Sensitivity Analysis for Business, Technology, and Policymaking: Made Easy with Simulation Decomposition (SimDec)

Kozlo a, Ma iia (Ed.); Yeomans, Julian Sco (Ed.)
Book
Sensi i i y Analysis o Business, Technology, and
Policymaking: Made Easy wi h Simula ion Decomposi ion
(SimDec)
Rou ledge Open Business and Economics
P o ided in Coope a ion wi h:
Taylo & F ancis G oup
Sugges ed Ci a ion: Kozlo a, Ma iia (Ed.); Yeomans, Julian Sco (Ed.) (2025) : Sensi i i y Analysis o
Business, Technology, and Policymaking: Made Easy wi h Simula ion Decomposi ion (SimDec),
Rou ledge Open Business and Economics, ISBN 978-1-040-12132-0, Rou ledge, Ox o d,
h ps://doi.o g/10.4324/9781003453789
This Ve sion is a ailable a :
h ps://hdl.handle.ne /10419/312726
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“This book on sensi i i y analysis by Ma iia Kozlo a and Julian Sco
Yeomans summa izes he s a e-o - he-a me hod o compu a ional model
analysis, he e olu iona y Simula ion Decomposi ion (SimDec). Fo eade s
like me wo king in he gene al a eas o modelling, op imiza ion, and
machine lea ning, I ind his book ex emely use ul because i essen ially has
e e y hing abou SimDec in one package, which makes i an e ec i e ool
o do global sensi i i y analysis. The esul s a e easy o unde s and, wi h
colo ul isualiza ion, unce ain y quan i ica ion, and a wide spec um o
di e se applica ions. In addi ion, he open-sou ce SimDec so wa e wi h code
packages in Py hon, R, Julia, and Ma lab will e olu ionize he ways o
aining nex -gene a ion scien is s and p ac i ione s o do he igh kind o
sensi i i y analysis so as o igu e ou he mos in luen ial ac o s co ec ly
and o suppo mo e in o med decision-making.”
Xin-She Yang, Reade a Middlesex Uni e si y London, Fellow o he
Ins i u e o Ma hema ics and I s Applica ions (FIMA), UK
“Simula ion Decomposi ion is an inc edibly powe ul echnique ha allows
esea che s and enginee s o iden i y key ac o s in luencing he pe o mance
o a sys em and make a ge ed imp o emen s. This book p o ides a simple
and accessible guide o unde s and and apply he echnique o p ac ical
p oblems. The accompanied open-sou ce SimDec code is he key o enable
he eade o quickly lea n and apply he me hod.”
Lei u Lei sson, Associa e P o esso , School o Ae onau ics and
As onau ics, Pu due Uni e si y, USA
“Simula ion Decomposi ion me hodology, a Mon e Ca lo–based compu a ional
algo i hm, is quickly becoming a game change in he wo ld o enginee ing,
indus y, and inance. In his newly published book, Julian Sco Yeomans
and Ma iia Kozlo a explo e he impo ance o his me hod in p o iding an
accu a e and de ailed holis ic pic u e o he beha io o complex sys ems.
The book del es in o he eal-li e applica ions o Simula ion Decomposi ion,
highligh ing i s e ec i eness in op imizing p ocesses and imp o ing p oduc
designs. Th ough de ailed case s udies and insigh s om indus y expe s,
eade s will gain a ho ough unde s anding o his powe ul me hodology
and i s po en ial o ans o ming he way we app oach complex sys ems.”
Kambiz Va an-Abadi, Chie Inno a ion O ice , CI Financial, Canada
“SimDec is an ingenious way o ame he combina o ial complexi y o
sys ems’ beha iou in eal-wo ld decision-making. I s decep i ely simple
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unce ain ou come. This new me hod o de e mining sensi i i y indices
seems a hidden gem. I s anspa ency is in aluable o p ac i ione s. C edi
is also due o he au ho s o making an o he wise challenging opic mos
en e aining and accessible o p ac i ione s. SimDec’s ease o use should
make i he de ac o s anda d o da a analysis in indus ial, enginee ing, and
scien i ic en i onmen s.”
Kalyan Moy Gup a PhD, Founde and Vice P esiden o Resea ch,
Knexus Resea ch, Washing on, DC, USA
“Black box unc ions wi h unce ain inpu s a e used o encode knowledge
in many a eas o science, enginee ing, and comme ce. The challenge is o ge
ha knowledge back ou o he bene i o use s. The cus oma y app oaches
ocus on sub le ma hema ics and expensi e compu a ions. This book p esen s
SimDec, which p oduces in e p e able g aphical ep esen a ions ha suppo
discussions and disco e y.” A Owen, Max H. S ein P o esso o S a is ics,
S an o d Uni e si y, USA
“The usion o sensi i i y analysis wi h unce ain y analysis h ough
SimDec, as p esen ed in his book, ma ks a wa e shed momen o business
p o essionals and GenAI de elope s alike. I ’s a guidebook o hose who da e
o challenge he s a us quo, o e ing no jus insigh s bu a comp ehensi e
oolki o ans o ma i e decision-making. A es amen o he powe o
in e disciplina y collabo a ion and open-sou ce inno a ion in shaping he
u u e o echnology. Essen ial eading o leade s d i ing inno a ion in
unce ain imes.”
An e ny Chen, CEO and Founde , Da a ac ion/Do sLi e.Com, Canada
“This book a icula es he SimDec me hod o global sensi i i y analysis by
combining a no el isual unce ain y analysis app oach wi h he disc imina o y
capabili ies o a newly-c ea ed echnique o calcula ing sensi i i y indices. The
eal beau y o SimDec is ha i can be s aigh o wa dly applied o i ually
any ield o da a analysis, i espec i e o he ma hema ical sophis ica ion o
he use . Iha e been wo king wi h sys em dynamics, op imiza ion, s ochas ic
p og amming, and o he analy ical app oaches o o e h ee decades. One
eg e Inow ha e is ha he e was no SimDec p ocedu e in exis ence a he
ime o suppo hese ac i i ies.”
Go don Huang, Canada Resea ch Chai and P o esso o En i onmen al
Sys ems Enginee ing, Uni e si y o Regina, Canada
Sensi i i y Analysis o Business,
Technology, and Policymaking
SimDec is a e olu ion in decision-making suppo . SimDec “ eases
ou ” inhe en cause-and-e ec ela ionships and e eals he in icacy o
ela ionships be ween se s o inpu and ou pu a iables. A i s co e, SimDec
is an amalgama ion o unce ain y and global sensi i i y analysis wi h an
inno a i e isualiza ion echnique. While s aigh o wa d and elegan , his
no el app oach signi ican ly enhances he analy ical capabili ies o use s by
eadily exposing seemingly, a p io i, coun e in ui i e beha iou s so ha hey
can be eadily unde s ood by bo h echnical specialis s and non- echnical
use s alike.
This book is he i s o a icula e he ubiqui ous applicabili y o SimDec
and has been w i en by he leading p oponen s o he echnique. The book
p o ides he necessa y backg ound o ully unde s and he unde lying
app oach and hen demons a es i s applicabili y o a wide spec um o ields,
such as inance, en ep eneu ship, ene gy, 3D manu ac u ing, geology, he
en i onmen , enginee ing, public policy, and e en supe conduc ing magne s.
To acili a e as widesp ead adop ion and pene a ion o SimDec as possible,
all suppo ing compu e codes a e a ailable, open-sou ce, in Py hon, Julia,
R, and Ma lab.
The inno a i e ma e ial will be o p ima y bene i o p ac i ione s and
esea che s analyzing da a om he social sciences, business, science,
enginee ing, ma hema ics, and compu ing.
Ma iia Kozlo a is an associa e p o esso a LUT Uni e si y Business School,
Finland, and a isi ing schola a S an o d Uni e si y, USA.
Julian Sco Yeomans is a p o esso and he di ec o o he MMAI and MBAN
p og ams a he Schulich School o Business, Yo k Uni e si y, Canada.

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Ch is ian Pie e Ho mann and Nadine S auß
Sensi i i y Analysis o Business, Technology,
and Policymaking
Made Easy wi h Simula ion Decomposi ion (SimDec)
Edi ed by Ma iia Kozlo a and Julian Sco Yeomans
Co po a e Social Responsibili y and he Supply Chain
CSR Collabo a ion wi h Supplie s
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Sensi i i y Analysis o
Business, Technology,
and Policymaking
Made Easy wi h Simula ion
Decomposi ion (SimDec)
Edi ed by Ma iia Kozlo a
and Julian Sco Yeomans
Fi s published 2025
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Names: Kozlo a, Ma iia (P o esso o business), edi o . |
Yeomans, Julian Sco , edi o .
Ti le: Sensi i i y analysis o business, echnology, and policymaking :
made easy wi h simula ion decomposi ion (SimDec) / edi ed by
Ma iia Kozlo a and Julian Sco Yeomans.
Desc ip ion: Abingdon, Oxon ; New Yo k, NY : Rou ledge,
2025. | Se ies: Rou ledge open business and economics | Includes
bibliog aphical e e ences and index.
Iden i ie s: LCCN 2024026905 (p in ) | LCCN 2024026906
(ebook) | ISBN 9781032592466 (ha dback) | ISBN 9781032592473
(pape back) | ISBN 9781003453789 (ebook)
Subjec s: LCSH: Sensi i i y heo y (Ma hema ics)—Simula ion me hods. |
Decision making—Simula ion me hods. | Decision suppo sys ems.
Classi ica ion: LCC QA402.3 .S4526 2025 (p in ) | LCC QA402.3
(ebook) | DDC 511/.8—dc23/eng/20240628
LC eco d a ailable a h ps://lccn.loc.go /2024026905
LC ebook eco d a ailable a h ps://lccn.loc.go /2024026906
ISBN: 978-1-032-59246-6 (hbk)
ISBN: 978-1-032-59247-3 (pbk)
ISBN: 978-1-003-45378-9 (ebk)
DOI: 10.4324/9781003453789
Typese in Sabon
by Apex CoVan age, LLC
To ou u y soulma es, who con ibu ed o his book
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Tibo Chengis
2008–2023 2008–2021
xi Figu es
6.6 Decomposi ion o he Uni cos o ba ch size=1 by Depo-
si ion a e and Ope a ion labo wi h equally-spaced s a e
o ma ion. 130
6.7 Decomposi ion o he Uni cos unde cu en unce ain y
le els by Ba ch size, Indi ec cos s, and Di ec cos s wi h
equally-spaced s a e o ma ion ( op le ) and sensi i i y indi-
ces ( op igh ). De ailed sensi i i y indices a e p esen ed in
Appendix 2. 132
6.8 Decomposi ion o he Uni cos unde u u e unce ain y
le els by Ba ch size, Indi ec cos s, and Di ec cos s wi h
equally-spaced s a e o ma ion (le ) and sensi i i y indices
( igh ). De ailed sensi i i y indices a e p esen ed in Appendix 3. 133
6.9 Decomposi ion o he Uni cos unde me ged cu en and
u u e unce ain y le els by Ba ch size, Indi ec and Di ec
cos s wi h equally-spaced s a e o ma ion. 134
7.1 Rela ionship be ween echnology de elopmen pa hs and
ma ke oppo uni ies. 146
7.2 Decomposi ion o Sco e by Ma ke oppo uni y (58% sensi-
i i y index). Ma ke oppo uni ies a e so ed by he inc eas-
ing mean Sco e. 154
7.3 Decomposi ion o Sco e by Asse Combina ion (28% sensi-
i i y index). 156
7.4 Decomposi ion o Sco e by M21 (52%) and T12 (44%). The
dis inc colou s ep esen di e en le els o M21 and di e -
en shades e e o di e en le els o T12 in each s a e o M21. 157
8.1 Li e cycle diag am o single-use polyp opylene-based medical
mask and eusable PLA mask. 169
8.2 Sys em bounda ies o he LCA s udy. 171
8.3 Decomposi ion o he o al global wa ming po en ial (GWP)
o bo h masks by mask ype (42%) and numbe o masks
used (62%). No e ha numbe o masks used is o di e en
uni s o he di e en mask ypes. 176
8.4 Decomposi ion o he o al global wa ming po en ial (GWP)
o eusable masks by numbe o masks used (33%) and
numbe o il e s used (32%). 177
8.5 Decomposi ion o he o al global wa ming po en ial (GWP)
o single-use masks by means o anspo (35%) and
numbe o masks used (45%). 178
8.6 Decomposi ion o he o al global wa ming po en ial (GWP)
o single-use masks means o anspo equal o Ai c a by
numbe o masks used (69%) and dis ance (24%). Low,
medium, and high s a es o dis ance a e p oduced by
di iding i s o al ange [50, 1000] km in o h ee equal
in e als. 180

Figu es x
8.7 Decomposi ion o he o al global wa ming po en ial (GWP)
o single-use masks means o anspo equal o Ship by
numbe o masks used (73%) and mask disposal (26%). 181
8.8 Decomposi ion o he o al global wa ming po en ial (GWP)
o single-use masks means o anspo equal o Lo y by
numbe o masks used (74%) and mask disposal (24%). 183
8.9 Decomposi ion o he o al global wa ming po en ial (GWP)
o eusable masks (le ) by LCA phases anspo and use
( op) and p oduc elemen s il e and anspo (bo om), and
o single-use masks ( igh ) by LCA phases anspo and EoL
mask ( op) and p oduc elemen s anspo and mask (bo om). 184
9.1 POMDP p oblem o mula ion o he mine al explo a ion case. 195
9.2 S a e ideli y o he subsu ace o e body shape o he min-
e al explo a ion p oblem. 197
9.3 En i onmen ideli y as g id esolu ion o he mine al explo-
a ion p oblem. 198
9.4 Planning ideli y using numbe o planning i e a ions in he
ee sea ch. 200
9.5 POMDP model- ideli y amewo k (PMFF) inpu a iables
and ou pu me ics. 201
9.6 Example ideli y con ou . Fideli y inc eases om he bo -
om le o he op igh , o example, he whi e poin a he
cen e is he mean un ime o he 30 × 30 g id wi h 1,000
planning i e a ions (o e 500 seeds). 203
9.7 Con ou maps o he discoun ed e u n o he mine al
explo a ion POMDP. 206
9.8 Decomposi ion o e u n by s a e shape, planning i e a ions,
and g id dimensions. Explained a iance o he ou pu by
his decomposi ion is 0.002. 207
9.9 Con ou maps o he 90 h pe cen ile o eg e o he mine al
explo a ion POMDP. 209
9.10 Decomposi ion o eg e by s a e shape, planning i e a ions,
and g id dimensions. Explained a iance o he ou pu by
his decomposi ion is 0.014. 210
9.11 Con ou maps o he un ime o he mine al explo a ion
POMDP. 211
9.12 Decomposi ion o un ime by planning i e a ions and g id
dimensions. Explained a iance o he ou pu by his
decomposi ion is 0.451. 213
9.13 Con ou maps o he bias in he inal es ima ed massi e o e
quan i y. 215
9.14 Decomposi ion o bias by g id dimensions and planning
i e a ions. Explained a iance o he ou pu by his
decomposi ion is 0.009. 216
x i Figu es
9.15 Con ou maps o he numbe o ac ions (i.e. d ills) o min-
e al explo a ion. 218
