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
Ci a ion: Kuda, F.; Dlask, P.;
Teichmann, M.; Be an, V. Time–Cos
Schedules and P ojec –Th ea s
Indica ion. Sus ainabili y 2022,14,
2828. h ps://doi.o g/10.3390/
su14052828
Academic Edi o s: Kel in K. L. Wong,
Simon Fong, Yu Lu and Dhanjoo
N. Ghis a
Recei ed: 16 Janua y 2022
Accep ed: 15 Feb ua y 2022
Published: 28 Feb ua y 2022
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A ibu ion (CC BY) license (h ps://
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sus ainabili y
A icle
Time–Cos Schedules and P ojec –Th ea s Indica ion
F an isek Kuda 1, Pe Dlask 2, Ma ek Teichmann 1,* and Vacla Be an 3
1Depa men o U ban Enginee ing, Facul y o Ci il Enginee ing, VSB-Technical Uni e si y o Os a a,
70800 Os a a, Czech Republic; [email p o ec ed]
2Depa men o Economic and Managemen in Ci il Enginee ing, Facul y o Ci il Enginee ing,
Czech Technical Uni e si y, 16636 P ague, Czech Republic; dlask@ s .c u .cz
3Depa men o Economics, Facul y o Economics, Uni e si y o Sou h Bohemia,
37005 ˇ
CeskéBudˇejo ice, Czech Republic; [email p o ec ed]
*Co espondence: ma [email p o ec ed]; Tel.: +420-596-991-963
Abs ac :
One o he mos common disciplines in a business o economic p ojec is iming and
esou ce e iew. Despi e he equency o use, he le el o sophis ica ion is no high enough o
main ain i s le el o impo ance. Exceeding deadlines and non-compliance wi h con ac ual cos s is
mo e han common. Mo eo e , he e a e p ojec s whe e unce ain ies a e a na u ally accompanying
phenomenon. Resea ch p ojec s, implemen a ion o solu ions in a ime-limi ed si ua ion, o in
an en i onmen o limi ed knowledge c ea es isk. Any p ojec p oposal aces u u e ealiza ion
isks when i s planning managemen does no know wi h ce ain y whe e he cu en isks and
unce ain ies may come om. Decision-making, isk managemen dynamics, and simula ions ha e
de eloped in ecen decades in o an e udi e and use ul discipline. The aim is o indica e how much
o he ime–cos schedule p oposal is s able, con ollable, and economically easible. The app oach is
based on he idea ha mode n esou ce scheduling equi es nonlinea dynamic calcula ing models
and simula ions. The me hodology p esen ed is based on he dynamics o unde lying physical and
economic p ocesses ha o m a spa ial pa e n o a ime se ies. The a icle’s objec i e is de o ed o
he ea ly indica ion o a dynamic p ojec schedule’s ins abili y and p edisposi ion o bi u ca ion and
chaos. In o he wo ds, he aim is o show no only wha will happen bu how di e se and damaging
he p ojec may become in he u u e.
Keywo ds:
ime scheduling; p oduc ion speed; p oduc ion accele a ion; simula ion; p ojec cos s;
du a ions; isk e alua ions; ci cula li e cycle; managemen dynamic
1. In oduc ion
The idea o p oduc ion planning, scheduling, and con ol (PPSC) has been used in
mode n economic and business applica ions o he las h ee cen u ies [
1
]. Today, isk,
unce ain y, and simula ion a e subs an ial pa s o en ep eneu ship and a e common o
economic dynamics. The expec a ions o PPSC migh su e om unin en ionally undesi able
chao ic consequences. Such a ime–cos schedule unde mines he e iciency o udimen a y
p ojec documen a ion [
2
,
3
]. Managemen decisions based on empi ical schedules can be
coun e p oduc i e and may ha e long- e m nega i e “T ojan ho se” consequences.
1.1. Publica ion F equency
The e m PPSC has been ci ed in 1584 publica ion links in he ci a ion da abase Web o
Science om 1.Q/2021 o p esen . The ke nel e ms a e ime and cos scheduling (TCS) and
e e o 25,752 publica ions, di ided in o esea ch segmen s, as shown in Table 1.
The de ini ion o isk in enginee ing is o mula ed as he p oduc o an ac i i y’s isk
p obabili y and (cos ) consequences e alua ion. A calcula ion o he isk may be conside ed
sa is ac o y o well-de ined si ua ions wi h a small numbe o in luences; ex ensi e eed-
back issues in isk e alua ion may esul in chaos and equi e imp o emen s [
4
]. Exceeding
Sus ainabili y 2022,14, 2828. h ps://doi.o g/10.3390/su14052828 h ps://www.mdpi.com/jou nal/sus ainabili y
Sus ainabili y 2022,14, 2828 2 o 16
deadlines and inc eased implemen a ion cos s cause his de ia ion om he desi ed esul .
