257
Se e al app oaches ha e been p oposed in he pas o sol e he p oblem o elimina ing ime ese es in ai c a g ound
handling. In many cases, manage ial decision-making me hods a e he key o he en i e a ionaliza ion p ocess. Mos o en,
CPM (C i ical Pa h Me hod) is used o iden i y he ime ese es o he sub-ac i i ies ha make up he p ojec . E en ai c a
g ound handling can be conside ed a comple e p ojec (Wilson, 2003; K oese e al., 2011; Popo a-Zeugmann, 2013;
Mamdouh e al., 2020).
CPM is a p ima y de e minis ic p ojec managemen me hod. When using i , ai c a g ound handling can be ep esen ed
by an edge- a ed acyclic dig aph, in which nodes ep esen he beginnings and ends o indi idual ac i i ies, edges ep esen
he ac i i ies hemsel es, and edge e alua ions ep esen he du a ions o unique ac i i ies. One o he goals o CPM is o
iden i y he so-called c i ical pa h, which in he e minology o g aph heo y, co esponds o he maximal pa h in he dig aph.
I is he mos ex ended sequence o ela ed ac i i ies s a ing a he node ep esen ing he beginning o he p ojec and ending
a he node ep esen ing he end o he p ojec . The c i ical pa h leng h ep esen s he sho es possible ime o he p ojec
o be sol ed. Fo he ac i i ies o ming he c i ical pa h (c i ical ac i i ies), hei a bi a y ex ension esul s in an ex ension
o he o al p ojec implemen a ion ime (when o he o ganiza ional measu es a e no implemen ed). CPM also allows he
calcula ion o he ime ese ed o each ac i i y. C i ical ac i i ies a e all ac i i ies wi h ze o o al ime ese e, and o he
ac i i ies a e no c i ical. De ailed in o ma ion abou CPM can be ound in se e al sou ces, (e.g., Wins on, 2003; Maylo ,
2010; Lockye & Go don, 1991; Field & Kelle , 1998). The second mos equen ly used ool is simula ion me hods, o
app oaches e e ed o as CDM (Collabo a i e Decision Making) (Kie zkowski & Kisiel, 2017; Kabongo e al., 2016;
End izalo a e al., 2016).
The i s wo k ha should be no ed in connec ion wi h he use o CPM o he p ocess o planning ai c a g ound handling
is he a icle (Van Blokland e al., 2008). In i , he au ho s desc ibe he p ocesses a Ams e dam-Schiphol ai po and moni o
he possibili ies o educing he u na ound o na ow-body and wide-body ai c a , speci ically he B737 and B747. The
con ibu ion o hei a icle lies in he p oposal o di ide he en i e p ocess o ai c a u na ound a he ai po ap on in o
wo sub-p ocesses – p ocesses ca ied ou in he space "abo e he wing" and he space "unde he wing". The p ocesses
ca ied ou in he space "abo e he wing" include he opening and closing o he boa ding s ai s, boa ding, and boa ding o
passenge s, eplenishmen o ca e ing, cleaning o he cabin, and ac i i ies ca ied ou by he ligh s a (inspec ion o he
ai c a deck). P ocesses pe o med "unde he wing" include a aching GPUs, secu ing unde ca iage wheel chocks,
unloading and loading baggage, goods, and mail, e illing po able wa e , d aining sep ic anks, e ueling, se ing ou a bu e
zone, and pushback. The whole p ocess is de ined by he ime o secu ing he ai c a 's wheels wi h s ops (Block on Time)
and he ime o emo ing he s ops om he ai c a 's wheels (Block o Time). Based on da a om he ca ie KLM, he
au ho s analyzed he u na ound p ocesses o wo ypes o ai c a using CPM o de e mine which ac i i ies can be educed
in du a ion o sho en he en i e ai c a u na ound p ocess. The au ho s also analyzed he si ua ion a A landa Ai po in
Sweden, whe e hey in es iga ed he ime-consuming p ocess o ai c a u na ound and ied o ind ac i i ies sui able o
educing he o al u na ound ime. A e implemen a ion, he changes p oposed by he au ho s educed he u na ound ime
o he B737 by 42% and o he B747 by 38%.
When e alua ing he e ec i eness o he ai c a handling p ocess as demons a ed by Kwasibo ska (2010), he au ho uses
Gan cha s and wo ks wi h s ochas ic ope a ing condi ions. The en y o ai c a in o he handling sys em is modeled by a
Poisson p obabili y dis ibu ion. To sol e and e alua e he e iciency o he handling p ocess, i uses a me hod based on he
heo y o mass se ice (Queueing Theo y). The connec ion wi h he sol ed p oblem lies in a di e en way o modeling he