9.16 Decomposi ion o numbe o ac ions by (a) g id dimensions,
(b) planning i e a ions, and (c) s a e shape. Explained a i-
ance o he ou pu a e 0.003, 0.052, and 0.052, espec i ely. 219
9.17 Con ou maps o he accu acy in he inal mine o abandon
decision. 221
9.18 Compa ison o his og ams ob ained wi h seed sampling
(a1 & a2) and andom sampling (b1 & b2). Resul s a e simila
o eg e (a1 & b1) and di e en o un ime (a2 & b2). 224
10.1 An o e iew o he common syn he ic d op-in uel p oduc-
ion pa hways and hei main p oduc s. MTG s ands o
Me hanol- o-Gasoline; MTO, Me hanol- o-Ole ins; MOGD,
Mobil ole ins o gasoline and dis illa es; and RWGS, e e se
wa e -gas-shi . 231
10.2 O e all diag am o he s udied p oduc ion ou e, di ided
in o ou sec ions. Some pu i ica ion and p ocessing s eps a e
simpli ied o cla i y. 233
10.3 Simula ion Decomposi ion o NPV (Base scena io) by Gaso-
line p ice (55%) and Hyd ogen p ice (16%). 241
10.4 Simula ion Decomposi ion o NPV by Scena io (66%) and
Gasoline p ice (7%). 243
10.5 Simula ion Decomposi ion o NPV by Scena io (12%) and
Gasoline p ice (27%). 246
10.6 Simula ion Decomposi ion o NPV (MeOH Elec olysis) by
Me hanol p ice (56%) and Elec ici y p ice (25%). 247
11.1 4R model desc ip ion. Inpu pa ame e s: (a) esidual s ess,
(b) ma e ial’s ul ima e s eng h a he hea -a ec ed zone
(HAZ), (c) applied s ess a io, and (d) weld oe adius, and
cyclic beha iou a no ch. 260
11.2 Ase ies o one-a -a- ime sensi i i y analyses o 4R model
ou pu o he ou inpu s (in columns). The ows ep esen
di e en le els o esidual s ess
es : high (uppe ow), neg-
ligible (middle ow), and comp essi e (lowe ow). 263
11.3 Main decomposi ion o he s uc u al eliabili y model
ou pu by he mos in luen ial h ee inpu pa ame e s,
explaining 96% o he a iance o he ou pu (sum o hei
sensi i i y indices) and po aying h ee second-o de e ec s
causing he e ogeneous inpu –ou pu ela ionship. The his o-
g am is s acked and exposes he en i e simula ion da a wi h-
ou o e lapping. The sha e o da a in each scena io (o he
p obabili y o scena io) is displayed in he igh mos column
o he legend. 269
Figu es x ii
11.4 Decision ee cons uc ed based on he mos p ominen
he e ogenei y in he e ec s o inpu a iables on he ou pu
s ess (deno ed wi h s ess concen a ion ac o K , e ). 270
11.5 Con ibu ion o esidual s ess o he a iance o he ou -
pu : 51% o he a iance is explained by he inpu a iable. 272
11.6 Con ibu ion o s ess a io o he a iance o he ou pu :
35% o he a iance is explained by he inpu a iable. 273
11.7 Con ibu ion o s eel g ade o he a iance o he ou pu :
10% o he a iance is explained by he inpu a iable. 274
11.8 Con ibu ion o a igue no ch ac o o he a iance o he
ou pu : 4% o he a iance is explained by he inpu a iable. 275
11.9 Supplemen a y decomposi ion o he s uc u al eliabili y
model po aying he in e ac ion e ec be ween esidual
s ess and s ess a io. Thei combina ion explains 86% o
he a iance o he ou pu . 276
11.10 Supplemen a y decomposi ion o he s uc u al eliabili y
model po aying he weak 4% in e ac ion e ec be ween
s eel g ade and s ess a io. Thei combina ion explains
43% o he a iance o he ou pu . 277
11.11 Supplemen a y decomposi ion o he s uc u al eliabili y
model po aying he co ela ion e ec be ween s eel g ade
and esidual s ess. Thei combina ion explains 55% o he
a iance o he ou pu . 278
12.1 C i ical su aces o supe conduc ing alloys app oxima ed
by he co ela ion o Bo u a (1999) and i ed o da a
poin s o Godeke e al. (2007) and Fe acin (2017). 285
12.2 (a) View o an Nb3Sn Ru he o d cable showing he s ands
and ibe glass insula ion. (b) Close-up o he s ands. (c)
C oss-sec ion o he eRMC/RMM Ru he o d ape consis -
ing o 40 s ands. (d) De ailed iew o one s and c oss
sec ion showing he Cu ma ix and he 120 ilamen s in a
honeycomb pa e n. (e) An eRMC coil being wound wi h
he cable; he bo om pancake laye has been comple ed. 286
12.3 CAD iew o an eRMC ( op) and RMM- ype (bo om) coils. 287
12.4 CAD iew o c oss sec ion o he eRMC coil pack, ea u -
ing he coils and he comp essing pushe s. 289
12.5 CAD iew o c oss sec ion o he RMM coil pack ea u ing
he RMM- ype coil be ween wo eRMC- ype coils, wi h he
bo e in he cen e, whe e he 16.5 T ield is a ge ed. 290
12.6 Le : Pic u e o he end o he eRMC magne showing he
coil pack su ounded by he yoke and he shell held in place
by some shims. Righ : CAD ans e sal c oss-sec ion. 291
12.7 RMM magne . Le : ull assembly. Righ : Cu o iew
showing 3/8 o he magne . 292
x iii Figu es
12.8 2D model o he RMM magne , depic ing a simpli ied
geome y. 294
12.9 2D model o he RMM magne depic ing wo possible
elemen mesh esolu ions o a same geome y. The e sion
on he igh co esponds o he calcula ions pe o med in
his s udy. 295
12.10 Example o a solu ion o a magne ic FEM simula ion
showing he magne ic ield in he magne . 296
12.11 BH cu es o he e i ic ma e ials u ilized in he model
(i on yoke and e ical pushe , and eRMC pole). 300
12.12 Simula ion Decomposi ion o he RMM supe conduc ing
magne model o ou pu a iable cu en . 306
12.13 Simula ion Decomposi ion o he RMM supe conduc ing
magne model o ou pu a iable ho izon al in e e ence. 311
12.14 Simula ion Decomposi ion o he RMM supe conduc ing
magne model o ou pu a iable coil s ess a s age 1. 314
12.15 Simula ion Decomposi ion o he RMM supe conduc ing
magne model o ou pu a iable coil s ess a s age 2. 316
12.16 Simula ion Decomposi ion o he RMM supe conduc ing
magne model o ou pu a iable coil s ess a s age 3. 319
12.17 Simula ion Decomposi ion o he RMM supe conduc ing
magne model o ou pu a iable bladde p essu e. 321
12.18 Sca e plo o ho izon al in e e ence o bladde p es-
su e wi h colou -coded g oups o shell hickness and yoke
adius pai s consis en o Figu e12.17. 322
12.19 Decomposi ion o bladde p essu e on a limi ed da ase
(yoke adius=360mm, shell hickness=40mm, and
numbe o windings=264) by cable heigh ha explains
86% o a ia ion o he bladde p essu e, and by ano he
ou pu o in e es – ho izon al in e e ence. Absen due o
co ela ion and a ely occu ing scena ios a e ma ked wi h
g ey on colou . 324
13.1 Dis ibu ion o u u e sa ings o di e en mon hly sa -
ing amoun (ma ked wi h di e en colou s) and unce ain
in e es a e. 334
13.2 Fu u e alue o €200 mon hly sa ings a 5% in e es a e as
an exponen o he numbe o yea s. 335
13.3 Fu u e sa ings alue unde unce ain in e es a e (0–10%),
a iable du a ion (1–50yea s), and mon hly paymen
(€100, €200, o €300). The X-axis is unca ed; he maxi-
mum amoun o sa ings app oaches se en million eu os
when all ac o s a e a ou able. 336
13.4 Accumula ed assessmen o coun y p e e abili y. 339
13.5 Language com o speci ic assessmen o coun y p e e abili y. 340
Figu es xix
13.6 One ealiza ion o he s ochas ic e e ence in e es a e and
he co esponding mo gage a e wi h a cap. 342
13.7 Decomposi ion o he loan e m (le ) and co esponding
o e all in e es expenses ( igh ) by on and o in e es cap
and a e age in e es a e. 343
13.8 Apowe law cu e o y=x0.3. 344
13.9 Language acquisi ion scena ios. 346
13.10 Ca eplacemen op ion assessmen . 348
13.11 Ca eplacemen op ion decomposed by he cos s. 349
13.12 Decomposi ion o body weigh and a pe cen age by mass
o a and lean issue. 351
Colou e sions o he a wo k a e a ailable in he eBook e sion o his i le
(9781003453789).

2.1 SimDec open-sou ce packages 41
2.2 Uses and a gumen s o he SimDec R package unc ions 46
2.3 Main unc ions o he SimDec Ma lab package 49
3.1 The o e iew o applica ion chap e s and hei hemes 62
3.2 Modelling app oaches and p ac ices o case owne s
p e-SimDec 64
4.1 Classic cash low model a angemen in a sp eadshee
en i onmen 81
4.2 Nume ic assump ions o he s ylized cash low model 85
4.3 Va ia ion in inpu pa ame e s in he di e en axa ion
schemes ( = andomized) 86
4.4 Va ia ion in inpu pa ame e s in luc ua ing demand case 88
4.5 Va ia ion in inpu pa ame e s in p ice hedging case 89
5.1 Unce ain y assump ions o inpu a iables 100
5.2 NPV gained by he wo pa ies, unde he h ee suppo s,
and in case o absence o suppo s 103
5.3 Resul s o sensi i i y analysis on Rg, LPVR, and a i s in
PC egula ion 104
5.4 Sensi i i y indices ( i s -o de e ec s) o inpu pa ame e s o
model ou pu s 109
6.1 Assumed indi ec cos s o 3DCP in cons uc ion 121
6.2 Assumed di ec cos s o 3DCP in cons uc ion 122
6.3 Single poin uni cos es ima ion equa ion 122
6.4 Inpu a iable assump ions o Mon e Ca lo (MC)
simula ion (-//- i unchanged) 125
7.1 Rela ionship be ween Asse s and Ma ke Oppo uni ies 148
7.2 Decision-making elemen s o new ool: he Technical
Ma ke Oppo uni y Na iga o 149
7.3 Va ia ion in simula ion inpu s 151
7.4 Sensi i i y indices o c i e ia o he agg ega e Sco e ac oss
all Ma ke oppo uni ies 152
8.1 Va ia ion in inpu pa ame e s (all dis ibu ions a e uni o m) 173
Tables
Tables xxi
8.2 Combined sensi i i y indices o he h ee means o
anspo s a es sepa a ely 179
8.3 Fi s -o de sensi i i y indices o LCA phases and p oduc
elemen s 182
9.1 Combined sensi i i y indices o all conside ed ou pu s 204
9.2 Sensi i i y indices o discoun ed e u n 205
9.3 Sensi i i y indices o eg e 208
9.4 Sensi i i y indices o un ime 212
9.5 Sensi i i y indices o bias 214
9.6 Sensi i i y indices o numbe o ac ions 217
9.7 Sensi i i y indices o accu acy 220
9.8 Decomposi ion o accu acy by s a e shape, planning
i e a ions, and g id dimensions 222
9.9 Combined sensi i i y indices o all ou pu s o he wo
sampling s a egies 223
9.10 Sensi i i y index o als 225
10.1 One-a -a- ime sensi i i y analysis 237
10.2 Scena io analysis 238
10.3 Va ia ion in inpu pa ame e s 239
10.4 Sensi i i y indices o Base scena io 240
10.5 Sensi i i y indices o all scena ios and he en i e da ase 242
10.6 Sensi i i y indices o he upda ed model wi h
elec olysis-only scena ios 245
11.1 4R inpu pa ame e alues and hei anges 264
11.2 Sensi i i y indices 266
11.3 S a es o inpu a iables o he main decomposi ion 267
11.4 S a es o ma ion o inpu a iables o he supplemen a y
decomposi ion by esidual s ess and s ess a io 276
11.5 S a es o ma ion o inpu a iables o he supplemen a y
decomposi ion by s eel g ade and s ess a io 277
11.6 S a es o ma ion o inpu a iables o he supplemen a y
decomposi ion by s eel g ade and esidual s ess 278
12.1 Mechanical ma e ial p ope ies 298
12.2 Inpu pa ame e s, hei e alua ion poin s, and physical
meaning 301
12.3 Ou pu a iables expec ed/ iable anges and conside a ion
wi hin he sensi i i y s udy 303
12.4 Sensi i i y indices o selec ed model ou pu s 304
12.5 Sensi i i y indices o cu en 305
12.6 Sensi i i y indices o conduc o a ea 308
12.7 Resul ing conduc o a ea om di e en combina ions o
cable heigh and numbe o windings 309
12.8 Sensi i i y indices o ho izon al in e e ence 310
12.9 Sensi i i y indices o coil s ess a s age 1 312
xxii Tables
12.10 Sensi i i y indices o coil s ess a s age 2 313
12.11 Sensi i i y indices o coil s ess a s age 3 317
12.12 E ec s o he hkey posi ion and cable heigh on maximum
on Mises s esses in he coil 318
12.13 Sensi i i y indices o bladde p essu e 320
13.1 Modelling cons uc o he six cases conside ed 333
13.2 Inpu s o mul i-c i e ia decision-making p oblem: choosing
a coun y based on se en c i e ia 337
13.3 De ails o he conside ed mo gage 341
13.4 Nume ic inpu s o he ca choice p oblem 347
13.5 Nume ic inpu s o he body a pe cen age calcula ion 350
An i Ahola
Labo a o y o S eel S uc u es, LUT
School o Ene gy Sys ems
LUT Uni e si y
Lappeen an a, Finland
Abid Alam
Economics Depa men
Queen’s Uni e si y
Kings on, ON, Canada
Luiz B andao
In o ma ion, Risk, and Ope a ions
Managemen , McCombs School
o Business
The Uni e si y o Texas a Aus in
Aus in, Uni ed S a es
IAG Business School
PUC-Rio, Rio de Janei o, B azil
Je Cae s
Mine al X
S an o d Uni e si y
S an o d, CA, Uni ed S a es
An hony Co so
S an o d In elligen Sys ems
Labo a o y
S an o d Uni e si y
S an o d, CA, Uni ed S a es
Manuel Ga cía Pé ez
Susana Izquie do Be múdez
CERN
Méy in, Swi ze land
Hannu Ka junen
Labo a o y o The modynamics,
LUT School o Ene gy Sys ems
LUT Uni e si y
Lappeen an a, Finland
Sini-Kaisu Kinnunen
Indus ial Enginee ing and
Managemen , LUT School o
Enginee ing Science
LUT Uni e si y
Lappeen an a, Finland
Ma iia Kozlo a
LUT Business School
LUT Uni e si y
Lappeen an a, Finland
Pe e i Laaksonen
LUT School o Ene gy Sys ems
LUT Uni e si y
Lappeen an a, Finland
A o Laa i
Sepa a ion Science, LUT School o
Enginee ing Science
LUT Uni e si y
Lappeen an a, Finland
Con ibu o s
xxx P e ace
In he pas , sensi i i y analysis has been employed o “shake he oun-
da ions o science” – whe e he ac ual de ini ion o science should be con-
side ed b oadly w i , he e. So he pu pose o he book is o es he new
SimDec me hod by “shaking he ounda ions o shaking he ounda ions o
science”. Namely, o explo e how well SimDec wo ks as a sensi i i y analysis
ool when applied o a di e se spec um o disciplines. Su p isingly, collec -
ing applica ion cases o he book u ned in o a ela i ely s aigh o wa d
ask, as many esea che s esponded no only e y posi i ely, bu also wi h
ema kable en husiasm o such a p ojec .
As a esul , he e a e 13 chap e s in he book. Chap e s1–3 p o ide he nec-
essa y backg ound o unde s anding SimDec and sensi i i y analysis – hese
chap e s should be ead in he p esc ibed o de and be conside ed “com-
pulso y” o all eade s. Chap e 1 in oduces he mul i a ious meanings o
sensi i i y analysis, i s science and p ac ice, and bene i s and sho comings.