Fu he discussion o his heo y and commen s a e a ailable in [5].
Table 1. The equency o publica ions o TCS opics. Sou ce: Web o Science 2021.
Reco d Coun 100% = 25,752;
Selec ion o >5.00% Reco ds %
enginee ing elec ical elec onic 5822 22.61
ope a ions esea ch managemen science 4347 16.88
compu e science heo y me hods 3308 12.85
enginee ing indus ial 2603 10.11
compu e science in o ma ion sys ems 2364 9.18
elecommunica ions 2086 8.10
compu e science in e disciplina y applica ions 2069 8.03
compu e science ha dwa e a chi ec u e 1768 6.86
compu e science a i icial in elligence 1686 6.55
managemen 1610 6.25
enginee ing manu ac u ing 1542 5.99
au oma ion con ol sys ems 1473 5.72
ene gy uels 1450 5.63
enginee ing ci il 1425 5.53
compu e science so wa e enginee ing 1328 5.16
The ea ly ecogni ion o he buil -in p e equisi es o chao ic ime and cos ins abili y
will help inc ease p ojec u ili y; howe e , his will only be e ec i e in he ea ly s ages o
he p ojec p oposal. The need o sophis ica ed managemen is p esen ed in he use ul
opinion o [
6
]: “Wi hou chaos he e would be no c ea ion, no s uc u e and no exis ence.
A e all, o de is me ely he epe i ion o pa e ns; chaos is he p ocess ha es ablishes
hose pa e ns. Wi hou his c ea i e sel -o ganizing o ce, he uni e se would be de oid o
biological li e, he bi h o s a s and galaxies-e e y hing we ha e come o know”.
The basic a i ude is ha i is desi able o de elop mo e comp ehensi e me hods and
ad anced compu e so wa e o he e alua ion o isk and i s o iginal oo s in o gani-
za ional s uc u e. Howe e , he p io i y o a mo e comp ehensi e isk managemen
s uc u e seems o be mo e u gen han he echnical indica o s hemsel es.
The e a e a ew undamen al app oaches [7–9] o isk e alua ion:
(a)
Pa ame ic me hods;
(b)
Simula ion on he basis o classical inpu –ou pu obse a ions;
(c)
Simula ions on he basis o he Mon e Ca lo me hod and pseudo- andom numbe s,
he p esen ed pape ex ends his scheme;
(d)
Iden i ica ion o build-in de e minis ic chaos in he s uc u e o a model.
The las wo me hodologies men ioned a e associa ed wi h he app oach p esen ed
in his pape , which was unde aken o emphasize ha isk e alua ion and indica o s a e
he only equi emen s o isk managemen as i maneu e s in o a coo dina ed p ocess.
Mode n managemen p ac ice equi es mo e complex ools o a wide ange o ou ine
managemen decisions, such as cos –bene i analysis, decision ees, game heo y, heu is ic
me hods, op imiza ion, e c. Inc eased indus ial p oduc ion and p oduc i i y equi e mo e
sophis ica ed ools o analysis [
10
] and decision suppo , which will undamen ally depend
on be e decision analysis [
11
,
12
]. Ex ensi e s udies o he escala ion o du a ions and cos s
in majo p ojec s yield su p ising esul s [
13
]. The ou come is ha long- e m p oduc i i y
declines in key echnological p ocesses. The jus i ica ion is mos ly he di e gence be ween
expec ed and ealized cos s [
14
]. Fo example, in nuclea powe plan s, he cos s o he
eac o con ainmen building mo e han doubled, p ima ily due o declining indus ial
in es men labo p oduc i i y. Cons uc ion p oduc i i y in ecen US nuclea powe plan s
epo ed up o 13 imes lowe p oduc ion speeds han o iginal indus y expec a ions [
13
].
The si ua ion in he EU indica ed a simila dynamic, as discussed in [15].
Sus ainabili y 2022,14, 2828 3 o 16
1.2. A icle Con ibu ions
The con ibu ion o his a icle is he ex ension o ools o he e alua ion o p ojec
p oposals and he implemen a ion o p epa a ions (in es men s, s a egies, esea ch ac-
i i ies, e c.). The dynamic p ope ies o design and implemen a ion (including use) ha e
no ye been e lec ed in he ools o enginee ing p ac ice. The po en ial o de elopmen
based on indus ial i ali y is being exhaus ed, and he lack o s abili y o economic and
echnical p ojec s is limi ing o de elopmen . A deepe analysis o p ojec easibili y is
necessa y. Visual ools p ocessed in he ex , such as phase po ai s in loops, show signs
o si ua ions ha equi e u he analysis. Phase po ai s wi hou loop o ma ions can be
desc ibed as p ac ically accep able. Responsible managemen should no c ea e s a emen s,
bu ind solu ions. Iden i ying h ea s and c i ical si ua ions is he i s s ep. Ta ge ed
p oposals o changes and adjus men s a e he second s ep. We also conside modi ica ions
(design, economic, e c.) o he pa ame e s o inpu s ( olumes, anges, p oduc ion speeds,
accele a ion o c i ical p ocesses, e c.) o indi idual pa ially implemen ed ac i i ies. Be-
hind he ou pu s a e he pa ame e s o he p ojec as a whole (deadlines, ealized o al
olumes, implemen a ion speeds, minimiza ion o changes in accele a ion +/
−
) du ing
implemen a ion, and mo e.