low o incoming ai c a in o he p ocess o ai c a g ound handling du ing hei check-in. The esul s o he esea ch can
be ollowed up in he u u e in connec ion wi h he issue o pa allel handling.
Maland i e al. (2019) ha e ecen ly shown he deal wi h he e iciency o he p ocesses associa ed wi h ai c a check-in a
he ai po in cases whe e he e iciency o he p ocess can be impai ed by ac i i ies ha a e beyond he con ol o he
ca ie s. An example o such dis up ion o p ocesses can be a s ike o pa o he g ound s a . I he numbe o wo ke s
dec eases, he ime equi ed o check in he ai c a will inc ease, which can lead o delays in he ac i i ies o he ai c a
check-in p ocess and he e o e he depa u e. The solu ion o he p oblem consis s in de ining he minimum numbe o
employees a which no delays occu . The solu ion was c ea ed using AnyLogic so wa e. The au ho s conduc ed hei
esea ch on he condi ions o he Lisbon Humbe o Delgado ai po . He e he e is a di ec link o he esea ch p esen ed in
he a icle because i is p ecisely in cases o s ikes by pa o he g ound s a ha he e is a need o ensu e ai c a g ound
handling wi h a minimum numbe o employees.
Okwi e al. (2017) ha e shown he analysis o he check-in p ocess using he Collabo a i e Decision Making (CDM)
me hod. The da a used o he calcula ion con ains 65,000 obse a ions om 2014 a Mad id Ai po . The au ho s moni o ed
he in luence o he so-called c i ical indica o s on he o al delay ime o he check-in p ocess. To con ol he smoo hness
o he p ocess o ai c a g ound handling, he au ho s p oposed an indica o called "S a Values", he p edic ion o which
can de e mine he minimum condi ions o delay and he o al handling ime. The a icle con i ms he sui abili y o using he
CDM me hod o in luencing he smoo hness o ai a ic om hei esea ch, he issue o c i ical indica o s wi h an e ec
on he o al ime o ai c a g ound handling was aken o e o ou a icle. C i ical indica o s a e ep esen ed by ac i i ies
on he c i ical pa h.
258
App oaches published in he pas o inc easing he e iciency o he p ocess o ai c a g ound handling use he en i e
spec um o ma hema ical and in o ma ics disciplines. Mos o en, modeling is based on ne wo k analysis and ma hema ical
p og amming me hods, which combine he ma hema ical app oach in he p esen ed a icle. In he p e ious app oaches, he
possible subs i u abili y o wo ke s wi h selec ed quali ica ions in ol ed in ai c a g ound handling was nowhe e
conside ed, which he p esen ed a icle admi s. The subs i u abili y o wo ke s wi h speci ied quali ica ions pa icipa ing in
ai c a g ound handling is cha ac e is ic, especially o smalle ai po s o egional impo ance (Taba es e al., 2021;
Schul z, 2018 and Shen e al. 2019).
2. Ma e ials and Me hods
The ma hema ical model, as demons a ed by Teichmann & Do da (2016), was used o c ea e a ma hema ical model o
planning pe sonnel secu i y o se ice p ocesses aking place du ing ai c a g ound handling wi h he possibili y o mu ual
subs i u abili y o g ound pe sonnel. The unc ionali y o he model was e i ied in Teichmann & Do da (2016) only on a
simple model example wi hou connec ion o a eal p ocess. Fo he needs o he sol ed op imiza ion p oblem, i was
necessa y o modi y he ma hema ical model in a o m ha mee s he pa ame e s de e mined by he ope a ion a he sol ed
ai po .
C ea ing a ma hema ical model o he sol ed ask is p eceded by c ea ing a ne wo k g aph o he p ojec and ob aining he
basic ime cha ac e is ics o indi idual ac i i ies using CPM.
In he ollowing pa ag aph, he p oblem o mula ion o he sol ed ask will be p esen ed, consis ing o a lis o inpu da a,
expec ed decisions ( equi ed esul s), and an op imiza ion c i e ion, acco ding o he alue o which he e ec i eness o he
p oposed solu ion is assessed.
The ollowing a e aken om he ma hema ical model:
𝑁 ⋯ se o ac i i ies ha make up he p ocess o ai c a g ound handling;
𝑃 ⋯ se o quali ica ion needed o implemen he ai c a g ound handling;
𝑃 ⋯ se o quali ica ions ha can pe o m he ac i i y 𝑖∈𝑁;
𝐿 ⋯ se o wo ke s' quali ica ions 𝑝∈𝑃;
𝑡