I shows how SimDec uni ies sensi i i y analysis and unce ain y analysis by
combining he bes ea u es om bo h o hei wo lds. Chap e 2 desc ibes he
SimDec algo i hm, deli e s ins uc ions o using he open-sou ce packages,
and o e s guidelines on how o in e p e SimDec esul s. Chap e 3 p o ides
a con enien synopsis o he a ious applica ions, so he mo i a ed eade
can quickly acqui e an o e all comp ehension o he collec ion o upcoming
applica ions and de e mine how o na iga e o he a eas mos ele an o
hei speci ic in e es s. Chap e s4–13 p o ide he applica ions s udied in he
book. The opics o each chap e e ol e a ound he speci ic p ojec s wi hin
each o he a ious disciplines. P og ession h ough hese applica ion chap-
e s can p oceed in any o de , depending upon he le els o in e es o he
eade . The gene al opics o he applica ion chap e s (wi h chap e numbe
in b acke s) a e co po a e inance (4), public suppo (5), 3D manu ac u ing
in cons uc ion (6), deep ech en ep eneu ship (7), ca bon oo p in analysis
(8), geology and model ideli y (9), P2X uels (10), s uc u al eliabili y (11),
supe conduc ing magne s (12), and pe sonal decisions (13).
I mus be duly ecognized ha nei he SimDec no sensi i i y analysis
should be conside ed as “spec a o spo s” – all eade s a e i mly encou -
aged o ge “s uck in” and pa icipa e. We wan you o apply SimDec o
wha e e sphe e o in e es you migh possess. Consequen ly, o p omo e
as widesp ead an adop ion and pene a ion o SimDec as possible, he book
has been made en i ely open-access and he downloadable elec onic copy
is ee-o -cha ge o all eade s. Fu he mo e, he SimDec applica ion, i sel ,
has been made comple ely open-sou ce wi h a web dashboa d1 and so wa e
packages eadily a ailable in Py hon, R, Julia, and Ma lab,2 all suppo ed
by an e e -expanding discussion-boa d communi y on Disco d.3 While hese
compu e codes can be used o conduc ing a comple e global sensi i i y
analysis as in he chap e s, hey can also be used sepa a ely as a isual ana-
ly ics package o unce ain y analysis and o he s andalone calcula ing o

P e ace xxxi
sensi i i y indices. Reade s a e encou aged o expe imen wi h he use o
SimDec on hei own da a and o ex end i o sui hei ci cums ances. When
ques ions ine i ably a ise, he Disco d communi y p o ides a g ea esou ce
o ad ice, suppo , and eedback.
No es
1 h ps://simdec.io/.
2 h ps://gi hub.com/Simula ion-Decomposi ion.
3 h ps://disco d.gg/8jkEyqXu2W.
Ma iia Kozlo a
As a habi ual in o e , I would ne e ha e suspec ed how many people
Iwould be g a e ul o, and enjoyed collabo a ions wi h, o success ully pu -
ing oge he his book p ojec . Coun less hanks go o Robe J. Moss (S an-
o d), Abid Alam (Queen’s), and Pamphile Roy (Aus ia), whose exci emen
abou SimDec and whose eage ness o implemen i in hei p e e ed p o-
g amming languages ul ima ely con inced me o SimDec’s pe asi e use ul-
ness. You unb idled passions cha ged all endea ou s wi h endless posi i e
ene gy – including he comple ion o his e y book. Special g a i ude belongs
o And ea Sal elli, he “god a he o global sensi i i y analysis”, whose in e es
in SimDec has been he bigges endo semen one could e e ha e hoped o .
And ea, you challenge, h own down like a gaun le in he Fo ewo d, has been
accep ed. Asince e THANK YOU o all con ibu o s o his book; i has been
an unbelie ably ewa ding expe ience o wo k wi h all o you in many senses.
To all who in ended o con ibu e bu e en ually could no make i ,
you a e
o gi en
, i is a pi y ha he iming did no wo k o us his ime. My g a i ude
is ex ended o ou commissioning edi o , p oduc ion eam, he e iewe s o he
book p oposal and he chap e s, and o Robe J. Moss, who kindly p epa ed a
supe b-looking o ma ing s yle adop ed h oughou he ex . Iam also g a e ul
o all hose who helped nu u e SimDec in he pas , including my Business Fin-
land p ojec eam and ad iso s, and my PhD supe iso s. My iends and am-
ily, you ha e con inued o suppo me h oughou he especially busy yea o
2023 and e en pa ien ly sus ained my occasional spells o g umpiness – hugs.
Special hanks o Olga, who pa ien ly lis ened o all my c azy ideas, doub s,
and complain s, ans o ming he la e wo in o echa ging laugh e . Finally, i
is JSY, wi hou whom we would no be w i ing hese lines. Iconside mysel a
emendously lucky pe son o ha e had such ul illing long- e m collabo a ion
illed wi h so much suppo and humou ! Soon, when his all-consuming book
is o ou shoulde s, we will be able o ge back o he no mal le els o joke
exchanges in ou communica ion. O should we do Volume II?
Ma iia Kozlo a, LUT Uni e si y
Acknowledgemen s
Acknowledgemen s xxxiii
Julian Sco Yeomans
As wi h any p ojec o his magni ude, he e a e a oo many pa ies o c edi
han may easonably appea wi hin he bounds o a sho acknowledge-
men – bu Iwill y. My since e g a i ude goes o all o ou con ibu o s o
indulging us by es ing his “new angled” SimDec app oach in hei espec-
i e ields and o allowing us o edi hei subsequen w i ings o i in o ou
book o ma (s yle, leng h, b e i y, wo ding, e c.) wi hou ( oo much) com-
plain . In doing so, he culpabili y o any e o s and omissions i mly esides
wi h he edi o s. I eally has been a pleasu e o wo k wi h (almos ) e e y
one o you and Ihope ha hese pa ne ships can be ex ended o u he
collabo a ions. Kudos o my amily (you know who you a e) o hei aci
suppo – o una ely, my wi e, eenaged daugh e , and dog all know exac ly
whe e o posi ion he ue signi icance o his p ojec wi hin li e’s b oade
con ex . Final hanks o MK o he now 5+ yea s o academic collabo a-
ion – his is no whe e I hough we would be when we s a ed (no e en
close!), bu i has p o ed o be he mos ewa ding jou ney imaginable. We
ha e clea ly gone whe e angels ea o ead. And, gi en he ime and ene gy
commi men s equi ed, I hink we can bo h pledge ha i will emain a i m
“no” o Volume II o ano he decade o wo – possibly e en h ee!
Julian Sco Yeomans, Yo k Uni e si y
***
The 2022–2024 esea ch wo k o his book was suppo ed in pa by g an
OGP0155871 om he Na u al Sciences and Enginee ing Resea ch Coun-
cil o Canada; by unding om Business Finland, g an #6713/31/2021; by
g an #00220167 om Jenny and An i Wihu i Founda ion; and by g an s
#220177 and #220178 om Finnish Founda ion o Economic Founda ion.
Pa I
In oduc ion

DOI: 10.4324/9781003453789-2
This chap e has been made a ailable unde a CC-BY-NC-ND 4.0 license.
Abs ac
Fo a compu a ional model o be use ul o decision-making pu poses, i s
ounda ions need o be “shaken” su icien ly so ha one can asce ain wha
migh happen i i s unde lying assump ions e e changed. This ype o obus -
ness assessmen is pe o med ia he echniques o sensi i i y analysis and
unce ain y analysis. These echniques supply many al e na i e pa hways
unde which such e alua ions can be conduc ed. In his chap e , we conside
a ull spec um o sensi i i y analysis ools – om se ing up compu e expe -
imen s, o analyzing hei esul s, o discussing he a ie y o me hods a each
phase, up o in es iga ing how he o e all p ocess migh ac ually be deployed
e ec i ely in p ac ice. Ou conclusions on he cu en “s a e o he p ac-
ice” a e wo ying. The mos commonly used one-a -a- ime sensi i i y analy-
sis me hods can se e ely mislead decision-make s. Fu he o ha , simple
Mon e Ca lo simula ions and he po aying o hei ou pu dis ibu ions a e
no su icien o unde s and he ac ual d i e s behind he model beha iou .
Ad anced global sensi i i y analyses a e o en so ocused on quan i ica ion
ha hey missany insigh s in o he na u e o he e ec s. Con e sely, he no el
Simula ion Decomposi ion (SimDec) me hod inco po a es he bes compo-
nen s om bo h sensi i i y analysis and unce ain y analysis – which enables
he p oduc ion o holis ic insigh s in a e y s aigh o wa d ashion – he eby
ein o cing i s conside able po en ial o widesp ead adop ion anywhe e a
global sensi i i y analysis is pe o med.
1 In oduc ion
The e m sensi i i y analysis (SA) can mean many hings and ake many
o ms. The undamen al idea behind i is abou “shaking” he model o see
wha alls ou o i . Bu i is he na u e o how we ac ually shake i ha c e-
a es a mul i ude o app oaches. The majo i y o esea che s and p ac i ion-
e s employ one-a -a- ime (OAT) analysis, pe o med by changing he alues
Chap e 1
Me hodological landscape o
sensi i i y analysis and he
place o SimDec
Ma iia Kozlo a, Samuele Lo Piano, and
Julian Sco Yeomans
4 Ma iia Kozlo a, Samuele Lo Piano, and Julian Sco Yeomans
o one ac o a a ime (Sal elli e al., 2019). Anecdo ally, such analysis is
pe cei ed as a simple, he o ical exe cise o such an ex en ha he ensuing
spide cha s and o nado diag ams ha e comple ely looded business epo s
and academic publica ions. Why mus his ubiqui ous, one-a -a- ime p inci-
ple be conside ed inadequa e? Because as soon as non-addi i e ope a ions
en e he pic u e, OAT inhe en ly dis ega ds signi ican po ions o he solu-
ion space, e en in he simples models.
Imagine a simple model in which ou losses a e desc ibed by wo ac o s:
(1) he numbe o cus ome s who ejec ou se ices, Ncancel, mul iplied by
(2) he cos o such ejec ion, cos cancel. The base case scena io is ha each
cus ome we lose cos s us $1,000. Pe o ming a one-a -a- ime sensi i i y
analysis on each o hese ac o s, sepa a ely, i we a y only he i s ac o
o see wha would happen i we los (say) i e cus ome s (i.e. a ying he
i s ac o while holding he second ac o cons an a $1,000), hen ou
losses would be $5,000 (= 5 × $1,000). I , ins ead, we a ied he second
ac o so ha ou cos s pe cancelled cus ome inc eased o $5,000 (i.e.
holding he i s ac o cons an a 1 cus ome while a ying he second
ac o ), hen ou losses would also be $5,000 (= 1 × $5,000). So pe o m-
ing his OAT-SA on he wo ac o s would indica e ha ou majo isks
add up o a maximum o $5,000 losses. The pe cep i e eade , howe e ,
would clea ly no ice ha , unde he un o una e si ua ion in which bo h
ac o s de e io a ed simul aneously, he ou come would esul in he much
mo e dele e ious loss o $25,000 (= 5 × $5,000). I one can obse e such a
disc epancy occu ing in he one-a -a- ime analysis o such a simple model,
imagine how much mis ep esen a ion could happen in signi ican ly mo e
complex models?
Mo e ad anced p ac i ione s employ Mon e Ca lo simula ion o ci cum-
en he sho comings o OAT-SA, which can be a ibu ed o unce ain y
analysis (Janssen, 2013). In Mon e Ca lo analysis, all unce ain ac o s a e
allowed o change, simul aneously, so ha ex eme scena ios can be e ealed
in he esul ing p obabili y dis ibu ion o he model ou pu . Howe e , while
he inadequacies o OAT a e o e come, unce ain y analysis simply po ays
he unce ain y anges wi hin he sys em bu canno di ec he decision-make
o he mos app op ia e cou se-o -ac ion.
The en i e ple ho a o app oaches a ailable o shaking a model all seem
o be channelling he mindse o a model explo e , which esul s in mo e
ques ions han answe s. Scena io analysis is accomplished by changing se -
e al ac o s a once bu o only a ew ins ances – namely, he e y scena ios,
hemsel es (Hassani & Hassani, 2016). Why only hese scena ios (Mo gan
& Kei h, 2008)? Why hese pa icula ac o s? And which o hem d i e(s)
he di e ence(s) in he ou come o di e en scena ios? Th eshold analysis is
used o iden i y c i ical alues o anges o inpu a iables whe e he model’s
ou pu changes signi ican ly o assumes ce ain alues – a ypical use in he
Me hodological landscape o sensi i i y analysis and SimDec 5
ield o en i onmen al impac assessmen (Bojó quez-Tapia e al., 2005), isk
assessmen (D ape e al., 1999), and b eak-e en analysis in in es men alu-
a ion (Jo ano ić, 1999). Could he e be o he combina ions o ac o s ha
esul in he same changes in he ou pu ? Is he e c i ical sys em beha iou
ou side o he s udied ange? Op imiza ion, in a sense, can also be consid-
e ed as “shaking” he model o ind he bes ou pu (Schwiege , 2007). Bu
should we no also lea n how o a oid undesi able ou pu alues? O which
combina ions o ac o s can lead us o good-enough ou pu s a he han
he bes ?
The Holy G ail o sensi i i y analysis is he aspi a ional global sensi i i y
analysis1 – a ield o science ha inco po a es a spec um o ma hema ically
ad anced me hods o compu e sensi i i y indices ha asc ibe a deg ee o
in luence o he indi idual (o g oups o ) inpu s on he model ou pu (Sal elli
e al., 2004). The p ac ice o his analysis is conside ed o be exempla y,
because o i s global na u e, in which he en i e space is s udied as all ac o s
a e changed simul aneously. Un o una ely, sensi i i y indices alone do no
ell he ull s o y, no ma e how good o eliable hey may seem. Sensi i -
i y indices only desc ibe he s eng h o an e ec , no i s shape. The e y
shape o an e ec is o en c ucial o unde s anding he model beha iou
and app oaching he decision-making su ounding i (Kozlo a, Moss, e al.,
2024).
Simula ion Decomposi ion, o SimDec, is a no el app oach ha cle e ly
agg ega es all o he bene i s o hese o he me hods. In essence, i is a isu-
aliza ion o a model ou pu dis ibu ion, decomposed and colou -coded
by he mul i- a iable scena ios, he a iables o which a e chosen based
on he global sensi i i y indices calcula ed (Kozlo a, Moss, e al., 2024).
Thus, SimDec inhe en ly amalgama es unce ain y analysis wi h global
sensi i i y analysis. Mo e impo an ly, i exposes he cha ac e o he
e ec s wi hin a model, he eby enabling deepe insigh s in o i s undamen-
al beha iou .
While many p e ious s udies ha e adop ed compe ing pe spec i es on he
ypology o sensi i i y analysis me hods (Pianosi e al., 2016; Lo Piano &
Benini, 2022; Sal elli e al., 2008), we ha e chosen o ocus on he insigh
de i a ion capabili ies o hese di e en app oaches. To mo i a e his iew-
poin , we conside he ac ual p ocess o he analysis as he mos app op ia e
lens o conduc ing ou me hodological o e iew and ex ensi ely exam-
ine i s co esponding a ionale h oughou each analy ical phase. SimDec
is subsequen ly g ounded wi hin his landscape, and i s ole is con as ed
wi h he capabili ies o hese o he me hods. Consequen ly, he goal o his
chap e is o depic he exis ing landscape o he a ious sensi i i y analysis
me hods p ac iced h oughou business, science, and academia and o i mly
es ablish he p e-eminen need o applica ions o SimDec analysis wi hin
his con ex .
12 Ma iia Kozlo a, Samuele Lo Piano, and Julian Sco Yeomans
based on a cumula i e dis ibu ion unc ion (Pianosi & Wagene , 2015)
a he han a p obabili y dis ibu ion unc ion. Howe e , se e al c i icisms
o i s obus ness ha e been aised (Puy e al., 2020a).
Owen (2014) p oposed he use o app oaches om coope a i e game
heo y in sensi i i y analysis, such as Shapley alues. Shapley alues we e
o iginally p oposed o de ine he su plus each playe in a coope a ion would
be en i led o (i.e. he alue o an n-pe son game). Shapley alues a e being
inc easingly used o he in e p e abili y o machine lea ning models (Mol-
na , 2020). Thei use in sensi i i y analysis has inc eased ecen ly due o hei
sui abili y o handling co ela ed inpu s.