Dynamical p ocesses, including economics, physics, ma hema ics, biology, enginee -
ing, and mo e, ha e played a p ominen ole in many disciplines o mo e han a cen u y.
Many ypes o esea ch ha e ocused on issues o s a ic and dynamic models, ac als,
sel -simila i y. The exagge a ion o objec i i y can be associa ed wi h he s a o mode n
de elopmen wi h he wo k o Leibni z (1646–1716) on ecu si e sel -simila i y, and la e
by Weie s asse, who desc ibes con inuous non-di e en iable unc ions. The i s ac al is
a ibu ed o he Czech ma hema ician Be na d Bolzano (1781–1848) in [
16
]; in e es ing de ails
a e p o ided in [
17
]. Dynamic p ocesses a e de eloped in o b oad, di e si ied a eas ega ding
long- ange dependences, long-memo y da a, ime se ies analysis, and nume ous o he s.
Ha od o e s in e es ing ea ly s andpoin s o dynamic heo y in [
18
], which s a es,
“S a ic heo y consis s o a classi ica ion o e ms wi h a iew o sys ema ic hinking,
oge he wi h he ex ac ion o such knowledge abou he adjus men s due o a change o
ci cums ances
. . .
”. He b ings up an inspi ing idea: “A emp s o cons uc a dynamic
heo y ha e ecen ly been p oceeding upon ano he line-namely, by he s udy o ime lags
be ween ce ain adjus men s”.
2. Me hods
The s udy add esses he issue o ime and cos dynamics as a basic ime-managemen
ool. Time and inancial esou ces a e conside ed o be he main endogenous ealiza ion
ac o s. I seeks pe spec i e o e alua ion iews ela ed o app oaches such as Time-
schedule, Gan g aphs, Cyclog am, Flow-Line diag ams, and many o he so wa e p oduc s.
Ea ly ecogni ion o scheduling quali y o i s u u e use is a sough -a e bene i . The need
o imely e alua ion is con i med by he equency o ailu es o la ge and cos ly p ojec s
in he pas .
In he p ojec inpu chain, he main de aul componen s a e based on ac i i y se A
and subsequen calcula ions. The dominan s uc u e is composed o links desc ibing he
easibili y o he p ojec , se up as g aph G
O g
(A). A e implemen a ion, i is gi en as a
calcula ion s uc u e:
PInpu s(A)=⇒[quan i ies Q→p ices π→cos s C→p oduc ion speeds (C’)in →du a ions (D)] | GO g(A) (1)
whe e:
PInpu s(A)—is a desc ip ion inpu o all ac i i ies A= (A1,A2, . . . , Am),
A—is a desc ip ion se a anged by GO g(A), whe e Aiex en is ∀i∈m,
Q—is se o quan i ies Q= (Q1,Q2, . . . , Qm), whe e Qi> 0, ∀i∈m,
π—is se o uni p ices π= (π1,π2, . . . , πm), πi≥0, ∀i∈m,
C—is se o cos s C= (C1,C2, . . . , Cm),
(C’)in —is se o p oduc ion low (C’)in . = ((C1’)in ., (C2’)in ., . . . , (Cm’)in .),
Sus ainabili y 2022,14, 2828 4 o 16
D—se o du a ions D= (D1,D2, . . . , Dm),
GO g(A)—o ganiza ional s uc u e o all ac i i ies (ne wo k s uc u e).
The elemen a y ou pu s a e he du a ion and cos o ac i i ies, o al p ojec cos s, and
p ojec du a ion. Reasonable s ands o implan schemes o ela ions a e gi en and ex ended
calcula ion in Table 2.
Table 2.
Inpu da a TAB
Inpu
(A) o he dynamic ime-schedule calcula ion—example. On he le a e
de e minis ic inpu s; on he igh a e he ela ions o he isk inpu s da abase.