⋯ ea lies possible s a o ac i i y 𝑖∈𝑁;
𝑡

⋯ he la es pe missible s a o he ac i i y 𝑖∈𝑁;
i … du a ion o ac i i y 𝑖∈𝑁 .
The o mula ion o he p oblem shown in (Teichmann & Do da, 2016) is supplemen ed wi h he ollowing inpu da a ypes:
𝐶 ⋯ he numbe o employees o be assigned o pe o m he ac i i y 𝑖∈𝑁;
𝑐 ⋯ numbe o wo ke s' quali ica ions 𝑝∈𝑃;
𝑎 ⋯ elemen o he ma ix ep esen ing he a ilia ion o he quali ica ion
wo ke 𝑝∈𝑃 o pe o m he ac i i y 𝑖∈𝑁 – when he wo ke
quali ica ion is 𝑝∈𝑃 is au ho ized o pe o m he ac i i y 𝑖∈𝑁,
hen 𝑎 =1, o he wise 𝑎 =0;
𝑏 ⋯ ma ix elemen allowing wo ke ans e s be ween ac i i ies –
when he wo ke is ans e ed o an ac i i y
𝑗
∈𝑁
a e ask 𝑖∈𝑁∪󰇝0󰇞, hen 𝑏 =1, o he wise 𝑏 =0.
The ask is o decide on he assignmen o wo ke s o indi idual quali ica ions o indi idual ac i i ies so ha he o al
numbe o wo ke s deployed o implemen ai c a g ound handling is minimal.
2.1 Sol ing he op imiza ion p oblem
Two g oups o a iables will be in oduced in o he model o sol e he p oblem. The i s g oup o a iables will consis o
bi alen a iables 𝑥 ep esen ing he ans e o wo ke 𝑙 ∈ 𝐿 quali ica ion 𝑝 ∈ 𝑃 om ac i i y 𝑖 ∈ 𝑁 ∪󰇝0󰇞 o
ac i i y 𝑗 ∈ 𝑁. T ans e s o wo ke s be ween ac i i ies a e only pe mi ed i a wo ke wi h he same quali ica ions can
pe o m bo h ac i i ies. I 𝑥 =1 a e he op imiza ion calcula ion is comple ed, hen he ans e o he gi en wo ke
J. Cíleček e al. / Jou nal o P ojec Managemen 9 (2024)
259
be ween ac i i ies will occu . I , a e he op imiza ion calcula ion, i is ue ha 𝑥 =0, hen he ans e o he gi en
wo ke be ween ac i i ies will no occu . The second g oup o a iables will consis o non-nega i e a iables 𝑧 ep esen ing
a possible ime shi o he s a o ac i i y 𝑖 ∈ 𝑁.
Fu he mo e, he a iables 𝑥 a e included in he model. I a e comple ion o he op imiza ion calcula ion, 𝑥 =1,
hen his means ha a wo ke 𝑙 ∈ 𝐿 wi h quali ica ion 𝑝 ∈ 𝑃, who has no ye pe o med any ac i i y in ai c a g ound
handling, will be deployed o pe o m ac i i y 𝑗 ∈ 𝑁.
I , a e he op imiza ion calcula ion, i is ue ha 𝑥 =0, hen he ans e o he gi en wo ke will no occu .
The ma hema ical model o he sol ed p oblem has he o m:
𝑚𝑖𝑛
𝑓
󰇛𝑥 𝑧󰇜=𝑥
∈
∈∈
(1)
Unde condi ions:

𝑎𝑥 =𝐶
∈
∈
∈∪󰇝󰇞
o
𝑗
∈𝑁 (2)
𝑥 ≤𝑐

∈
∈
o 𝑝∈𝑃 (3)
𝑥 ≤𝑎
 o 𝑖∈𝑁∪󰇝0󰇞;
𝑗
∈𝑁; 𝑝∈𝑃; 𝑙∈𝐿
 (4)
𝑥 ≤𝑏
 o 𝑖∈𝑁∪󰇝0󰇞;
𝑗
∈𝑁; 𝑝∈𝑃; 𝑙∈𝐿
 (5)
𝑥

∈ ≤1 o 𝑖∈𝑁; 𝑝∈𝑃;𝑙∈𝐿
 (6)
𝑥
∈∪
󰇝

󰇞
=𝑥
∈∪
󰇝

󰇞
o
𝑗
∈𝑁; 𝑝∈𝑃;𝑙∈𝐿
 (7)
𝑡

+ 𝑧+𝑡≤𝑡


+𝑧+𝑀∙1−𝑥  o 𝑖∈𝑁;
𝑗
∈𝑁; 𝑝∈𝑃;𝑙∈𝐿
 (8)
𝑧≤𝑡


−𝑡

o 𝑖∈𝑁 (9)
𝑥 ∈󰇝0 1󰇞 o 𝑖∈𝑁∪󰇝0󰇞;
𝑗
∈𝑁; 𝑝∈𝑃;𝑙∈𝐿
 (10)
𝑧∈𝑅

 o 𝑖∈𝑁 (11)
Func ion (1) ep esen s he o al numbe o wo ke s deployed o pe o m ai c a g ound handling. The se o cons ain
condi ions (2) ensu es ha each ac i i y 𝑗 ∈ 𝑁 is assigned he equi ed numbe o wo ke s. The g oup o limi ing condi ions
(3) ensu es ha no mo e wo ke s han a e a ailable a e used in each quali ica ion g oup 𝑝 ∈ 𝑃 wi hin he ask solu ion.
The g oup o limi ing condi ions (4) ensu es ha i a wo ke wi h he quali ica ion 𝑝 ∈ 𝑃 canno pe o m ac i i y 𝑗 ∈ 𝑁,
hen he wo ke o he gi en p o ession will no be employed o pe o m he gi en ac i i y. A g oup o limi ing condi ions
(5) o obse ing a logical sequence o ac i i ies acco ding o he cons uc ed ne wo k g aph wi h a c i ical pa h iden i ied
by he CPM. The g oup o limi ing condi ions acco ding o ela ion (6) ensu es ha e e y wo ke 𝑙 ∈ 𝐿 who can pe o m
ac i i ies 𝑖 ∈ 𝑁 and 𝑗 ∈ 𝑁 will swi ch o a mos one ac i i y 𝑗 ∈ 𝑁 a e comple ing ac i i y 𝑖 ∈ 𝑁. The g oup o
limi ing condi ions acco ding o ela ion (7) will ensu e he con inui y o he wo ke 𝑙 ∈ 𝐿 quali ica ion 𝑝 ∈ 𝑃 ∩𝑃
.
I means ha when a wo ke 𝑙 ∈ 𝐿 o quali ica ion 𝑝 ∈ 𝑃 ∩𝑃
 is assigned o ac i i y 𝑗 ∈ 𝑁, he mus also be emo ed
om his ac i i y a e i s comple ion. A g oup o es ic i e condi ions acco ding o ela ion (8) will p e en empo ally
inadmissible ime shi s o wo ke s. I means ha i a wo ke 𝑙 ∈ 𝐿 o quali ica ion 𝑝 ∈ 𝑃 ∩𝑃
 assigned o ac i i y 𝑖 ∈
𝑁 does no each he s a ime o ac i i y 𝑗 ∈ 𝑁, hen his ans e be ween ac i i ies 𝑖 ∈ 𝑁 and 𝑗 ∈ 𝑁 will no occu ( he
symbol 𝑀 ep esen s a p ohibi i e cons an ). The g oup o limi ing condi ions acco ding o ela ion (9) ensu es ha he ime
shi o he ac i i y 𝑖 ∈ 𝑁 can ake place only in he in e al bounded by he ea lies possible ime o he ac i i y and he
la es pe missible s a o he ac i i y. The g oups o limi ing condi ions (10) and (11) de ine he de ini ion domains o he
a iables used in he model.
Since he objec i e unc ion only minimizes he numbe o wo ke s deployed, he e is a possibili y ha an undesi able
de ia ion om he echnical p ocedu es used in p ac ice occu s. This undesi able de ia ion consis s in he ac ha a wo ke
wi h a quali ica ion ha is designa ed o he pe o mance o his ac i i y as second o hi d in o de will be deployed o
pe o m a ce ain ac i i y, while a wo ke wi h a quali ica ion ha is in ended o pe o m he gi en ac i i y is i s in o de
is ee. To p e en his undesi able echnological de ia ion (e en i i was caused by he educ ion o he o al numbe o
wo ke s deployed o ai c a g ound handling, i is ad isable o pe o m one mo e phase o he op imiza ion calcula ion