One o he ecen de elopmen s, he simple binning me hod (Kozlo a
e al., 2023), con e s he gene al concep o a iance-based sensi i i y indi-
ces di ec ly in o ma hema ics o hei compu a ion. The me hod in ol es
binning he da a by X, compu ing he a e ages o Y in hose bins, and hen
aking he a iance o hose a e ages. Fi s -o de , second-o de , and com-
bined (o closed) sensi i i y indices can be eadily compu ed. The me hod
wo ks wi h gi en da a and cap u es co ela ed inpu s, which show up as
nega i e second-o de e ec . The sum o combined indices equals one e en in
he p esence o in e ac ions and co ela ions, i all andomness in he model
has been accoun ed o .
In all he desc ibed me hods and o global sensi i i y analysis, in gene al,
he sole goal is o compu e sensi i i y indices ha show how much unce -
ain y in he model ou pu is a ibu ed o di e en inpu a iables (Sal elli
e al., 2008). All p e ious phases we e jus s epping-s one p epa a ions o
his e ela ion. Mos o hese me hods do no wo k wi h dependen inpu s.
The e a e nume ous wo ks ha in oduce modi ica ions o exis ing me hods
o enable hem o cap u e dependencies in he model (Da Veiga, 2015; Lam-
boni & Kuche enko, 2021; Ma a e al., 2015; Bo gono o e al., 2024), bu
hese all equi e di e en ea men s o he da a wi h dependen a iables.
The only excep ions o his addi ional complica ion a e Shapley alues and
he simple binning me hod, which wo k wi h co ela ions wi hou a need
o supplemen al adjus men s. Fu he mo e, mos o hese me hods equi e
access o he model in o de o conduc mul iple simula ions. Only a hand ul
o me hods a e able o wo k wi h a gi en da ase , including (1) he app oaches
ha compu e i s -o de indices (Ma zban & Lahme , 2016; Plischke, 2012)
and (2) he simple binning me hod ( ha also p oduces second-o de indices
as well as cap u ing in e ac ions), which has been shown o p oduce eli-
able es ima es e en wi h a simple andom sampling o 1,000 poin s (Kozlo a
e al., 2023).
2.1.5 Visualiza ion
The wo main isualiza ion ypes employed in one-a -a- ime sensi i i y anal-
ysis a e o nado plo s (Figu e1.2A) and spide cha s (Figu e1.2B) (Kozlo a,

Me hodological landscape o sensi i i y analysis and SimDec 13
Moss, e al., 2024). To nado plo s a e es ic ed o wo e alua ion poin s in
addi ion o he base case and, hus, lack he capabili y o communica e non-
linea i ies in he unde lying model. Howe e , since he X-axis o he o nado
cha depic s he ac ual alues o he ou pu , any assump ions made ega d-
ing inpu a ia ion do no ha e o be symme ic and can, he e o e, be e
e lec eali y. On he o he hand, spide cha s place hei ou pu alues on
he y-axis wi h he co esponding pe cen o ac o change alues on he
x-axis. Hence, his s uc u e equi es ha all inpu s a y wi hin symme ical
anges, which is a ely a ealis ic assump ion (Sal elli e al., 2019). The abil-
i y o spide cha s o po ay se e al e alua ion poin s o each ac o (e.g.
±10%, ±20%, and ±30%) enables hem o communica e he shape o unde -
lying ela ionships and o expose he exis ence o nonlinea i ies wi hin he
model. Rega dless o he speci ic ad an ages and disad an ages o hese wo
isualiza ion ypes, he p edominan ailu e o hei app oach is ha only one
ac o is a ied a a ime, which means ha any in e ac ions o inpu s in he
model canno be cap u ed.
S udies ha employ global sensi i i y analysis usually s op a one o he
p e ious phases and do no sys ema ically p oceed in o isualiza ion. The
only commonly employed isualiza ion echnique is a box plo ha cha -
ac e izes he con e gence o index es ima es unde di e en condi ions (Shi
e al., 2023; Ba & Rabi z, 2023; Shang e al., 2023). Occasionally, indices
hemsel es a e depic ed wi h a ba cha (Puy e al., 2021; Vuillod e al.,
2023; Thapa & Missoum, 2022). Consequen ly, nei he o hese isualiza-
ions can unco e he inhe en cha ac e is ics o he e ec s. Ne e heless,
a ious ypes o isualiza ions do spo adically make an appea ance in one
o m o ano he in di e en global sensi i i y analysis s udies.
Sca e plo s (Figu e1.2C) a e some imes used in conjunc ion wi h GSA
(Sal elli e al., 2008; Wainw igh e al., 2014; Pala e al., 2023) and a e also
ecommended o he ini ial isual inspec ion o he inpu –ou pu ela ions.
The sca e plo s a e p oduced om global simula ions bu a e es ic ed
isually o a single inpu a iable, he eby limi ing he pe cep ion o complex
join e ec s in a model. Fo example, i a sca e plo consis s o a non-linea
end, i is unclea which o he inpu (s) a e esponsible o i and how. He -
e oskedas ici y (i.e. a a ia ion o he ou pu ange unce ain y agains he
alues o he inpu alue) is a clea sign o highe -o de in e ac ions wi h (an)
o he inpu a iable(s), bu does no su ice o iden i y which a iables a e
esponsible o i .
O en, as a pa o unce ain y analysis (Lo Piano & Benini, 2022),
esea che s display a dis ibu ion o he model ou pu in he o m o a his o-
g am (Figu e1.2D). This isualiza ion, howe e , possesses limi ed in o ma-
ion con en on he model beha iou . I me ely displays he o e all unce ain y
in he model ou pu and i s shape. Desc ip i e s a is ics o he ou pu a ia-
ion (such as expec ed mean, minimum, maximum, s anda d de ia ion, e c.)
can be de i ed. Howe e , he his og am alone canno be used o de e mine
14 Ma iia Kozlo a, Samuele Lo Piano, and Julian Sco Yeomans
which inpu a iables a ec he ou pu and does no display he na u e o
hei in e ac ion.
Hea maps (Pleil e al., 2011; Owen e al., 2019) (Figu e1.2E) and esponse
su aces (Mye s e al., 2016) a e equen ly used o depic he ela ionship
be ween wo inpu a iables and he ou pu . Howe e , hey bo h equi e
dimensionali y educ ions conce ning all o he inpu s ( hey a e no mally
ixed, and he analysis happens in a wo-a -a- ime mode). Bo h isualiza ion
ypes equi e a wo-dimensional ma ix o ou pu alues associa ed wi h dis-
c e e alues o he wo inpu s. Thus, such g aphics a e mo e o en p oduced
wi h a ull- ac o ial design sampling s a egy, because all o he andomized
app oaches would equi e u he da a ans o ma ion.
Pa allel coo dina e plo s (Figu e1.2F) a e ano he ype o g aphic, whe e
each pa allel coo dina e ep esen s each inpu and ou pu , and he lines con-
nec ing hem p o ide a isual associa ion wi hin each simula ion un (Pianosi
e al., 2015). Chao ically in e sec ing lines be ween an inpu and he ou pu
signi y no in luence, while all o he pa e ns indica e he opposi e. Howe e ,
simula ions a e o en comp ised o housands o uns, which ansla es in o
housands o lines on he pa allel coo dina e plo s, making hem un eadable
o all p ac ical pu poses (Hein ich & Weiskop , 2013). Va ious emedies o
he isual o e loading p oblem ha e been p oposed (S einpa z e al., 2010;
Roy e al., 2018). Ne e heless, he inc easing numbe o inpu a iables and
he p oblem o he op imal o de ing o coo dina es p e en his isualiza ion
ype om widesp ead adop ion.
O e all, al hough many di e en isualiza ion ypes exis , hey all possess
limi a ions in depic ing he unde lying beha iou o a compu a ional model.
None o he isualiza ions has been sys ema ically ecognized as he uni e sal
s anda d o global sensi i i y analysis s udies. Hence, he lack o isualiza-
ion is a majo sho coming in global sensi i i y analysis as i p e en s an
unde s anding o he na u e o he models and p o es o be a majo impedi-
men o well-in o med decision-making (Kozlo a, Moss, e al., 2024).
2.2 The place and ole o SimDec
The SimDec p ocedu e comp ehensi ely spans wo speci ic phases o sensi i -
i y analysis: (4) compu ing sensi i i y indices and (5) isualiza ion. Because
i ully encompasses phase 4, SimDec ine i ably engages all he p e ious da a
gene a ion phases. Speci ically, SimDec ecei es a simula ed da ase as inpu ,
calcula es sensi i i y indices using he simple binning app oach, and hen c e-
a es a isualiza ion o he mos in luen ial ela ionships in a model (Kozlo a,
Roy, e al., 2024). Consequen ly, SimDec cap u es he en i e quan i ica ion
p ocess o sensi i i y analysis and communica es he “shape” o hese e ec s
ia an in elligen isualiza ion mechanism. This p ocess esul s in a mo e
holis ic sensi i i y analysis app oach and p o ides conside able quan i ies o
ac ionable insigh (Kozlo a, Moss, e al., 2024).
Me hodological landscape o sensi i i y analysis and SimDec 15
SimDec p ojec s a isualiza ion o key mul idimensional model ela ion-
ships on o a wo-dimensional g aph. The SimDec isualiza ion is gene a ed
by i s own dis inc algo i hm ha equi es ce ain ope a ions o be pe o med
on he da a, in con as o o he , mo e “di ec ” isualiza ion app oaches. The
mechanism in ol es decomposing he da ase in o scena ios based on com-
bina ions o s a es o he mos in luen ial inpu a iables. The colou -coding
logic is designed in acco dance wi h o med scena ios, whe e he s a es o
he mos in luen ial inpu a e assigned dis inc p ima y colou s, and all o he
s a e subdi isions assume shaded g ada ions o hese p ima y colou s. The
Figu e 1.2 Schema ic ep esen a ion o di e en isualiza ion ypes.
(colou image
is accessible ia he link)
16 Ma iia Kozlo a, Samuele Lo Piano, and Julian Sco Yeomans
decomposi ion p oduces a legend which depic s which colou s and s a es o
inpu s a e a ibu ed o speci ic scena ios and indica es how each da a poin is
assigned o a co esponding scena io. This in o ma ion is used o cons uc he
ac ual isualiza ion. The p e alen SimDec isualiza ion app oach is o con-
s uc a s acked his og am in which he colou ed scena ios a e di ec ly mapped
on o he dis ibu ion o he model ou pu . Po en ially, he se ies could be o e -
layed as opposed o s acking, bu he pe cei ed ela i e simplici y a ibu -
able o o e laying possesses se e al no able de iciencies (Kozlo a & Yeomans,
2020). Box plo s could also be employed i ei he he dis ibu ion has a poo ly
eadable shape o some scena ios ha e low p obabili ies and a e no isible ( o
examples, see Chap e 2, Kozlo a, Roy, e al., 2024).
To summa ize he majo new con ibu ions o SimDec o he o e all land-
scape o sensi i i y analysis me hods: (1) i elies on a mo e e icien and accu-
a e quan i ica ion app oach (Kozlo a, Moss, e al., 2024); (2) i p oduces
a mo e powe ul isualiza ion in e ms o in o ma ion con en and o e all
eadabili y (Kozlo a e al., 2023); and (3) i o ces a much mo e sys ema ic
deploymen o isualiza ion so ha he p ocedu e o sensi i i y analysis does
no s op a quan i ica ion bu con inues o explo e model beha iou mo e
holis ically. Essen ially, i is he only isualiza ion echnique o sensi i i y
analysis ha eadily (1) exposes in e ac ions, (2) displays he da a o mo e
han h ee dimensions, and (3) p ese es eadabili y simul aneously (see
Chap e 2 (Kozlo a, Roy, e al., 2024) o speci ic de ails on using SimDec
and o guidance in i s in e p e a ion).
3 Usage o me hods
3.1 The p ocess o sensi i i y analysis in eali y
The p ocess o sensi i i y analysis po ayed in Figu e1.1 has a ely been
used wholly in p ac ice, esul ing in incomple e expe imen al designs.
The majo i y o s udies ha adop sensi i i y analysis ha e op ed o he
one-a -a- ime me hods (Lo Piano & Benini, 2022; Pianosi e al., 2016; Sal-
elli e al., 2019), ocusing on only wo phases ou o i e – (3) sampling
and (5) isualiza ion – which ha e hen been implemen ed wi hin equen ly
ques ionable expe imen al designs. As a esul , bo h a p ope “shaking” o
he model (phase 2, a ia ion) and quan i ica ion (phase 4, compu ing sen-
si i i y indices) a e missing. E en s udies by he au ho s o his chap e can
be conside ed guil y o such insu iciencies (Kozlo a e al., 2019; Lo Piano &
Mayumi, 2017). Ano he ai ly common p ac ice has been he adop ion o
unce ain y analysis in he o m o Mon e Ca lo simula ion, wi h he esul -
ing ou pu displayed in dis ibu ional o m, he eby skipping he quan i a i e
phase (phase 4, compu ing sensi i i y indices). Coupled wi h he limi a ions
o he dis ibu ion as a isualiza ion ype, such analysis emains comple ely
de icien wi h espec o iden i ying exac ly which ac o s con ibu e o he
a iabili y o he ou pu .
Me hodological landscape o sensi i i y analysis and SimDec 17
The expanding body o esea ch indica es ha global sensi i i y analysis
no mally concludes a phase 4, compu ing sensi i i y indices, a he han
assessing he shape o he disco e ed e ec s by p oceeding o he (5) isuali-
za ion phase (Shi e al., 2023; Ba & Rabi z, 2023; Vuillod e al., 2023; Wang
& Jia, 2023; Jung & Ta lanidis, 2023; Shang e al., 2023; Balles e -Ripoll &
Leonelli, 2022; Thapa & Missoum, 2022; Xiong e al., 2022; Yang, 2023).
Ra e excep ions o his con en ion possess no sys ema ized logical easoning,
wi h he a ious app oaches anging om colou ed sca e plo s (Pala e al.,
2023) o 3D Ki ia cha s (Roy e al., 2018). Howe e , he na u e o his
unsys ema ic implemen a ion p e en s he isualiza ion phase om becom-
ing an in eg al pa o he sensi i i y analysis p ocess.
3.2 Up ake o sensi i i y analysis in business and academia
Co po a e up ake o sensi i i y analysis me hods is no encou aging. In he
a eas o co po a e inance and isk managemen , he concep o global sen-
si i i y analysis has no been ecognized a all (Ryan e al., 2002; G aham &
Ha ey, 2001; Hubba d, 2020). A ecen (2022) inqui y by he au ho s in o
he ope a ions o a dozen Eu opean companies o di e en sizes and indus-
ies showed ha mo e han a hi d did no use any sensi i i y analysis a all,
hal employed simple one-a -a- ime sensi i i y analysis, and one company
used Mon e Ca lo simula ion o decision-making.
In academia, he up ake o global sensi i i y analysis has ea u ed much
mo e p ominen ly. Since i s incep ion in he 1980s, a communi y o nume i-
cal modele s has shown g ea in e es in employing he compu a ional
app oaches p o ided by he me hodology (Iooss & Lemaî e, 2015). Mo e
ecen ly, sensi i i y analysis has been ecognized as possessing na u al syne -
gies in he a iable selec ion p oblems o s a is ical lea ning, especially o
machine lea ning (Da Veiga e al., 2021). I espec i e o he disciplina y ield,
all he s ages o ma hema ical model building can clea ly bene i om pe -
o ming app op ia e sensi i i y analyses (Bo gono o & Plischke, 2016), as
desc ibed in he “Me hodological landscape” sec ion.