Dynamic Schedule Inpu s
Simula ion
100×
Inpu s Inpu s Inpu s Calcula ion Inpu s
Ac i i y AQuan i y QA
inpu s (*)
P ice πpe QA
uni
Cos s
CA=πAQA
Speed (**)
Q0A
Ac i i y A120 5 100.00 19.00
Ac i i y A27.5 10 75.00 12.00
Ac i i y A310 55 550.00 87.00
Ac i i y A420 20 400.00 48.00
Ac i i y A55 20 100.00 25.00
To al Cos s (TC) 1225.00
(*) # o wo king hou s, m3, m2, ons, .€, . . . . (**) Ex e nal in luence, isk anges, . . . .
The eali y is ha he inpu da a is bu dened wi h isks and unce ain ies. Simpli ied
ime scheduling examples and in e ela ed cos low shows how o e alua e isk by e y
mode a e calcula ion based on sp eadshee s.
The diag am in Figu e 1deals wi h he calcula ion o he inpu da a o indi idual
ac i i ies A. This is an isola ed de e minis ic and s a ic calcula ion. The calcula ion o
s a ic ( ixed) p ojec inpu a iables is in Table 2. Howe e , o he needs o schedules, we
conside ime se ies ou pu s wi h medium- e m o long- e m ime s abili y. This knowledge
is a ailable based on Table 2’s da a and knowledge abou G
O g
. The ou pu p esen a ion
P
Ou pu
is p o ided in Table 3. In his con ex , he able p ocesso calcula ion in Table 3is
a quasi-au o eg essi e (AR) model. The au o eg essi e model is a pa o a p ocess ha
desc ibes ime- a ying p ocesses in economics, echnology, design, e c.
Figu e 1.
Mapping o quan i ies Q, cos C, du a ions D, and in eg a ion o o al cos s. The TC
P ojec
and TD
P ojec
a e calcula ed in Tables 2and 3, and Figu e 2; ans o med in he speci ica ion—(a ow
symbols, in e sion ool, s anda d, e c.) in o a easible economic in e p e a ion. Sou ce: adap ed and
ex ended om [19].
Sus ainabili y 2022,14, 2828 5 o 16
Figu e 2.
Dynamic schedule example: ex e nali ies based on G
O g
(A), calcula ion o cos and du a ion.
Table 3.
Ex e nal inpu s, calcula ion, ime dependency o ac i i ies, ime and esou ces schedule: (*)
hou s, m
3
, m
2
, ons, .
€
,
. . .
, (**) Unce ain es ima ion, ed colo indica es Q
0
, yellow colo indica es
p ojec ime se ies {Q0 }, {Q00 }, {Q000 }, g een colo indica es cumula i e p ojec ime se ies {Q }.
Dynamic Schedule: Cos s Dynamic Schedule: Du a ions
Ex e nal Da a Inpu s Calcula ion
Ac i i y AQuan i y
Inpu s (*)
P ice pe
QUni Cos s [ . €]Speed (**) o
P oduc ion S a [Weeks] Du a ion
[Weeks] End [Weeks] End [Weeks]
Ac i i y A120 5 100.00 15.00 1.00 7.00 8.00 8.00
Ac i i y A27.5 10 75.00 12.00 6.00 7.00 13.00 13.00
Ac i i y A310 55 550.00 70.00 9.00 8.00 16.00 16.00
Ac i i y A420 20 400.00 60.00 11.00 7.00 18.00 18.00
Ac i i y A55 20 100.00 20.00 16.00 5.00 21.00 21.00
To al Cos s TC . . . 1225.00
Dynamic Ne wo k: P oduc ion Speed. Accele a ion. P od. Cumula ed
Ac i i y A8.1 9.1 10.1 11.1 12.1 13.1 14.1 15.1 16.1 17.1 18.1 19.1 20.1 21.1 22.1 23.1 24.1 25.1 26.1 27.1
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Ac i i y A115 15 15 15 15 15 10
Ac i i y A212 12 12 12 12 12 3
Ac i i y A370 70 70 70 70 70 70 60
Ac i i y A460 60 60 60 60 60 40
Ac i i y A520 20 20 20 20
Cash Flow{Q´
}15 15 15 15 15 27 22 12 82 82 142 133 130 130 130 140 60 20 20 20
Accel. {Q´´
}15 0 0 0 0 12 −5−10 70 0 60 −9−3 0 0 10 −80 −40 0 0
Impuls {Q´´´
}15 −15 0 0 0 12 −17 −5 80 −70 60 −69 6 3 0 10 −90 40 40 0
Cumul. p od {Q }15 30 45 60 75 102 124 136 218 300 442 575 705 835 965 1105 1165 1185 1205 1225
The ec o s desc ibed in Table 3mimic he de ini ions o a physical applica ion. Fo
he needs o p ocess p ocessing, hei enume a ion is conside ed as a ec o o olumes,
symbolically as Q= (Q
1
,Q
2
,
. . .
,Q
m
). Simila ly, in he case o cos s, i is a lis o pa ame e s
C= (C1,C2, . . . , Cm).