260
consis ing in sol ing a model con aining a sys em o limi ing condi ions (2) – (11) supplemen ed by a pu pose unc ion
(12),
min
𝑓
󰇛𝑥 𝑧󰇜=𝑟𝑥
∈
∈∈
(12)
in which he cons an s 𝑟 a e he elemen s o he penal y ma ix. The penal y ma ix is c ea ed based on he ollowing
conside a ions. Since he objec i e unc ion (12) is o he minimiza ion ype, he elemen 𝑟 ep esen ing he deploymen
o he quali ica ion 𝑝 ∈ 𝑃 in ended o pe o m he ac i i y 𝑗 ∈ 𝑁 as he i s in he sequence will be assigned he lowes
penal y alue – e.g. 1, he elemen 𝑟 ep esen ing he deploymen o he quali ica ion 𝑝 ∈ 𝑃 de e mined o he
pe o mance o ac i i y 𝑗 ∈ 𝑁 as he second in o de , will be assigned a highe penal y alue - e.g. 100, and he elemen
𝑟 ep esen ing he quali ica ion 𝑝 ∈ 𝑃 in ended o pe o m ac i i y 𝑗 ∈ 𝑁 as he hi d in o de will be assigned he highes
penal y alue - e.g. 1000.
Howe e , in he second phase o he op imiza ion calcula ion, he esul o he i s phase o he op imiza ion calcula ion
mus be espec ed, ha is, a g ea e numbe o wo ke s han was calcula ed in he p e ious phase mus no be used o he
ai c a g ound handling. Le his minimum numbe be deno ed by 𝑄. The condi ion ensu ing he ul illmen o he s a ed
equi emen will ha e he o m Eq. (13). This condi ion will ensu e ha he numbe o employees calcula ed in he 1s phase
o he op imiza ion calcula ion will no be exceeded du ing he implemen a ion o ai c a g ound handling.
𝑥
∈
∈∈ ≤𝑄 (13)
3. Compu a ional expe imen s wi h p oposed model
Compu a ional expe imen s wi h he designed ool will be conduc ed in he egional Leoš Janáček In e na ional Ai po in
Os a a in he Czech Republic. A Leoš Janáček Ai po in Os a a, ai c a g ound handling is pe o med by only one
handling company, which he ai po ope a es. I is a legal monopoly ha complies wi h Council Di ec i e 96/67/EC o 15
Oc obe 1996. Se en g oups o wo ke s wi h di e en numbe s o de ined quali ica ions wo k a he abo e-men ioned
ai po . Fou g oups a e made up o ai po s a , and he o he h ee a e hi ed ex e nally o ca y ou speci ic ac i i ies such
as e uelling o cleaning he ai c a deck. The di ision o g oups in o indi idual wo ke s is in oduced o p ocess modelling
o be able o ans e wo ke s be ween ep esen a i e ac i i ies indi idually. Con e ing he en i e g oup wi h mo e
employees may no bene i pe sonnel, economy, and capaci y.
Compu a ional expe imen s wi h he model (1) – (13) we e conduc ed in he condi ions o ai c a u na ound o cha e
ligh s ope a ed by he Boeing 737 ai c a . In he case o he ai c a g ound handling, he p esence o ansi passenge s on
boa d was no conside ed. As he calcula ion ela es o ai c a g ound handling, i does no ma e whe he he ligh was
pe o med inside o ou side he Schengen a ea. The da a used o he compu a ional expe imen was ob ained om a eal
p ocess o ai c a g ound handling a he ai po . This cou se o ai c a g ound handling is ypical o he ai po and
co esponds o mos ligh s in he summe season. In his way, app oxima ely 250-300 ai c a a e handled a he ai po
du ing he 3-mon h summe season. I was abou he ai c a g ound handling o ligh s ca ying passenge s. A handling
agen manages he ai c a g ound handling a he abo e-men ioned ai po . Two mobile s ai s a e used a Os a a ai po
o boa ding and disemba king passenge s on Boeing 737 ai c a , and wo bel con eyo s a e used o unloading and
loading luggage. Only checked baggage was loaded in he ca go a ea o he ai c a . Loading o checked baggage and mail-