In gene al, es ima es o he use o global sensi i i y analysis ange be ween
12% (Lo Piano & Benini, 2022) and 20% (Sal elli e al., 2019) cases. How-
e e , he majo i y o academic e iews ha e e alua ed esea ch ha al eady
includes some kind o sensi i i y analysis. Wha abou s udies ha do no ?
Namely, how high is he up ake o sensi i i y analysis in compu a ional mod-
elling in gene al? This is a di icul ques ion o answe , conside ing he mag-
ni ude o he ield and he physical impossibili y o e iewing all publica ions
wi hin i . Akeywo d sea ch in he SCOPUS da abase using a que y wi h
“model*” in i le, abs ac , and keywo d ields e u ned mo e han 15mil-
lion esul s. Cons aining his ou pu o hose which included “sensi i i y
analysis” educed he o al o only 1% o hese esul s o hose using a
one-a -a- ime sensi i i y analysis (OAT)2 and o only 0.03% o hose using
global sensi i i y analysis (GSA)3 (Figu e1.3).

18 Ma iia Kozlo a, Samuele Lo Piano, and Julian Sco Yeomans
Figu e 1.3 Adop ion o sensi i i y analysis (SA) and global sensi i i y analysis (GSA).
(colou image is accessible ia he link)
Me hodological landscape o sensi i i y analysis and SimDec 19
These numbe s mus be iewed wi h an elemen o scep icism since we
canno ensu e ha all 15million pape s ha men ion “model*” ac ually
pe o m a compu a ional modelling exe cise.4 I espec i ely, he b eak-
down o he esul s by he subjec a ea magni ies he exp essed conce ns
(Figu e1.4). Psychology, e e ina y, and heal h- ela ed a eas a e less likely
o e e o compu a ional models. Howe e , many o he a eas (including
ma hema ics, compu e science, and en i onmen al science) p o ide a ea-
sonable ma ch. Clea ly, he e is a deg ee o imp ecision in he es ima e o
he sha e o SA s udies ( i s column), bu a less so o he es ima e o he
sha e o GSA in SA s udies – since he mo e speci ic keywo ds e u n less
noisy esul s.
Figu e 1.4 Adop ion o sensi i i y analysis (SA) and global sensi i i y analysis
(GSA) by opical a ea. (colou image is accessible ia he link)
20 Ma iia Kozlo a, Samuele Lo Piano, and Julian Sco Yeomans
Figu e 1.5 Adop ion o sensi i i y analysis (SA) and global sensi i i y analysis (GSA) in
selec ed modelling ields. (colou image is accessible ia he link)
To inc ease he accu acy o he exe cise, we examined a selec ion o mo e
speci ic modelling domains and app oaches (Figu e1.5). The sha e o SA in
modelling pape s appea s o be he highes a 7% in se e al small domains.
These domains include li e cycle assessmen (LCA), cos –bene i analysis
(CBA), and mul i-c i e ia decision-making (MCDM). The emainde o he
amewo ks exhibi no mo e han 3% o pape s e e ing o SA. The sha e
o global s udies among SA is unde 10% in each ca ego y. Mo e conce ning
a e he numbe s o he sha e o s udies ha employed GSA o e all – which
all all below 1%.
4 Conclusions
Sensi i i y analysis has become a e m ha can be unde s ood e y di e en ly
by di e en g oups o esea che s and p ac i ione s. This chap e a emp s o
uni y hese di e en pe spec i es and ame hem in o he lenses o sensi i -
i y analysis as a p ocess o in es iga ing a model. Ou main inding is he
ailu e o he en i e spec um o me hods o be su icien ly use ul in unde -
s anding model beha iou and o suppo ing decision-making. Speci ically,
one-a -a- ime sensi i i y analysis me hods p o e insu icien (and e en mis-
leading) because hey ail o cap u e in e ac ions and do no co e he space o
a iabili y p ope ly. On he o he hand, mo e ad anced me hods (i.e. global
sensi i i y analysis) end o be p ema u ely sa is ied wi h a quan i ica ion o he
s eng h o he e ec s bu ail o conside he shape o hese e ec s. Employing
isualiza ions wi hin he sensi i i y analysis ield is a e and no sys ema ic.
Me hodological landscape o sensi i i y analysis and SimDec 21
Assessing exis ing li e a u e e iews and sea ching h ough app op ia e
scien i ic da abases leads one o he conclusion ha he adop ion o sensi-
i i y analysis (especially global sensi i i y analysis) h oughou all ields o
compu a ional modelling is ex emely limi ed. Fewe han 10% o he exis -
ing compu a ional s udies adop ed any sensi i i y analysis a all, and i ually
none o hese ac ually pe o med global sensi i i y analysis. O he e iew-
e s ha e epo ed simila indings (Lo Piano & Benini, 2022; Pianosi e al.,
2016), while some ha e indica ed sligh ly highe adop ion a es bu selec-
i ely o highly-ci ed pape s (Sal elli e al., 2019). Fu he mo e, in indus y
and business, we ha e no encoun e ed he use o global sensi i i y analysis
a all. The only excep ional cases occu ed when he employees, hemsel es,
we e ained in i and we e de eloping so wa e o i (Baudin e al., 2015).
O he wise, he ma hema ical complexi y and he lack o ins uc ion in global
sensi i i y analysis appea o be he o e iding impedimen o i s dissemina-
ion and implemen a ion (Sal elli e al., 2019).
SimDec possesses he signi ican po en ial o emedying all hese sho -
comings. I s algo i hm and ocus on isualiza ion seem o make i he ine i-
able ool o e ec i ely co e ing he en i e p ocess o sensi i i y analysis.
I s sophis ica ed quan i ica ion o inpu a iable in luence and i s accessible
isualiza ion o he shape o he unde lying e ec s a e inhe en ly inco po-
a ed in o i s uni ying me hodology. A he same ime, he simplici y o he
p ocedu e and he ac ha ha d- o-unde s and quan i ica ion is con ained
wi hin a hidden ins umen al phase o he me hod make i easie o adop
o people no exp essly ained in ei he sensi i i y analysis o design o
expe imen s. Thus, he alue o SimDec appeals o he en i e spec um o
use s – om no ice use s o highly expe ienced sensi i i y analysis p ac-
i ione s. To accele a e i s adop ion, SimDec open-sou ce codes ha e been
made eely a ailable5 in Py hon, R, Julia, Ma lab, and Excel/VBA – oge he
wi h an in e ac i e web-based dashboa d – all suppo ed wi h ex ensi e
ins uc ions on how o use hem and how o in e p e hei esul s (Kozlo a,
Roy, e al., 2024).
Acknowledgemen s
This esea ch was suppo ed in pa by g an OGP0155871 om he Na u al
Sciences and Enginee ing Resea ch Council; by unding om Business Fin-
land, g an #6713/31/2021; and by g an #220177 om Finnish Founda ion
o Economic Founda ion.
No es
1 As indica ed by se e al e iew s udies, global sensi i i y analysis me hods ha e
e ylimi ed pene a ion o he p ac ice (Pianosi e al., 2016; Lo Piano & Benini,
2022a), which is o en a ibu ed o i s limi ed appea ance in he eaching p og ams
(Sal elli e al., 2019).
28 Ma iia Kozlo a e al.
he conside a ion o app op ia e co ec i e ini ia i es, such as: Wha a e he
al e na i es? Wha can be done o achie e he desi ed ou come ange? A e
he e any eadily iden i iable al e na e manoeu es? Wha shielding om isk
is uly possible?
Simula ion Decomposi ion (SimDec) p o ides an al e na i e, me hodo-
logical pa hway o edi ec he analysis o compu a ional models owa ds
ac ionabili y. In essence, SimDec in elligen ly maps a ious mul i a iable sce-
na ios on o he dis ibu ion o an ou pu . This mapping exposes ac ionable
insigh s ha a e c i ical o decision-making, including:
• How o achie e he desi ed ou pu ange while a oiding undesi able ones
(which combina ions o inpu a iable s a es esul in desi able ou pu
anges)?
• Wha is he ex en o con ol ha can be exe cised o e he sys em unde
he unce ain y condi ions p esen (how much o e lap is he e be ween
di e en scena ios)?
• A e he e speci ic scena ios ha educe he le els o unce ain y mo e han
o he s (wha is he ela i e wid h o he scena ios)?
• Wha is he na u e o in e ac ions wi hin he model (does an inpu a iable
in luence he ou pu only unde ce ain ci cums ances)?
SimDec can acili a e he o e all in e ac i i y o many decision-making
p ocesses and can p o e ema kably powe ul in e ealing he unde lying
na u e o model beha iou . I also p o ides a use ul ool o assis ing in
model c ea ion and o ensu ing ha models unc ion in hei in ended way.
This chap e p o ides guidelines o hose seeking a be e unde s anding o
he algo i hm behind SimDec (Sec ion2), wishing o lea n how o in e p e
SimDec esul s (Sec ion3), o in using any o he a ailable open-sou ce pack-
ages (Sec ions4 and 5).
2 SimDec algo i hm
Fundamen ally, he SimDec algo i hm maps mul i a iable scena ios on o a
dis ibu ion o model ou pu in an in elligen ashion, he eby enabling a is-
ualiza ion o he c i ical cause–e ec ela ionships inhe en wi hin he model.
As i s name implies, SimDec decomposes all da a ( om simula ion uns o
measu ed da ase ) in o au oma ically c ea ed scena ios cons uc ed om he
combina ions o anges (s a es) o he in luen ial inpu a iables. SimDec is a
ully au oma ic p ocedu e ha e u ns a isualiza ion depic ing model beha -
iou ha explains he mos impo an sou ces o a ia ion wi hin he ou pu
(see Figu e2.1).
The algo i hm consis s o wo undamen al pa s: (1) a compu a ion
o sensi i i y indices (Kozlo a e al., 2023) ha disce n which in luen ial

SimDec algo i hm and guidelines o i s usage, in e p e a ion 29
Figu e 2.1 Co e idea behind SimDec. (colou image is accessible ia he link)
30 Ma iia Kozlo a e al.
a iables should be used in he decomposi ion, ollowed by (2) a co e is-
ualiza ion o he decomposed ou pu dis ibu ion (Kozlo a & Yeomans,
2022).
2.1 Sensi i i y indices compu a ion
The sensi i i y indices compu ed a he beginning o he SimDec p ocedu e
a e global a iance–based indices. The i s -o de index SXi is compu ed as
a a iance o he expec a ion o Y condi ioned on Xi weigh ed by he o al
a iance o Y.
Va (( YX )
Si)
Xi= (1)
Va
()
Y
The second-o de indices ha e a simila o mula ion, bu he expec a ion
o Y is now condi ioned on a pai o inpu a iables, and he co esponding
i s -o de e ec s a e deduc ed o cap u e he pu e excess e ec (i.e. i would
equal ze o in a pu ely addi i e model, indica ing no in e ac ion).
Va (( YX|,X
Sij
))
XX
ij=--SS
Va
()
YXX
ij
(2)
A combined (o closed) index is c ea ed o agg ega e he i s - and
second-o de e ec s by adding he i s -o de index o he sum o all
second-o de e ec s ela ed o his inpu a iable. The “hal ing” is necessa y
o en o ce a condi ion ha he sum o all combined e ec s equals o 1 when
he ull a iabili y o he ou pu is explained.
Kinpu S
SS
c
XX
ii
=+
sXX
ij
(3)
j=12
ij
Equa ions (1) and (2) can be de e mined using a ious ma hema ical
me hods and a e abs ac ions o classical Sobol’ (1993) exp essions. The
sensi i i y indices used in SimDec a e compu ed ia an inno a i e binning
app oach (Kozlo a e al., 2023) in which he condi ional expec a ion o Y o
X (s) is de e mined by binning he X (s) and hen calcula ing he a e ages o
Y in hose bins. Kozlo a e al. (2023) ha e shown ha indices calcula ed by
his binning app oach possess consis en ly high accu acy, e en on e y small
da ase s. These sensi i i y indices can be calcula ed wi hou any modi ica-
ions o he algo i hm o ei he simula ed da a o any measu ed da ase (i.e.
con aining inpu and ou pu a iables).
SimDec algo i hm and guidelines o i s usage, in e p e a ion 31
2.2 Decomposi ion p ocedu e
Figu e2.2 p esen s a s ep-by-s ep illus a ion o he decomposi ion p oce-
du e on a s ylized example model.
The decomposi ion algo i hm equi es six s eps. S ep 1 and s ep 2 a e used
o de e mine which inpu a iables o selec o he isualiza ion. S eps 3–6
cons uc he explici isual decomposi ion o he model.
1. Compu e sensi i i y indices. The combined ( i s - and second-o de ) e ec s
a e calcula ed.
2. O de and selec inpu s. A h eshold o cumula i e impo ance is es ab-
lished. Inpu s a e selec ed (in dec easing o de o hei sensi i i y index
alues) un il he cumula i e sum o he indices equals o exceeds he
h eshold. (The h eshold could be hough o as es ablishing “how much
explana ion o he ou pu a iabili y should be cap u ed by he selec ed
a iables”.)
3. Di ide inpu s in o s a es. The au oma ic p ocedu e b eaks down he
nume ic ange o each selec ed inpu in o wo o h ee s a es – wi h he
same numbe o obse a ions in each. Th ee s a es a e chosen i he e
a e wo o ewe a iables selec ed in s ep 2. O he wise, wo s a es a e
o med. I an inpu a iable consis s o i e o ewe unique alues, he
numbe o s a es c ea ed co esponds o he numbe o alues (i.e. each
alue co esponds o exac ly one s a e).
4. Fo m scena ios. All combina ions o all s a es o he selec ed inpu a i-
ables o m an exhaus i e se o scena ios. This associa ion is used o con-
s uc he legend in he isualiza ion.
5. Map simula ed ou pu s o scena ios. Each ou pu alue om he da ase
is ma ched o a speci ic scena io based on he co esponding alues o
i s inpu s and he associa ion c ea ed in s ep 4. (The scena io alloca ions
enable a subsequen isualiza ion o he da a. As wi h “classic simula-
ion”, he isualiza ion in SimDec is a his og am depic ing he dis ibu ion
o ou pu alues.)
6. Colou -code he ou pu dis ibu ion. The simple ou pu his og am is con-
e ed in o a s acked his og am (which p ese es he o iginal shape), wi h
he scena ios om s ep 4 as he se ies. The colou -coding ollows a speci ic
ule: he s a es o he mos impo an a iable a e assigned dis inc p ima y
colou s, while all o he pa i ions assume shades o hese main colou s.
The s acked his og am colou ing logic o SimDec can be used in o he
ypes o isualiza ions. Fo example, box plo s can be used when some sce-
na ios con ain e y li le da a, he shape o he dis ibu ion is incon enien
o isualiza ion, o he da a sample is oo small o enable he c ea ion o a
meaning ul his og am (see Sec ion5.3).
32 Ma iia Kozlo a e al.
Figu e 2.2 SimDec algo i hm illus a ed on an example model.1 (colou image is accessible ia he link)
Sou ce: Kozlo a e al. (2024).
SimDec algo i hm and guidelines o i s usage, in e p e a ion 33
3 Ho w o ead SimDec
The a ious concep s needed o cons uc an e ec i e in e p e a ion o he
SimDec esul s include an unde s anding o :
• Wha do he sensi i i y indices ac ually mean?
• How o ead a his og am?
• How o judge he deg ee o in luence o one inpu on he ou pu using
SimDec?
• How o ead join e ec s o se e al inpu s on he ou pu using SimDec?
3.1 Sensi i i y indices
The sensi i i y indices used in SimDec a e global a iance–based indices.
Global means ha hey a e compu ed when e e y hing is changing simul ane-
ously (as opposed o one-a -a- ime analysis), and a iance-based means ha
he index shows how much a iabili y/ a ia ion o he ou pu is explained.