Inco po a ing isks and unce ain ies in o he model allows u he mul iple simula-
ions, based on Table 3as he sou ce o a a iable p ocess. The model esul s a e p esen ed
and discussed in Sec ion 2.1 and u he . Table 3is able o abso b and exp ess ime- a ying
ex e nal p ocesses in economics, managemen , decision making, e c. [
20
]. The AR model’s
ou pu a iables depend on i s own p ojec s uc u e and on imp ecisely p edic able inpu s.
In his iew, he model is a o m o ex ensi e s ochas ic di e ence equa ions o ecu ence
ela ions. Howe e , he o mula ion based on di e en ial equa ions is di icul o achie e
in cons uc ion o in es men p ac ice. Ou pu s can be di ided in o (a) physical olumes
de e mining he scope and schedule o esou ces and (b) p o iding he scope and schedule
in inancial e ms. We will call bo h pa icula quan i a i e se ies in Table 3 ela ed o Aas

Sus ainabili y 2022,14, 2828 6 o 16
inpu s
A
,
πA
,C
A
,C
0A
, columns
∀i∈m
in Table 3. Rela ed ou pu s ollow in Table 3based
on G
O g
(A). The ou pu s o pa icula p ojec ac i i y A
i
a e dis ibu ed due o du a ions
in o quan i ies, speeds, accele a ions, impulses. Table 3shows only p oduc ion speed (see
ed-colo ed calenda ba cha ) [21].
POu pu s(A)=[DA, S a , End, {Q }, {Q0
}, {Q0 0
}, {Q0 0 0
}] | GO g(A), o ∀ ∈n(2)
whe e:
POu pu s(A)—is ime and esou ce schedule o all ac i i ies,
D= (D1,D2, . . . , Dm), and Di> 0, ∀i∈ma e du a ions o ac i i ies Di= D(Qi,Qi0),
S a
= (
S
1
,
S
2
,
. . .
,
S
m
), whe e
S
i≥
0, and
S
i
=
S
(G
O g
(A), D), o
∀
i
∈
m, a e ac i i y s a ing ime,
End
= (
E
1
,
E
2
,
. . .
,
E
n
), whe e
E
i
.
≥
0, and
E
i
=
E
(G
O g
(A), D), o
∀
i
∈
m, a e ac i i y ending ime.
{Q
}—is sum o p ojec ime se ies cumula i e quan i ies o all p ojec ac i i ies A
i
whe e
∀
i
∈
m. Values a e posi ioned in ime, like esul s p oduced by di e en ial equa ions in [
22
],
{Qi}— ime se ies quan i ies o indi idual ac i i ies, whe e > 0 ∀ ∈n.
Time se ies a e gi en om he calcula ion o changes in implemen a ion olumes in ,
see s uc u e POu pu s(A) in (2):
{Q
} o as {C
0
}
. . .
ime se ies o
∀
∈
no esou ces- low, o cash- low du ing p oduc ion
ime needed o each ac i i y Ai o ∀i∈m,
{Q
0
} o as {C
0
}
. . .
ime se ies o
∀
∈
no esou ces- low, o cash- low du ing p oduc ion
ime needed o he p ojec ac i i ies Aas a whole,
{Q
00
} alias {C
00
}
. . .
ime se ies o
∀
∈
no esou ces- low o cash- low changes (accele a-
ion) c ea ed in ime o each ac i i y Ai o ∀i∈m,
{Q
00
} alias {C
00
}
. . .
ime se ies o
∀
∈
no esou ces- low o cash- low changes (accele a-
ion) c ea ed in ime o he all Ao p ojec as a whole,
{Q
000
} alias {C
000
}
. . .
ime se ies o
∀
∈
no changes o accele a ion (impulses) in o
p ojec ac i i ies Ai,
{Q
000
} alias {C
000
}
. . .
changes o accele a ions (impulses) in ime o
∀
∈
n o p ojec as a
whole A.
The calcula ion is based on wo wo king s eps, Ad1 and Ad2:
(1)
Concen a ion o in o ma ion con en om he desc ip ion o p ojec ac i i ies as a
whole and decomposi ion o A o A
1
,A
2
,
. . .
,A
m
. Decomposi ion de ines he con ex
and obliga ions such as echnical d awings, epo s, no ms, s anda ds, en i onmen ,
en i onmen al, legal, economic, mo al, and mo e, han he con empla e in o P
Inpu s,
see Table 2.
(2)
C ea ing a singula o m o ime and cos schedule o esou ces:
• o indi idual ac i i ies Aiwhile espec ing he links o GO g,
•
o agg ega ion o ime se ies o esou ces and indica o s o he p ojec as a whole.
Ma hema ical no a ion p oposed by Zindulka in [
19
] is he e adap ed o use in Ad1
and Ad2.