in con aine s was no conside ed. Baggage is loaded bo h in he on and in he ea ca go a ea o he uselage. Re uelling
o he ai c a akes place om he ehicle when he e a e no passenge s on boa d he ai c a ( he e is, he e o e, no need
o he assis ance o ai po i e igh e s in he ai po a ea du ing ai c a g ound handling. Consequen ly, he app oach and
emo al o i e engines a e also no pa o ai c a g ound handling).
Fig. 1. Hie a chy o wo ke s in ai c a g ound handling a Os a a ai po
J. Cíleček e al. / Jou nal o P ojec Managemen 9 (2024)
261
The ollowing echnological speci ica ions a e de ined o ai c a g ound handling in he condi ions o he abo e-men ioned
ai po . A Os a a Ai po , depa ing and boa ding passenge s c oss he ou e om he plane o he ga e and back on oo .
Boa ding o passenge s begins a e he ai c a is e uelled, and ai c a a e no pushed ou o he s and using pushback.
Fig. 1 shows indi idual g oups o wo ke s in ol ed in ai c a g ound handling a he ai po . Thei hie a chy is also shown.
I also implies he subs i u abili y o indi idual quali ica ions. The solid lines in Figu e 1 show he ela ionship be ween
di ec supe io /subo dina e wo ke s. As al eady men ioned, he highes - anking wo ke in ai c a check-in is he handling
agen . Dashed lines indica e indi ec ela ionships. Indi ec managemen ela ionships mean he indi ec subo dina ion o
wo ke s p o iding he gi en ac i i y (wo ke s o ex e nal companies). The lis o ac i i ies and he au ho iza ion o wo ke s
wi h indi idual quali ica ions o pe o m hem a e shown in Table 1. Table 1 also shows he o de in which ano he can
ep esen a gi en wo k g oup. Fo example, he ac i i y o app oaching bel con eyo s is p ima ily pe o med by wo ke s
o quali ica ion 4 (ai c a loading wo ke s). Seconda ily i can be ca ied ou by wo ke s o quali ica ion 3 (specialis ) and
e ia y by a wo ke wi h quali ica ion 2 (ma shalling wo ke ). The las ow o Table 1 shows he numbe o wo ke s o
indi idual quali ica ions pa icipa ing in ai c a g ound handling in he cu en s a e.
The highes - anking wo ke in ai c a check-in, as al eady men ioned, is he handling agen . Indi ec ela ionships a e
indica ed by dashed lines. Indi ec managemen ela ionships mean he indi ec subo dina ion o wo ke s p o iding he
gi en ac i i y ( hese a e wo ke s o ex e nal companies). The lis o ac i i ies and he au ho iza ion o wo ke s o indi idual
quali ica ions o pe o m hem a e shown in Table 1.
Table 1
Tasks and numbe o wo ke s needed
Task/Quali ica ion
Handling agen
Ma shaling wo ke
Specialis
AC loading wo ke
Cleaning wo ke
Ca e ing wo ke
AC e ueling wo ke
1 Guide he ai c a o he s and 1
2 The wedge o he ai c a 1
3 Se ing up and connec ing a GPU 2 1
4 C ea ion o a sa e zone 1 2 3
5 Visual inspec ion o he ai c a 1
6 Apposi ion o s ai s 3 2 1
7 Opening ca go spaces 3 2 1
8 Deli e y o a bel con eyo and a ac o wi h olleys o checked baggage 3 2 1
9 Unloading baggage 1
10 Exi o passenge s 1
11 Re uelling 1
12 Loading ca e ing 1
13 Loading d inking wa e 2 1
14 Emp ying la a o y sys em 2 1
15 Cleaning he in e io o he ai c a 1
16 Baggage loading 1
17 Pa king o a bel con eyo and a special baggage ehicle 3 2 1
18 Closing ca go spaces 3 2 1
19 Boa ding o passenge s 1
20 P epa a ion o depa u e documen a ion 1
21 Pa king o s ai s 3 2 1
22 Disconnec ion and pa king o he GPU 2 1