The simple binning algo i hm (Kozlo a e al., 2023) used in SimDec com-
pu es h ee ypes o indices: i s -o de (o main) e ec s, second-o de (o
in e ac ion) e ec s, and combined (o closed) indices. The combined indi-
ces agg ega e he i s - and second-o de e ec s and p o ide he de aul
measu es used o iden i y he mos in luen ial inpu a iables selec ed o
decomposi ion.
The i s -o de indices indica e how much each inpu a iable con ibu es
indi idually o he a iance o he ou pu . Fo example, in a si ua ion o
YX=, he i s -o de index o X would be 1.0 (as i explains 100% o he
a iabili y). In an addi i e model YX=+
12
X, whe e X1 and X2 ha e iden ical
dis ibu ions (o nume ic anges), bo h inpu s would ha e i s -o de indices
o 0.5 (as, o his model, each explains 50% o he a iabili y). An inpu
a iable can ha e close o 0 in luence, i i s nume ic ange is small compa ed
o o he a iables o i he model mechanics dic a e ha he e is li le impac
om i .
The second-o de indices desc ibe how much a pai o inpu a iables con-
ibu es o he a iance o he ou pu on op o hei indi idual in luence.
These indices would necessa ily be ze o o addi i e models. Fo example, in
YX=+
12
X, he second-o de index o he pai XX
12
would be equal o 0.
Second-o de indices can be posi i e i he inpu a iables a e mul iplied in
he model o possess a mo e complex in e ac ion (see 3.4.1, “In e ac ions”).
Aposi i e second-o de index means ha he pai o a iables a ec s he ou -
pu syne gis ically (i.e. oge he hey p oduce mo e in luence han simply a
sum o hei indi idual e ec s). Second-o de indices can assume nega i e al-
ues, which indica e an o e lapping e ec o hese a iables (i.e. a co ela ion
o dependency) in he model. Fo example, i X1 and X2 assume he same al-
ues in e e y single simula ion un o he model YX=+
12
X, hei second-o de
e ec would be −1.0, deno ing a ull o e lap o hei e ec s. In si ua ions

34 Ma iia Kozlo a e al.
whe e bo h co ela ions and in e ac ions a e p esen , he second-o de index
akes he sign o whiche e e ec is mo e p onounced (Kozlo a e al., 2023).
Combined sensi i i y indices a e calcula ed o e e y inpu a iable as he
sum o hei i s -o de index and a hal ed sum o hei second-o de indices
wi h all o he inpu a iables. The hal ing is needed o a oid double-coun ing
when summing up all he indices. In he p e ious example o YX=+
12
X,
wi h X1 and X2 aking iden ical alues in e e y simula ion un, he i s -o de
e ec s o bo h will be 1.0 (since each inpu sepa a ely explains he ull a i-
abili y o he ou pu ), he second-o de e ec o his pai o inpu s would be
−1.0, he combined index o each inpu is hen 0.5 [= 1.0 + (−1.0)/2], and he
sum o he combined indices is 1.0 [= 0.5 + 0.5]. The inal summa ion alue
o 1.0 means ha , o e all, he en i e a iance o he ou pu is explained by
hese wo inpu a iables.
The sum o he combined indices p o ides a good es ima ion o whe he
he selec ed inpu a iables ully explain he a ia ion o he model ou pu .
I he sum is lowe han 1.0, i migh indica e ha he e is unaccoun ed an-
domness occu ing wi hin he model (e.g. i some inpu a iables a e no
egis e ed o he analysis, he e migh be some s ochas ici y coming om he
model mechanics o i s en i onmen ). An al e na e explana ion migh in ol e
he exis ence o conside able hi d-o de e ec s. Howe e , hi d-o de e ec s
a e a a e phenomenon. Asum o combined indices conside ably highe han
1.0 indica es a signi ican o e lapping o in o ma ion con en in he model/
sys em and is a common a ibu e om he analysis o di e en model laye s
(e.g. agg ega es o andom inpu a iables) o empi ical da a.
One should bea in mind ha sensi i i y indices ep esen app oxi-
ma e es ima es and a e p one o nume ic noise, especially in small-sample/
high-numbe -o - a iables si ua ions. Unde such ci cums ances, all indices
(especially he second-o de ones) can be a ec ed by noise (e.g. many indices
would hold alues in he 0.01–0.02 ange). The ocus o analysis should be
edi ec ed on o hose inpu a iables wi h indices o e 0.05, while all hese
low- alue-e ec a iables can be sa ely disca ded.
In SimDec, he sensi i i y indices p o e ins umen al in helping o selec
which inpu s o choose o he decomposi ion, while any ac ual epo ing o
hei calcula ed alues emains op ional.
3.2 P obabili y dis ibu ion/his og am
A his og am p o ides a ep esen a ion o he dis ibu ion o nume ical da a.
I s ho izon al axis shows he ange o he a iable o in e es , and i s e ical
axis deno es he coun (also called equency) o he p obabili y (i he coun
has been di ided by he o al numbe o da a poin s). One could hink o
c ea ing a his og am as he delibe a e ac o dis ibu ing cubes wi h numbe s
(da a poin s) ac oss baske s (bins) ha designa e he speci ied numbe ange.
Figu e2.3 demons a es an example o such an ac ion on a small scale.
SimDec algo i hm and guidelines o i s usage, in e p e a ion 35
Figu e 2.3 A his og am buil o an a ay o Y={11, 12, 25, 28, 28, 29, 31, 35, 39,
41}. (colou image is accessible ia he link)
In Figu e2.3, he Y-axis can be con e ed om coun o p obabili y i di ided
by he o al numbe o da a poin s, 10. I s labels would be con e ed om 1 o
0.1 and om 4 o 0.4. The 0.4 ma k implies ha bins which each i con ain
40% o da a (since he bin 20–30 con ains 4 cubes, which is 40%). One should
no e ha changing a bin wid h would also a ec he Y-axis o a his og am.
A dis ibu ion alone can supply only limi ed in o ma ion abou he da a – i s
minimum, maximum, shape (whe e mos o he da a occu s), oge he wi h
some addi ional desc ip i e s a is ics. Howe e , an explici mapping o which
inpu alues lead in o which speci ic egions o he ou pu dis ibu ion (as
p o ided by SimDec) enables a mo e de ini i e exposu e o he unde lying
model beha iou .
3.3 S eng h o in luence
When decomposing a his og am by a speci ic single inpu a iable, one can
isually pe cei e i s deg ee o in luence. Figu e 2.4 demons a es a ious
single- a iable decomposi ions ha p ojec commonly obse ed sca e plo
pa e ns on o hei cong uen SimDec isualiza ions.
I an inpu a iable has no e ec on he ou pu , hen i s s a es (e.g. low
and high) would lie on op o each o he in he SimDec his og am, wi h
ully o e lapping ou pu anges. In such a case, he bo de be ween he s a es
would be essen ially ho izon al, and he co esponding sensi i i y index
would be equal o 0. I an inpu a iable has a s ong e ec and explains
mos o he a iance o he ou pu , he bo de s be ween i s s a es on he Sim-
Dec his og am would appea mo e e ical. Such isualiza ions ha e impo -
an decision-making implica ions (e.g. i he high s a e o X can be ixed
by he decision-make , i would gua an ee a ce ain ange o alues o Y).
36 Ma iia Kozlo a e al.
Figu e 2.4 Schema ic isualiza ion o di e en deg ees o in luence o an inpu
a iable on a model ou pu in wo di e en isualiza ion ypes. (colou
image is accessible ia he link)
The cases in-be ween possessing low- o-s ong e ec s would display a mo e
“diagonally-appea ing” bo de di ision be ween s a es. The less he s a es
o e lap each o he , he la ge he e ec o X on Y. While ho izon al displace-
men s o sub-dis ibu ions on he SimDec his og am a e key o in e p e ing
he esul s, e ical posi ionings occu based solely on he echnical plo ing
o de o he se ies in he s acked his og am.
3.4 Join e ec s
When wo o mo e inpu a iables a e used o decomposi ion, i becomes
possible o examine hei join e ec s. The e a e, undamen ally, h ee ways
ha a pai o inpu a iables can join ly a ec he ou pu :
• The same as he sum o hei indi idual e ec s (i.e. an absence o co ela-
ion o in e ac ion)
• A syne gy o ex a e ec on op o he sum o hei indi idual e ec s (i.e.
in e ac ion)
• A edundancy o o e lapping e ec (i.e. co ela ion)
SimDec algo i hm and guidelines o i s usage, in e p e a ion 37
This subsec ion illus a es how SimDec po ays he di e en cases behind
in e ac ions and co ela ions in con as o he no-join -e ec si ua ion.
3.4.1 In e ac ions
The schema ic isualiza ion in Figu e2.5 depic s how di e en ypes o in e -
ac ions o inpu a iables on he ou pu appea in SimDec isualiza ions.
Figu e2.5A shows how he a ious sub-dis ibu ions ( he di e en col-
ou s) o an addi i e model in which bo h inpu a iables a e equally impo -
an would be uni o mly shi ed. The co esponding second-o de e ec o
such inpu s would be equal o ze o.
Figu e 2.5B illus a es he linea in e ac ion e ec ha is cha ac e is ic o
mul iplica i e models. In he SimDec his og am, he sub-dis ibu ions become
shi ed mo e-and-mo e along he ho izon al axis. The e ec o one inpu on he
ou pu becomes inc easingly mo e magni ied wi h he inc easing alue o he
o he inpu . The sensi i i y index compu ed o he second-o de e ec o such
inpu a iables would be non-ze o. The model o an elec ic ai c a lying ange
as a unc ion o he capaci y o i s ba e ies and he powe o i s elec ic mo o
p o ides an example o such a linea in e ac ion e ec (Kozlo a e al., 2021).
In ano he ype o in e ac ion, Figu e 2.5C demons a es how one
inpu a iable can swi ch he di ec ion o in luence on he ou pu in di -
e en s a es o he o he inpu a iable. Such an e ec migh occu due
o a sign change in a model. The calcula ed second-o de e ec would be
non-ze o. Such an in e ac ion was obse ed in he ca bon oo p in model
o Kozlo a and Yeomans (2022), whe e, in he case o disposal ia land ill-
ing, an inc eased usage imp o ed he oo p in . Howe e , o he case o
disposal ia incine a ion, he opposi e oo p in e ec happened. Namely,
an inc eased usage de e io a ed he oo p in because o accoun ing o neg-
a i e ca bon emissions.
Figu e2.5D demons a es ha o he ypes o nonlinea in e ac ions can
occu in models. Fo example, an inpu a iable migh ha e no e ec on
he ou pu in one s a e o ano he a iable ( he ed-shaded sub-dis ibu ions
lying on op o each o he ) bu exhibi a s ong e ec o he wise ( he shi ed
blue pa e n sub-dis ibu ions). Such non-linea e ec s will possess non-ze o
second-o de sensi i i y indices. The c ying baby model o Kozlo a e al.
(2024) illus a es such an in e ac ion in which he model pa ame e s only
a ec he ou pu when a pa icula ype o op imiza ion is used.
Figu e2.5 displays one example wi hou in e ac ion (Figu e2.5A) and
h ee cases possessing e y di e en ypes o in e ac ions (Figu es2.5B–2.5D).
In Figu es2.5B–2.5D, he in e ac ion e ec s a e de ec ed by he calcula ion o
non-ze o second-o de indices. Howe e , i is impossible o asce ain exac ly
wha ypes o in e ac ions a e p esen wi hou he accompanying SimDec
isualiza ions. Teasing ou he na u e o he unde lying in e ac ion e ec s in a
compu a ional model and unde s anding he beha iou , in gene al, is c ucial
o e ec i e decision-making.
44 Ma iia Kozlo a e al.
Figu e 2.7 The ou pu o he SimDec Py hon package. (colou image is accessible
ia he link)
> au o_ is$simdec_plo
> au o_ is$legend_ able
The a iables o decomposi ion can also be use -de ined ( a he han
de e mined au oma ically), and he colou s and appea ance o he esul ing
his og am can be cus omized manually. Fo example, o modi y he look o
he s acked his og am, one could execu e he ollowing lines o code.

SimDec algo i hm and guidelines o i s usage, in e p e a ion 45
Figu e 2.8 Web-based SimDec dashboa d simdec.io. (colou image is accessible ia he link)
46 Ma iia Kozlo a e al.
> colo s <- c(‘#8c5e ’, ‘# e252’, ‘#0dd189’)
> cus om_ is <- simdec_ isualiza ion(ou pu ,
inpu s, SI, main_colo s = colo s)
> cus om_ is$simdec_plo
> cus om_ is$legend_ able
Table 2. 2 Uses and a gumen s o he SimDec R package unc ions
Func ion Pu pose Inpu s Ou pu s
sensi i i y_ Compu es – inpu – SI – combined sensi i i y
indices.R sensi i i y – ou pu indices
indices – FOE – i s -o de e ec s
– SOE – second-o de
e ec s
simdec_ Au oma ically – inpu – scena ios – ec o o
isualiza ion.R gene a es – ou pu scena io indices o size
SimDec’s – SI N uns * 1
s acked – scen_legend – associa ion
his og am be ween inpu s’ s a es and
isualiza ion scena ios
– bounda ies – nume ic
bounda ies o he o med
s a es
– simdec_plo – SimDec
s acked his og am
isualiza ion
– legend_ able – a legend
o he plo
A delibe a e choice was made du ing he de elopmen p ocess so ha
he unc ion sensi i i y_indices would no include any dependencies
in o de ensu e ha u u e “upda e”- ela ed main enance issues we e min-
imized. Despi e his design decision, he o e all SimDec package emains
compu a ionally e icien . Con e sely, he simdec_ isualiza ion unc ion
does possess se e al dependencies. Howe e , hese dependencies ha e been
ca e ully chosen o ensu e ha only egula ly main ained packages a ail-
able h ough CRAN ha e been elied upon. Cu en ly, simdec_ isu-
aliza ion depends on ggplo 2, dply , colo space, g idEx a,
and kableEx a. The manda o y a gumen s o each o he unc ions a e
desc ibed in de ail in Table2.2, whe eas he up- o-da e lis o op ional
a gumen s can be accessed in SimDec R package documen a ion in
Gi Hub.
SimDec algo i hm and guidelines o i s usage, in e p e a ion 47
4.3 Julia
The scien i ic compu ing language Julia is designed o nume ical compu a-
ion wi h a syn ax like Ma lab and Py hon bu wi h he speed o C++ (Bezan-
son e al., 2017). The ligh weigh Julia package, Simula ionDecomposi ion.
jl, can be ins alled using he ollowing commands:
A e ins alla ion, he use can impo he Simula ionDecomposi ion
package in o he Julia REPL. As uc u e con aining he da a able and bins
is c ea ed by i s loading he da a, selec ing he inpu a iables, selec ing a
a ge ou pu a iable, and numbe o bins, hen calling.
The colou ed his og am and able can hen be displayed o u he analy-
sis using he unc ions plo and able, which esul in a simila isualiza ion
o ha o Figu e2.7.
An example no ebook using he Plu o.jl package can be ound in he
Gi Hub eposi o y.5
4.4 Ma lab
The SimDec Ma lab package employs wo main unc ions (see Table2.3).
The Ma lab unc ions6 mus be downloaded and hei co esponding olde
mus be explici ly ac i a ed as a pa h in Ma lab. The inpu da a needs o be
p o ided in he o m o wo a iables: inpu s (o he size NK
uns *inpu s) and
ou pu (o he size N uns *1).
julia>] # o en e package mode
(@ 1.9) pkg> add h ps://gi hub.com/Simula ion-Decompo-
si ion/Simula ionDecomposi ion.jl
julia> using Simula ionDecomposi ion
julia> da a = load_da a(“da a_enginee ing.cs ”)
julia> inpu s = [:Ba e y, :Mo o ]
julia> a ge = :Dis ance
julia> nbins = 50
julia> simdec = SimDec(da a, a ge , nbins)
julia> plo (simdec)
julia> able(simdec)
48 Ma iia Kozlo a e al.
A e he ou pu and he inpu a iables ha e been o mula ed in he Ma -
lab wo kspace, he en i e SimDec p ocedu e can be un ia hese wo unc-
ions, which will p oduce a isualiza ion simila o Figu e2.7.