Ad1 is ocused on he decomposi ion and classi ica ion o ma e ial componen s o he
p ojec . This is a echnical, economic, con ac ual sequence o he p ojec p oposal in he
ime and esou ce de ini ion o A
i
. Fo mal en y o quan i a i e inpu s o he calcula ion,
ollowing Figu e 1and on consolida ion in Table 2, we will s a e in (1).
Ad2 aims o calcula e he ime and esou ce schedule TAB
Ou pu
o indi idual quan-
i a i e pa ame e s o ac i i ies A( o example, cos , ene gy, e c.) while espec ing he
o ganiza ional ela ionships, whe e G
O g
(A) is node o ien ed acyclic g aph and {
·
} a e ime
se ies quali a i e ou pu s, see ows o p ojec dynamic lows in Table 3.
2.1. The Basic Time-Scheduling Ou pu s
We will summa ize o an illus a i e example o a schedule how o sol e he cal-
cula ion o (a) he e ms and links be ween ac i i ies implemen ed in G
O g
and how o
Sus ainabili y 2022,14, 2828 7 o 16
add ess (b) he alloca ion o esou ce needs o e ime. The ou pu s om ela ions (1) and
(2) ha e he cha ac e o ime se ies—dynamic quan i a i e lows and quali a i e indica o s.
Quan i a i e ou pu s ep esen ime se ies o indi idual ac i i ies {Q
}
A
and o he p ojec
as a whole {Q
}
A
. Table 3shows bo h he quan i a i e side (le pa ) and he quali a i e
pa —indica o s o indi idual ac i i ies {Q
0
}
A
, e en ually de i ed {Q
00
}
A
, {Q
000
}
A
. Fo he
p ojec as a whole, quali a i e indica o s {Q
0
}
A
, {Q
00
}
A
, {Q
000
}
A
. They a e use ul o inding
weaknesses ( isks) in assessing he p ojec design as a whole. Subsequen p ojec ion o
knowledge in o he de ails o ac i i ies c ea es a pa h o he necessa y changes, e isions,
and comple ions. This is a p ocess ha in luences p ojec e iciency. In addi ion, i allows
he con ol o ex e nal en i onmen al, legal, e hical, municipal, and o he in luences. The
implemen ed TAB
P ojec
(A) and G
O g
(A) a e a composi e o knowledge. The able p ocesso
p esen a ion is a use ul, lexible, bu s ill limi ed su oga e o eali y; howe e , i is gene ally
he only a ailable one [23].
Howe e , as he analysis o eal p ojec s in [
13
,
15
,
23
] shows, eal p ojec s a e p edis-
posed by he ime schedule ne wo k opology bu s ongly p o i -o ien ed; in sho , hey
a e cos -inc ease d i en. The opology o ime schedules dynamics is s ill no ou inely
e i ied o indica o s such as dynamic s abili y, chaos, e c. [24].
2.2. Commen on he S uc u e GO g(A)
Indica o s o he e iciency o he ollow-up p ocess can be de i ed om quan i a i e
and quali a i e ime se ies TAB
P ojec
p ojec ed in o he schedule. In Table 3, he ou pu s
ha e he capaci y o cap u e bo h he s uc u e o causal links o ac i i ies and he ola ili y
o ex e nal in luences (p ices, legisla ion, design laws, echnology, ecology, sa e y, hi d
pa y ha m, and o he in luences).
The inpu s o he calcula ion may include a b oade con ex o ac i i ies. They enable
he complexi y o pop-is: physical olumes, uni p ices, ealiza ion p oduc i i y, isk nodes,
and ac i i ies. These a e nes ed da a in ac ual desc ip ion A. Tables 2and 3a e ollowed
by pa ame e s such as:
Calcula ion o du a ion D
A
, whe e D
A≈
Q
A
/Q
A00 ≈
End −
S a
. Howe e , he inal
esou ce and p oduc i i y amewo k co ec s he b oade con ex G
O g
. The calcula ion o
quan i a i e and quali a i e cha ac e is ics o a p ojec and o an indi idual A
i
is gaining
bo h complexi y and impo ance.
In addi ion, he da a o desc ip ion A a e mos ly based on he echnical documen a ion
and economic speci ica ions (design, assignmen , con ac ual de ini ion) o he p ojec .
The de aul ask TAB
P ojec
can be ad an ageously used o simula e he e ec s o
ex e nal in luences. Agg ega ed ou pu s o he p ojec as a whole {Q}
Sim
, {Q
0
}
Sim
, including
de i ed quali a i e ime se ies o indica o s {Q
00
}
Sim
and {Q
000
}
Sim
, hey enable a compa ison
o he consequences o ex e nali ies ( isks, unce ain ies, changes in echnical design, e c.).