23 Closu e o sa e zone 1 2 3
24 Visual inspec ion o he ai c a 1
25 Clea ance o he ai c a 1
26 Ma shalling 1
Numbe o employees 1 1 1 6 5 1 1
To implemen he compu ing expe imen , i was necessa y o c ea e an o e iew o he ac i i ies aking place du ing ai c a
g ound handling and o assign g oups o wo ke s who can pe o m hem, including hei subs i u abili y, o indi idual
ac i i ies. This is done in Table 1. The i s column ep esen s he numbe o ai c a g ound handling ac i i ies o he B737
ai c a a he ai po . The second column con ains he name o he ai c a g ound handling ac i i y o he B737 ai c a a
he ai po . Columns ma ked 1 – 7 co espond o he indi idual wo kg oups in ol ed in handling. The las ow o Table 1
shows he numbe o wo ke s wi h he gi en quali ica ion who cu en ly p o ide ai c a g ound handling a he ai po .
Numbe s 1 - 3 in he ows o he able co esponding o indi idual ac i i ies ep esen p io i ies in assigning indi idual
g oups o indi idual ac i i ies. The able ield co esponds o ow 8 and he column labelled 2 shows he numbe 3. This
means ha i is ecommended ha wo ke g oup 2 ( he ma shalling wo ke ) pa icipa e only hi d o ensu e ac i i y 8. The
able ield co esponding o ow 8 and he column ma ked as 3 shows he numbe 2. This means ha i is ecommended ha
262
he g oup o wo ke s 3 (specialis s) pa icipa e second o ensu e ac i i y 8. The able ield co esponding o ow 8 and he
column ma ked 4 shows he numbe 2. This means, ha i is ecommended ha wo ke g oup 4 (ai c a loading wo ke )
pa icipa es i s o ensu e ac i i y 8. When an ai c a loading wo ke is no a ailable, a specialis can eplace him in ac i i y
8. When an ai c a loading o ice o specialis is no a ailable, a ma shalling o ice may ill in o hem.
Names o he quali ica ions lis ed in Table 1: 1 - handling agen , 2 - ma shalling wo ke , 3 - specialis , 4 - ai c a loading
wo ke , 5 - ai c a cleaning wo ke , 6 - ca e ing wo ke , 7 - ai c a e uelling wo ke .
To ind a solu ion o he abo emen ioned p oblem, i was necessa y o c ea e a ne wo k g aph. The ne wo k diag am o he
ai c a g ound handling o a B 737 ai c a se ing a cha e ligh handled a he abo e-men ioned ai po was made in
compliance wi h all he abo e en y condi ions and is shown in Figu e 2. Ve ices a e numbe ed acco ding o he p inciples
o he c i ical pa h me hod. The es ablished numbe ing is help ul o he needs o he sol ed ask. Ma king he edges is key.
Edge e alua ion is composed o wo pa s. The numbe be o e he pa en hesis ep esen s he ac i i y numbe . This numbe
co esponds o he numbe in he i s column o Table 1. The numbe in pa en heses ep esen s he du a ion o he ac i i y.
Fig. 2. CPM o ai c a g ound handling
J. Cíleček e al. / Jou nal o P ojec Managemen 9 (2024)
263
A de ailed calcula ion o he indi idual alues shown in Fig. 2 is e iden om Table 2. Table 2 shows a lis o all ac i i ies
planned o ai c a g ound handling in he abo e-men ioned ai po condi ions. Each edge in he g aph ( ep esen ing an
ac i i y du ing ai c a g ound handling) in e sec s wi h wo e ices 𝑣 and 𝑣, whe e he e ex 𝑣 ep esen s he s a o
he ac i i y and he e ex 𝑣 ep esen s he end o he ac i i y. The ac i i ies lis ed in he able a e a anged in a logical
sequence.
Table 2 also con ains he ime equi emen o indi idual ac i i ies (du a ion 𝑡) and he calcula ed ea lies possible s a
imes o indi idual ac i i ies (𝑡), he la es pe missible s a imes o ac i i ies (𝑡