% ge ing he da a
Ma ix = xls ead (“example_da a.xlsx”);
ou pu = Ma ix(:,1);
inpu s = Ma ix(:,2:end);
% unning SimDec
[SI, FOE, SOE] = sensi i i y_indices (ou pu , inpu s)
[scena ios, scen_legend, bounda ies] = simdec_ isualiza-
ion (ou pu , inpu s, SI);
Se e al op ional a gumen s a e a ailable o he simdec_ isualiza ion.m
unc ion in o de o cus omize a decomposi ion (see he up- o-da e lis o
op ional a gumen s in he documen a ion o SimDec Ma lab unc ion on
Gi Hub).
The op ional a gumen s a e se as in any s anda d Ma lab ins ance. Fo
example, he ollowing code speci ies he names o he a iables and changes
he colou pale e.
% cus om names and colo s
ou pu _name = ‘Ou pu ’;
inpu _names = {‘Inpu 1’,’Inpu 2’,’Inpu 3’,’Inpu 4’};
colo s = {‘#3F45D0’,’#DC267F’,’26DCD1’};
[scena ios, scen_legend, bounda ies] = simdec_ isualiza-
ion (ou pu , inpu s,. . .
SI,’Ou pu Name’,ou pu _name,’Inpu Names’,inpu _
names,’MainColo s’,colo s);
4.5 Excel empla e
The Excel empla e is designed o wo k wi h sp eadshee models. The em-
pla e is downloadable ia Gi Hub7 and con ains an example model, a main
shee o he SimDec in e ace, and a VBA mac o ha pe o ms he equi-
si e SimDec unc ionali y. The SimDec in e ace (see Figu e2.9) consis s o
(1) he Mon e Ca lo simula ion a ea, (2) a decomposi ion se -up, and (3) he
SimDec algo i hm and guidelines o i s usage, in e p e a ion 49
esul ing ou pu g aphics, oge he wi h app op ia e summa y s a is ics and
a legend.
De ailed ins uc ions o u ilizing he empla e can be ound ei he in a
speci ically dedica ed ideo u o ial8 o in Kozlo a and Yeomans (2022). The
mos impo an dis inc ion be ween his Excel ool and all emaining Sim-
Dec packages is ha sensi i i y indices a e no compu ed in he empla e.
Any decision o selec which a iables o use in he decomposi ion (and hei
o de ing) emains en i ely a he disc e ion o he use .
5 Usage nuances
Se e al ques ions come o mind when s udying a model wi h SimDec: How
many inpu a iables should be andomized? Wha should he sample size
be? How should he da a be sampled? Which a iables o choose o decom-
posi ion? How o o m scena ios o he decomposi ion? Wha a e he al e -
na i es o s acked his og am isualiza ions, and when o use hem? These
ques ions all a e add essed in his sec ion.
5.1 Selec ion o inpu a iables o decomposi ion
By de aul , SimDec uses sensi i i y indices o indica e exac ly which a iables
o selec o decomposi ion. The de ac o me hod-o -choice is he simple bin-
ning app oach o Kozlo a e al. (2023) and his p ocedu e is inco po a ed
in o all SimDec packages. Howe e , any o he me hod o compu ing sen-
si i i y indices could be used, i p e e ed. Va iance-based me hods make
mo e sense, since hey s aigh o wa dly ansla e highe alues in o mo e
widely dispe sed a iable s a es in he his og am. I is also easie o wo k
Table 2. 3 Main unc ions o he SimDec Ma lab package
Func ion Pu pose Inpu s Ou pu s
sensi i i y_ Compu es – inpu s – SI – combined sensi i i y
indices.m sensi i i y – ou pu s indices
indices – FOE – i s -o de e ec s
– SOE – second-o de e ec s
simdec_ Au oma ically – inpu s – scena ios – ec o o scena io
isualiza ion.m c ea es Sim-– ou pu s indices o size N uns * 1
Dec s acked – SI – scen_legend – associa ion
his og am be ween inpu s’ s a es and
isualiza ion scena ios
– bounda ies – nume ic bound-
a ies o he o med s a es
– s acked_his og am – objec
ha e u ns he isualiza ion
and he legend

50 Ma iia Kozlo a e al.
Figu e 2.9 SimDec Excel empla e.
(colou image is accessible ia he link)
SimDec algo i hm and guidelines o i s usage, in e p e a ion 51
wi h me hods ha can ope a e on he gi en da a (Plischke, 2012; Puy e al.,
2024; Kozlo a e al., 2023), since he same da ase is la e used o build he
isualiza ion.
Con e sely, selec ion o inpu a iables o decomposi ion could also
be done manually – whe he o explo a o y da a analysis pu poses o o
sa is y al e na e decision con ex s. In complex nonlinea models, explo ing
he na u e o sepa a e in e ac ion e ec s o he shape o a single-inpu a i-
able in luence on he ou pu can p oduce addi ional insigh s in o he model
beha iou (Ahola e al., 2024). Some decision p oblems migh dic a e he
speci ic choice o a iables (e.g. he public policy equi emen s o p ojec
pe o mance in Kozlo a e al. (2016)).
5.2 S a es and scena io o ma ion
One impo an dis inc ion o SimDec om scena io analysis is ha he se
o scena ios is no a bi a ily decided upon bu esul s om lis ing all s a e
combina ions in he ac ual decomposi ion. Howe e , he choice o he num-
be and nume ic bounda ies o s a es is mo e lexible. By de aul , SimDec c e-
a es h ee s a es i wo inpu a iables a e selec ed and wo s a es o he wise.
An excep ion occu s when an inpu a iable can assume no mo e han i e
unique alues, in which case, each alue ins ance becomes i s own sepa a e
s a e. The numbe o s a es can always be modi ied in esponse o he speci ic
needs o he decision con ex . Fo example, in one o he SimDec applica ion
chap e s, a decomposi ion in o nine s a es is c ea ed in o de o depic he
sub-dis ibu ions o nine dis inc ma ke oppo uni ies (Mye s e al., 2024).
I is impe a i e o supply he co esponding numbe o HEX codes o he
main colou s o he unc ion in o de o ensu e i s p ope unc ioning.
Fo es ablishing he nume ic bounda ies be ween s a es, he de aul p o-
cedu e is o ensu e an equal appo ionmen o da a in o each s a e. An
al e na i e, inbuil op ion is o choose equally-sized nume ic in e als o
he s a es. The wo app oaches c ea e an iden ical se o s a es i he inpu
a iables a e uni o mly dis ibu ed. Fo non-uni o mly dis ibu ed a iables,
he “equal-in e al” p inciple alloca es di e en amoun s o da a in o each
s a e. The choice should be based on he speci ic decision con ex . Fo exam-
ple, use he “equal-amoun -o -da a” op ion o e lec he equal p obabili ies
o occu ence o di e en s a es o ex e nal a iables no con olled by he
decision-make . Howe e , equal-sized-in e al s a es would be p e e able i
he a iable is unde he decision-make ’s con ol. Cus om nume ic bound-
a ies ha e been p esc ibed o e lec ce ain key h esholds imposed by a
decision-make , whe e SimDec can hen be used o see whe he achie ing ha
h eshold (o no ) p o es bene icial (Kozlo a e al., 2016).
Howe e , i he pu pose o an analysis is o s udy he beha iou o he
unde lying model, hen he de aul s a e o ma ion me hod is ad ised in
o de o p e en possible isual dis o ions in he isualiza ion. Fo example,
52 Ma iia Kozlo a e al.
an inc easing numbe o da a poin s in s a es o a uni o mly dis ibu ed inpu
a iable can be con used wi h linea in e ac ion (see Figu e1.5B), while e o-
neous bounda y se ing ha esul s in no da a in a s a e can be con used
wi h co ela ion (see Figu e1.6C). I empi ical da a is analyzed, algo i hms
ha de ec na u al b eaking poin s o de ining he s a e bounda ies migh
p o ide he judicious choice. S udying he applica ion o SimDec o empi ical
da a p o ides a po en ially ui ul a enue o he di ec ion o u u e esea ch
and de elopmen .
5.3 Sample size and sampling s a egies
Sample size, in conjunc ion wi h he numbe o andomized inpu a iables,
can a ec SimDec pe o mance in wo ways: (1) accu acy o he compu ed
sensi i i y indices, and (2) smoo hness o he s acked his og am isualiza ion.
Fo compu ing sensi i i y indices, he la ge he sample size and he
ewe he numbe o a iables, he highe he accu acy o esul ing es ima-
ions. Fi s -o de indices con e ge soone (Ma zban & Lahme , 2016) han
second-o de ones (Kozlo a e al., 2023). In gene al, as ew as 1,000 da a
poin s a e su icien o gene a e s able and eliable sensi i i y indices o
models possessing six inpu a iables (Kozlo a e al., 2023). Fu he mo e,
quasi- andom sampling can be used o imp o e he accu acy (Kozlo a e al.,
2023). Inc easing noise combined wi h highe numbe s o inpu a iables
esul s in much noisie second-o de e ec s (mos o he pai s o inpu a i-
ables show join 0.01–0.02 e ec s ins ead o ze o). In such si ua ions, he
esul ing sum o indices has been obse ed o o e shoo he expec ed 100%.
Ne e heless, e en wi h ei he a smalle sample size o a la ge numbe o
a iables, i s -o de indices ha e been eliably used o judge he ela i e
impo ance o inpu a iables. Examples o his ange o eliabili y can be
obse ed o an applica ion wi h 29 inpu s and 1,000 sample (Pelleg ino
e al., 2024) and o a case o a pa ial da ase o only 152 poin s (Pé ez e al.,
2024).
In a isualiza ion, he mo e da a poin s he e a e, he smoo he he his o-
g am i sel and he mo e dis inc he bo de s be ween he scena ios appea
(see Figu e2.10). One housand da a poin s appea o es ablish he basic
minimum amoun o da a o clea eadabili y. Howe e , i he compu a-
ional cos s a e bea able, hen 10,000 da a poin s a e ecommended, as his
can p oduce a e y smoo h and c isp isualiza ion. An inc eased numbe
o unce ain a iables causes mo e unce ain y in he model ou pu . This
unce ain y esul s in a la ge o e lap o consecu i e scena ios. The choice
o he numbe o andomized inpu a iables o he simula ion (o da a
analysis) should app op ia ely e lec he ask a hand – a highe numbe o
mo e ealis ic modelling o he sys em and a lowe numbe o s udying he
key beha iou s in he model. I e a i e analysis wi h consequen emo al o
SimDec algo i hm and guidelines o i s usage, in e p e a ion 53
less-in luen ial inpu s (o he adding o o he a iables i some hing impo -
an had been missed) enables in-dep h explo a ion o a model beha iou .
I can be obse ed ha di e en sampling s a egies do no p oduce sig-
ni ican di e ences (see each column in Figu e2.10). Quasi- andom sampling
and ull ac o ial designs esul in sligh ly smoo he isualiza ions a sam-
ple sizes o 10,000. Howe e , ull ac o ial designs in ol e apid escala ions
in compu a ional cos s as he numbe o inpu a iables inc eases. Thus,
quasi- andom sampling can be ecommended as he bes app oach o da a
gene a ion in SimDec, as his simul aneously imp o es bo h he quan i a i e
and isual aspec s o he esul s.
5.4 Al e na i e isualiza ion ypes
Figu e2.11 shows ha he same in o ma ion depic ed in s acked his og ams
can also be isualized using box plo s. In he igu e, each scena io indica ed
p e iously wi h a speci ic-colou ed sub-dis ibu ion in he s acked his og am
is now ep esen ed by a sepa a e box in he box plo . Fu he mo e, a de ailed
acing indica es ha each box is loca ed p ecisely unde he co espondingly
colou ed sub-dis ibu ion o he his og am abo e.
Box plo s p o ide a use ul al e na i e unde he ollowing ci cums ances.
• Some o he scena ios con ain e y li le da a and a e no isible on he
his og am (see an example in Figu e2.12).
• The shape o he dis ibu ion is incon enien o his og am isualiza ions
( o example, he oo-skewed dis ibu ion in an exponen ial model).
• The da a sample is oo small, and he his og am is oo dissec ed
(e.g. Figu e2.10, bo om ow).
The colou -coding o sca e plo s acco ding o he alues o ano he inpu
ha e occasionally appea ed in he li e a u e (see, o example, Pala e al.,
2023). Howe e , a mul i a iable decomposi ion colou ing on he sca e plo
did no yield any in o ma i e isualiza ions. Sca e plo isualiza ions end
o be obscu ed by he o e lapping o he do s in he scena ios and by he need
o ead he e ec o one inpu a iable ela i e o he do s’ loca ion while
eading (an)o he s ela i e o hei colou s.
O e lay cha s ha e also been conside ed as an al e na i e isualiza ion
o ma and ha e been inco po a ed as an op ional display in a numbe o he
comme cial sp eadshee add-ins. The idea is analogous o he scena io po -
ayal in a s acked his og am, bu ins ead o he s acking, hese “scena ios”
a e o e layed ins ead. Howe e , his o e laying app oach possesses mul iple
d awbacks, including p oblems in isualizing mul iple scena ios, simul ane-
ously, which is an essen ial “mus -ha e” p e- equisi e p o ided by SimDec
(Kozlo a & Yeomans, 2020). Consequen ly, s acked his og ams (and box
DOI: 10.4324/9781003453789-4
This chap e has been made a ailable unde a CC-BY-NC-ND 4.0 license.
Abs ac
This chap e p o ides an o e iew o he collec ion o SimDec applica ion
cases in his book. Agene al summa y o case hemes, angles o analysis,
modelling choices, and pos -p ocessing p ac ices is p esen ed. The chap e
also in oduces se e al o he b igh es “aha momen s” gene a ed om Sim-
Dec, whe he he unco e ing o complex e ec s p e iously hidden wi hin
he models o he e i able “unshackling” o mindse s expe ienced by he
modele s hemsel es.
1 In oduc ion
The bigges con ibu ions o his book appea in he applica ion chap e s
used o demons a e how SimDec has been implemen ed in se e al, e y di -
e en con ex s. The sole goal o his chap e is o p e iew hese applica ions
in o de o p o ide he eade wi h an o e all imp ession o wha is o come
and/o o di ec hem o a ele an po ion o he book ha migh cap i a e
hei in e es . Howe e , i is no only he con ex ha he eade migh be
willing o conside . Independen ly o he con ex , some cases migh p esen a
ele an ma hema ical amewo k, o a cu ious app oach o sensi i i y analy-
sis, o an in iguing e ec ha he speci ic model ha bou s.
The chap e p oceeds by ou lining he a ious hemes and a ionale
behind each o he cases. Then i p o ides an o e iew o he modelling
app oaches, wi h a speci ic ocus on he model analysis p ac ices ha he
con ibu o s had been using p io o SimDec. Finally, i highligh s he mos
“peculia ” cha ac e is ics and indings obse ed ac oss he chap e s. These
aspec s include: (1) he appa en con en ional ine ia behind de e minis ic
hinking, (2) he ela i e ubiqui y o in e wined he e ogeneous e ec s exis -
ing wi hin e en he simples o models, and (3) how he ple ho a o no el
unc ionali y accompanying SimDec leads o a libe a ion o sensi i i y analy-
sis om i s p e ailing cus om o examining he e ec o inpu s on he ou -
pu s. The chap e concludes by summa izing how much mo e can be done
Chap e 3
O e iew o SimDec applica ions
Ma iia Kozlo a and Julian Sco Yeomans

O e iew o SimDec applica ions 61
analy ically wi h SimDec and p ojec ions o he au ho s’ u u e aspi a ions
o he me hod.
2 Themes
Thema ically, he applica ion chap e s ha e been pa i ioned in o ou dis inc
domains: (1) Business, (2) En i onmen , (3) Enginee ing, and (4) Beha iou al
Science (see Table2.1). Each chap e has been assigned an abb e ia ed “code
name” so ha i can be e e ed o concisely wi hin he body o he ex .