To he ou pu ime se ies {Q
0
}
Sim
bo h he inpu da a o he simula ion calcula ion Table 3
and he ecalcula ions om he e ec o ex e nali ies a e included.
Mic oeconomics gene ally sol es p oblems o many dimensions, mo eo e bu dened
by he ola ili y o inpu pa ame e s. The ob ained ou pu s place demands on he imagina-
ion o managemen . Visualiza ion is a kind o subsidia y ool o in e p e ing he ob ained
indica o s. The in e p e a ion o he p o ided ou pu da a gene ally equi es he abili y o
e lec he speci ics o he economics o he p ojec design. We a e looking o applica ions
in compa ing (a) a ian solu ions, (b) managemen measu es, (c) al e na i es, (d) subs i u-
ion o esou ces (ma e ial, people, machines, in o ma ion), (e) aking isks, unce ain ies,
( ) ma king c isis pe iods o he implemen a ion o he p ojec , and mo e.
2.3. Ex ension o In e p e a ion
The ime se ies elemen s Q
A0
a e de i ed o Q
A
, and a e in e p e ed he e as he
p oduc ion speed. Fu he , we see o ganiza ional and managemen in o ma ion included
as causal ela ions o pa ial ac i i ies. The p incipal calcula ion scheme is ela ed o
Figu e 1’s scheme.
Sus ainabili y 2022,14, 2828 8 o 16
The p ac ical applica ions a e suppo ed mos ly by node-o ien ed g aphs (o he com-
me cial p esen a ions a e ee g aphs, ch onog ams, cyclog ams, e c.); hese echniques
desc ibe causal (o ganiza ional) dependencies o p ojec ac i i ies A. Fo he pu pose o
his s udy, causal g aphs we e designa ed as GO g(A).
The calcula ion example in Figu e 2is an illus a ion o (le pa ) ex e nali ies wi h
e e ences o sepa a e ex e nal da a iles and ( igh pa ) dependencies be ween indi idual
ac i i ies wi hin he calcula ion o he o ganiza ional s uc u e o he implemen a ion
o ac i i ies.
2.4. Time Se ies o P oduc ion Speeds-Simula ion
The Cash Flow [
24
] is shown in Figu e 3 o he linea (uppe (a) pa ) and logis ic
(lowe (b) pa ) esou ce dis ibu ion o ac i i ies A. The indi idual phases o he wa e-
o ms in he g aphs a e shown o 100 simula ions.
Figu e 3.
P ojec mul iple cash lows {Q
0
}
Sim
(100 imes), in e p e a ion as p oduc ion speed
pe ime uni ; compa a i e segmen s (
a
,
b
) show linea and logis ic esou ce dis ibu ion unc ion,
compa a i e analysis.
The commen blocks in he con ex o G
O g
(A) a e ma ked as
Sus ainabili y 2022, 14, x FOR PEER REVIEW 10 o 18
(b)
Figu e 3. P ojec mul iple cash lows {Q ′}Sim (100 imes), in e p e a ion as p oduc ion speed pe ime
uni ; compa a i e segmen s (a,b) show linea and logis ic esou ce dis ibu ion unc ion, compa a i e
analysis.
The commen blocks in he con ex o GO g(A) a e ma ked as sepa a ely, and u -
he supplemen ed by commen s (a) Com 1–6, (b) Com 1–4. A isual compa ison be ween
he 2 pa s o Figu e 3 indica e signi ican di e ences be ween he linea dis ibu ion o
esou ces ( inancial esou ces Q in e ms o cos s C) and he use o logis ics unc ions o
he dis ibu ion o esou ces C.
2.4.1. Linea Resou ce D awing Schedule—Commen
Com 1: The s a o he p ojec assumes a jump in p oduc ion capaci y. The jump inc ease
does no co espond o he p ac ice o implemen a ion.
Com 2: The onse o ollow-up ac i i ies Ai misses he ollow-up o he ongoing s a -up
ac i i ies; changes a e needed in GO g(A).
Com 3: Some ollow-up ac i i ies do no con inue in pa allel wi h ongoing ac i i ies. Fo
some ac i i ies, he p oduc ion speed dec eases. The oppo uni y o inc ease p oduc ion
speed s eadily is was ed.
Com 4: O ganiza ional and echnological con inui y o ac i i ies lead o dis u bances in
he low o p oduc ion speeds. A dec ease o he le el o he s a o implemen a ion can
be expec ed wi h he concu ence o some ex e nal in luences. Inc easing p oduc ion
speed seems unwo kable.
Com 5: The consequences o he missed oppo uni ies commen ed on in poin s 1 o 4 lead
o conges ion o ac i i ies. The expec ed consequences a e chao ic s a es o coo dina ion
o ac i i ies, space cons ain s du ing implemen a ion, de ec s in he quali y o execu ion,
and mo e.