), and calcula ed ese e ime alues o
indi idual ac i i ies.
Table 2
Inpu in o ma ion o c ea ing a ne wo k g aph
Task
𝒌 𝒊 𝒋 𝒕𝒌
(min) 𝒕𝒌

(min) 𝒕𝒌

(min) CR VR ZR NR
1 0 1 2 0 0 0 0 0 0
2 1 2 1 2 2 0 0 0 0
3 2 3 2 3 3 0 0 0 0
4 3 4 3 5 5 7 0 0 0
5 4 5 3 8 15 7 0 0 0
6 3 6 3 5 5 0 0 0 0
7 3 7 3 5 5 18 0 18 0
8 7 8 3 8 26 18 0 0 0
9 8 9 8 11 29 18 0 0 0
10 6 10 10 8 8 0 0 0 0
11 10 11 15 18 18 0 0 0 0
12 10 12 10 18 18 5 0 5 0
13 10 13 3 18 18 9 0 9 0
14 13 14 3 21 30 9 0 0 0
15 10 15 15 18 18 0 0 0 0
16 9 16 8 19 37 18 0 0 0
17 16 17 3 27 45 18 0 0 0
18 17 18 3 30 48 18 0 0 0
19 11 19 10 33 33 0 0 0 0
20 19 20 3 43 43 0 0 0 0
21 20 21 2 46 46 0 0 0 0
22 21 22 3 48 48 0 0 0 0
23 22 23 3 51 51 0 0 0 0
24 23 24 5 54 54 0 0 0 0
25 24 25 1 59 59 0 0 0 0
26 25 26 3 60 60 0 0 0 0
As seen in Fig. 2 and he calcula ions shown in Table 2, he c i ical pa h has a leng h o 63 minu es. The alues in he column
labeled CR ep esen he o al ese es o indi idual ac i i ies. The alues in he column labelled VR ep esen indi idual
ac i i ies' ee ese es. The alues in he column labelled ZR ep esen he dependen ese es o indi idual ac i i ies, and
he alues in he column labeled NR ep esen s he independen ese es o indi idual ac i i ies.
CR - ep esen s he o al ese es o indi idual ac i i ies. VR – he maximum ime by which i s ea lies possible s a can
be delayed so ha he ea lies possible s a s o ac i i ies immedia ely ollowing his ac i i y a e no a ec ed. ZR – he
maximum ime by which i s la es pe missible s a can be delayed so ha he la es pe missible s a s o ac i i ies di ec ly
connec ed o his ac i i y a e no a ec ed.
NR – he maximum ime by which he la es pe missible s a o he ac i i y can be delayed so ha he ea lies possible
s a o ac i i ies di ec ly connec ed o his ac i i y is no a ec ed.
In he nex s ep, i is necessa y o c ea e ma ices A, B, and R. Table 3 con ains he basis o he c ea ion o ma ix A. Table
3 has bi alen alues o combina ions o indi idual ac i i ies and quali ica ions o ai po pe sonnel. I a wo ke o
quali ica ion p
∈
P can pe o m ac i i y j
∈
N, hen he alue one is gi en a he in e sec ion o he ow and he column.
O he wise, he alue 0 is gi en a he in e sec ion o he ow and he column. The exis ence o subs i u abili y o wo ke s is
ma ked in colou . P ima ily, he ac i i ies a e ca ied ou by he wo king g oup wi h a ed ield colou , seconda ily wi h a
yellow ield colou , and e ia y wi h a g een ield colou . Fo example, i an ai c a loading wo ke canno open he ca go
hold, a specialis wo ke can eplace him. I a specialis wo ke pe o ms ano he ac i i y, a ma shalling wo ke can eplace
him. This able con ains da a on he numbe o wo ke s needed o each ac i i y and he numbe o wo ke s wi h indi idual
quali ica ions.