Com 6: A wide ange o p ojec comple ion da es, he comple ion slippages ep esen
abou 1/3 o he o al p ojec du a ion.
A change in he me hod o inancing is chosen as a a ian solu ion. The linea dis i-
bu ion o he unding sou ce is o be eplaced by ano he esou ce dis ibu ion cu e; his
example uses a logis ic cu e. Indi idual ac i i ies di e mainly in he pace o de elop-
men and e mina ion o p oduc ion p ocesses.
2.4.2. Commen o he Schedule o D awing Resou ces by he Logis ics Func ion
Com 1: The achie ed pace o implemen a ion is no used o es ablish ollow-up ac i i ies.
The dynamics o implemen a ion speeds a e los .
sepa a ely, and u he
supplemen ed by commen s (a) Com 1–6, (b) Com 1–4. A isual compa ison be ween
he 2 pa s o Figu e 3indica e signi ican di e ences be ween he linea dis ibu ion o
esou ces ( inancial esou ces Qin e ms o cos s C) and he use o logis ics unc ions o he
dis ibu ion o esou ces C.
Sus ainabili y 2022,14, 2828 9 o 16
2.4.1. Linea Resou ce D awing Schedule—Commen
Com 1: The s a o he p ojec assumes a jump in p oduc ion capaci y. The jump inc ease
does no co espond o he p ac ice o implemen a ion.
Com 2: The onse o ollow-up ac i i ies A
i
misses he ollow-up o he ongoing s a -up
ac i i ies; changes a e needed in GO g(A).
Com 3: Some ollow-up ac i i ies do no con inue in pa allel wi h ongoing ac i i ies. Fo
some ac i i ies, he p oduc ion speed dec eases. The oppo uni y o inc ease p oduc ion
speed s eadily is was ed.
Com 4: O ganiza ional and echnological con inui y o ac i i ies lead o dis u bances in he
low o p oduc ion speeds. A dec ease o he le el o he s a o implemen a ion can be
expec ed wi h he concu ence o some ex e nal in luences. Inc easing p oduc ion speed
seems unwo kable.
Com 5: The consequences o he missed oppo uni ies commen ed on in poin s 1 o 4 lead o
conges ion o ac i i ies. The expec ed consequences a e chao ic s a es o coo dina ion o ac i i ies,
space cons ain s du ing implemen a ion, de ec s in he quali y o execu ion, and mo e.
Com 6: A wide ange o p ojec comple ion da es, he comple ion slippages ep esen abou
1/3 o he o al p ojec du a ion.
A change in he me hod o inancing is chosen as a a ian solu ion. The linea dis i-
bu ion o he unding sou ce is o be eplaced by ano he esou ce dis ibu ion cu e; his
example uses a logis ic cu e. Indi idual ac i i ies di e mainly in he pace o de elopmen
and e mina ion o p oduc ion p ocesses.
2.4.2. Commen o he Schedule o D awing Resou ces by he Logis ics Func ion
Com 1: The achie ed pace o implemen a ion is no used o es ablish ollow-up ac i i ies.
The dynamics o implemen a ion speeds a e los .
Com 2: Indi idual ac i i ies s a wi h a ime delay. The achie ed ealiza ion speeds a e
no linked in such a way ha he e is an e ec o inc easing he ealiza ion speed.
Com 3: Ac i i ies ha a e supposed o c ea e a p econdi ion o he apid comple ion o
p ojec implemen a ion s a wi h a ime delay.
Com 4: The inishing p ocess is diso ganized and ex ensi e.
The weakness o he p oposed implemen a ion schedule o he in es iga ed p ojec
is he low compac ness (looseness) o he s uc u e G
O g
(A) in he implemen a ion o
he p oposal.
In a simila way, i is possible o compa e p oposals o he implemen a ion o al e na-
i e solu ions (design, o ganiza ional, ene gy in ensi y, sa e y measu es, and mo e).
2.5. Simula ion o he Du a ion o he P ojec as a Whole DA
Schema ic model TAB
P ojec
|Sim in Figu es 2and 3p o ides a a ie y o ac ual inpu
da a and calcula ed ime se ies da a [
25
]. In addi ion o he a e o u iliza ion o esou ces
is he knowledge abou he po en ial o du a ions D
A
ola ili y. G aphical p esen a ion
and s a is ical analysis o he ime se ies [
19
] allows assessing he po en ial dynamics o
ex e nal in luences ( o example, he expec ed de elopmen o ma e ial p ices, wages,
labo a ailabili y, a ic in ensi y, machine y, and o he ex e nali ies). The du a ions a e
dominan applica ion ou pu s o Figu e 3, lis ed as {DA}Sim in Figu e 4.
Sus ainabili y 2022,14, 2828 16 o 16
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