The Business domain encompasses cases de o ed o a ious ace s o
s a egic decision-making. The i s chap e in he domain builds on a clas-
sic co po a e inance example o in es men alua ion and expands i wi h
conside a ions o unce ain y and design o sui able manage ial ac ions
(4_In es ). Nex , he pe spec i e shi s om an in es o o a policymake
in a s udy examining public policy ins umen s o acili a ing p i a e–pub-
lic pa ne ships (5_Public). Fu he , he con ex shi s om egula o
cu ing-edge: an eme ging echnology o cons uc ion ia 3D p in ing is ana-
lyzed om he uni cos pe spec i e (6_Cons ). The Business domain con-
cludes wi h an audacious expe imen ha ansla es a quali a i e amewo k
(Ma ke Oppo uni y Na iga o ) in o a quan i a i e ool (7_Deep ech).
The En i onmen al domain consis s o h ee e y di e se applica ions. 8_
Ca bon p o ides a classic s udy o emissions o ming pa o he con en ious
deba e on whe he single-use o eusable p oduc s a e mo e sus ainable. 9_
MinEx examines a sequen ial decision-making model buil o mine al explo-
a ion which, by concen a ing on he model ideli y, shi s he ocus om
“how good is he decision” o “how good is he model”. 10_P2X ad ances
he conse a i e p ac ices o classic echno-economic analysis using an exam-
ple o powe - o-X echnology.
The Enginee ing domain conside s wo dis inc ly cap i a ing s udies.
11_Reliable in oduces a model o p edic a igue in he welded join s o
s eel s uc u es ha possess a e y peculia nonlinea beha iou ha he
au ho s had s uggled o con ey p io o SimDec. 12_Magne p esen s a
simula ion-based s udy o a compu a ionally in ensi e, h ee-laye ed model
o a supe conduc ing magne a CERN ha e ec i ely con as s he pe o -
mance o al e na i e magne design op ions.
F om he Beha iou al Science domain, he applica ions conclude wi h 13_
Choice. This chap e ma ks a depa u e om he ealm o o mal academic
and indus ial applica ions owa ds mo e pe sonal decision si ua ions – ang-
ing om ponde ing mo gage condi ions o choosing a coun y o esidence.
Wi hin his domain, SimDec is used o ans o m in ui ion and in e wined
pe sonal p e e ences in o a isual ep esen a ion o he di e en choice ou -
comes which, in many cases, led o new ealiza ions h ough he e aming
and/o edesigning o he speci ic decision si ua ion.
62 Ma iia Kozlo a and Julian Sco Yeomans
Table 3. 1 The o e iew o applica ion chap e s and hei hemes
)
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W)alze e al., 2024
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Moss e al., 2024)
ence
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Vini skaia e al., 2024
o e al., 2024
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Ka junen e al., 2024
Ahola e al., 2024)
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iou
-
-
.
e
gage,
y de
ellness
es men b
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.
.
elopmen oppo
.
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.
y
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.
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e
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ec
.
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Designing a p
Unde s
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S udying he e
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Communica ing complex nonlinea beha
o he model.
In
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language lea ning
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onmen
Enginee ing
iou al
Domain
Business
i En
Beha
Code
4_In es
5_Public
6_Cons
7_Deep ech
8_Ca bon
9_MinEx
10_P2X
11_Reliable
12_Magne
13_Choice
u ing
o
Deep ech ma k
oo p in
ion
e
s
uni ies
id mask
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o Co
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Public suppo
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u
alua ion
in as uc
s
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explo a ion
y
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X
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conduc
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eliabili
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w
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e sonal
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In
P
P
#
4
5
6
7
8
9
10
11
12
13
O e iew o SimDec applica ions 63
3 Models and p e-SimDec p ac ices
The cases in he book cap u e a wide a ie y o modelling con en ions, wi h
he au ho s mo e accus omed o hei di e en , discipline-speci ic, ollow-up
p ac ices o model analysis shown in Table3.2.
Mos o cases had been analyzed p e iously using p e-exis ing compu-
a ional models. The ela i ely simple models o cash lows (4_In es ,
5_Public, and 10_P2X) had all been implemen ed in Excel. Re lec ing
he na u e o i s ield, he a i hme ically s aigh o wa d li e cycle assess-
men (LCA) model (8_Ca bon) possesses hea y unde lying da a collec ion
equi emen s. Accoun ing o ma e ial and join p ope ies, 11_Reliable
builds upon a no el cus om model ha p edic s he a igue in welded join s
a be e han he mo e commonly used eg ession models. One ma hema i-
cally complex model in he book in ol ed s ochas ic op imiza ion by pa -
ially obse able Ma ko decision p ocess (POMDP) o a anging sequen ial
decisions (9_MinEx). The mos compu a ionally-in ensi e model in he book
is he one o e alua ing he magne ic and mechanical p ope ies o a com-
plica ed geome ic s uc u e app oxima ed wi h a ini e elemen me hod
(12_Magne ). Asingle e alua ion o his model ook 13 minu es on a e age
o sol e using a supe compu e .
Th ee applica ion chap e s did no possess any p e-exis ing models, so
ha hei en i e modelling exe cise was inspi ed solely by he capabili ies o
SimDec. The uni cos es ima ion model was buil wi hin 6_Cons when
i became clea ha unce ain y in echnology de elopmen , he e ec o
economies o scale, and a ia ions in many o he pa ame e s could be s ud-
ied simul aneously. The p oponen s o he 7_Deep ech case we e us a ed
by he exis ing quali a i e app oaches o unce ain y in deep ech en u es
and eage ly a ailed hemsel es o he oppo uni y o ans o m hei p ob-
lem in o a quan i a i e model. The esul ing mul i-c i e ia decision-making
amewo k con ibu ed a ha monic solu ion equi ing only minimal adjus -
men s o hei exis ing quali a i e ool. 13_Choice was inspi ed by he powe
o SimDec o sol e mo e “uncon en ional” applica ions and anscends he
expe iences o any single pe son. The unde lying models include (1) wo
basic unc ions (summa ion/wellness and powe /lea ning), (2) compu a ions
based on annui ies in wo o he cases (sa ings and mo gage), and (3) wo
simple mul i-c i e ia decision-making models (ca and coun y choice). 13_
Choice demons a es ha modelling “ egula ” li e choices wi h SimDec can
encou age mo e as u e beha iou (delayed g a i ica ion), while con e ing
decision-making in o decision-si ua ion-making.
All case con ibu o s had used o he model analysis p io o hei wo k
wi h SimDec, wi h some using a single analysis app oach and o he s employ-
ing se e al me hods (see Table3.2). One-a -a- ime sensi i i y analysis and
scena io analysis we e he mos common me hods employed by he con-
ibu o s. Hea maps and Mon e Ca lo simula ion had been conside ed
less equen ly. Ne e heless, nei he o hese ypes o analysis can c ea e
64 Ma iia Kozlo a and Julian Sco Yeomans
Table 3. 2 Modelling app oaches and p ac ices o case owne s p e-SimDec
MC§
–
–
–
Hea maps‡
–
–
–
s
ios†
ysi
Scena
–
–
–
.
odel anal
*AT
–
–
–
M
O
) e alua ion cases
al Ball
celx
ys
, EA
e
C
, Ma lab
ou ee o
wa
h
cel
cel, C
cel
cel
So
x
x
E
E
E
GaBi L
cel
x
x
x
E
Julia
E
Ma lab
ANSYS
celx
ew (
E
-magne ic models
o a
e a ied a he same ime.
c i e ia
.
o
y analysis
, mul i-
.
ain inpu s a
low model
ions
y analysis
ype
unc
odel
w modello
c i e ia decision-making
e al inpu s a a ime, bu only
Uni cos es ima ion
cle assessmen y
decision-making
M
Mul i-
Sequen ial decision-making
w model
a igue assessmen F
Mechanical and elec
e all unce
lo
Cash
-a- ime sensi i i
es changing se
-a -a- ime sensi i i
Cash
e c
o
Li
Cash
Simple
w
odel
ol
ed
-a
s
–
–
–
ically a
xi
M
o one
e
ands
e Chap
4_In es
5_Public
6_Cons
7_Deep ech
8_Ca bon
Reliable
9_MinEx
10_P2X
12_Magne
T s A
_11
13_Choice
* O
† Scena io analysis in
‡ Hea maps is p ac
§ MC is Mon e Ca lo simula ion, whe
O e iew o SimDec applica ions 65
a holis ic pic u e o he model beha iou (Kozlo a, Lo Piano, e al., 2024).
Be e oppo uni ies a ise when an analysis is pe o med i e a i ely o e di -
e en se s o model condi ions in he model (i.e. he 9 i e a ions o OAT in
5_Public and he 12 i e a ions in 11_Reliable). Howe e , disce ning any
app op ia e insigh s om so many sepa a e g aphs is a highly complica ed
exe cise, ma ched only by he complexi ies o communica ing such insigh s
o o he s akeholde s. No ably, pu suing a mo e concise sys ema ic solu ion
o his i e a i e exe cise es ablished he ini ial g oundwo k o c ea ing Sim-
Dec (Kozlo a e al., 2017).
Fo each case con ibu o , hei wo k wi h SimDec p o ided hei i s
exposu e o global sensi i i y analysis (GSA). This widesp ead “igno ance”
o GSA illus a es ano he mani es a ion wi hin mode n modelling cul u e.
Sal elli e al. (2019) had indica ed ha he neglec o GSA occu s due o i s
ela i e analy ical complexi y, combined wi h a pauci y o exposu e o i in
academic eaching.
4 SimDec pea ls
4.1 Away om de e minism
De e minis ic models possess se e al pi alls. Fi s ly, a modele ’s capaci y o
ind mis akes is limi ed. In gene al, only when he ou pu alues de ia e sig-
ni ican ly om hei expec ed ange can one de e mine ha an e o has c ep
in o he model. Sp eadshee models (which appea in se e al chap e s) a e
especially p one o hese mis akes. In sp eadshee s, a line o code can be ep-
esen ed ac oss mul iple cells, wi h each cell edi able sepa a ely (e.g. he same
equa ion migh be sp ead o e di e en ime pe iods). Whene e a single cell
in one “line” is edi ed, i does no become immedia ely appa en , because he
o mula is hidden and only isible when ha cell is selec ed. E en i he cell
is edi ed in en ionally, once he model is copied and adap ed o ano he case,
such speci ic edi s a e easily o go en and may con inue o dis o he esul s
o many cases in he u u e. Mul iple ins ances o such inhe i ed mis akes
ha e occu ed in he au ho s’ co po a e expe ience.
When applying SimDec o i s ime, se e al au ho s disco e ed model
inconsis ences ha had o be co ec ed p io o he o mal analysis. Se e al
addi ional nuances we e unco e ed. In he CERN model o 12_Magne , Sim-
Dec unco e ed a p e iously unno iced ela ionship pa e n be ween in e e -
ence, bladde p essu e, and he cable heigh , o which he au ho s ha e s ill
no ye been able o es ablish a physical explana ion. SimDec in o med he
model building p ocess o 7_Deep ech, in which he i s i e a ion con ained
lawed links ha only became appa en a e he SimDec isualiza ion. In
he 8_Ca bon case, SimDec iden i ied which inpu a iables and p ocess ele-
men s had negligible impo ance e en wi h ex eme nume ic anges, he eby
enabling he in es iga o s o adjus he di ec ion o hei bu densome da a

66 Ma iia Kozlo a and Julian Sco Yeomans
collec ion p ocess. Unde such ci cums ances, SimDec p o es o be an inc ed-
ibly con enien ool o assis ing wi h model building and es ing.
Secondly, de e minis ic models can ail o cap u e he a ying deg ees
o unce ain y in di e en model elemen s o compu a ional scena ios. Two
simila ly p o i able in es men oppo uni ies in he base case may be e y
di e en in e ms o hei isks and po en ial. Thus, hey would a ac a
di e en ype o in es o o , as in he case o 5_Public suppo , also en ail
a di e en deg ee o budge deple ion o he go e nmen . Simila ly, di -
e en 7_Deep ech oppo uni ies encompassed di e en le el isks. In he
mul i-c i e ia choice o coun y o esidence in 13_Choice, he di e en
wid h in he sco ing o coun y al e na i es was caused by he a ia ion o
cha ac e is ics wi hin a coun y and imp ecision o hei es ima es – bo h
adding an impo an slan o he decision-making si ua ion and p omp ing a
na owing o he scope.
Thi dly, basing decisions on de e minis ic ou pu s leads o unnel ision and
p ecludes s a egizing. Aclassic and widely used ule in in es men app aisal
is o “in es i NPV>0”. Chap e 4_In es c i icizes such an app oach and
shows how much mo e can be achie ed i a p ope unce ain y and sensi i -
i y analysis has been allowed o ake place. A igid in es men oppo uni y
con aining a lo o isks was ans o med in o an allu ing endea ou wi h
buil -in lexibili y o add ess he mos c i ical sou ce o p o i abili y unce -
ain y – demand. I was sugges ed ha he s a ic e m in es men app aisal
be subs i u ed wi h he mo e ac ionable and unce ain y-encompassing e m
in es men design.
In LCA s udies compa ing single-use and eusable p oduc s, he key
ques ion is an examina ion o he b eake en usage o he eusable p od-
uc . Beyond his poin , i becomes mo e sus ainable o u ilize he eusable
op ion a he han he single-use p oduc . Chap e 8_Ca bon emphasizes
he absu di y o such ques ions when he e a e so many dynamic elemen s
in ol ed. Ab eake en usage numbe is any hing bu de e minis ic, being, in
ac , nonlinea ly dependen on se e al ac o s in he p oduc li e cycle. Thus,
designing a policy based on a single b eake en numbe would c ea e an unde-
si able e ec unde all ci cums ances (excep , o cou se, o he ex emely
a e case when all ac o s jus happen o assume hei mean alues as in he
solu ion o he de e minis ic model). The deeply- oo ed cus om o policy-
making based on such c isply p ecise na a i es has been hea ily c i icized
by many hough -leade s (Sal elli e al., 2020; Sa age & Ma kowi z, 2009).
4.2 He e ogeneous e ec s
I is no simply anges ha ma e (i.e. how unce ain he ou pu alues
appea ); i is wha d i es hem ha makes he di e ence in decision-making.
This d i e cap u es he essence o SimDec – o be able o display he ou -
pu dis ibu ion and he mos in luen ial ac o s behind i on a single g aph.
O e iew o SimDec applica ions 67
Figu e 3.1 SimDec displaying nes ed he e ogeneous e ec , adop ed om 11_Reliable. (colou image is accessible ia he link)
Sou ce: Ahola e al. (2024).
Colou A B C
Low
Low 1
2
High 1
2
Medium
Low 1
-
High 1
-
High Low -
2
High -
2
68 Ma iia Kozlo a and Julian Sco Yeomans
The deg ee o ha in luence is he mos c i ical piece o in o ma ion o
decision-making. Kozlo a, Moss, e al. (2024) show ha he e ec s o inpu
a iables on he ou pu can be he e ogeneous: (1) one inpu can g adually
inc ease i s in luence on he ou pu in combina ion wi h he highe alues
o ano he inpu , (2) he di ec ion o in luence on he ou pu o one inpu
can be e e sed based upon di e en anges o ano he inpu , o (3) he e y
p esence o he in luence o one inpu on he ou pu can be condi ioned
o ano he inpu . In he p esence o he e ogeneous sys em beha iou s, he
decision-make mus ca e ully accoun o such case-speci ic beha iou in
de ising an e ec i e way o wa d.
The applica ions illus a e a ious cases o he e ogeneous e ec s.
11_Reliable showcases a beau i ully in ica e, nes ed he e ogeneous e ec
in ol ing h ee inpu a iables. To illus a e i , le us deno e he mos impo -
an inpu a iable as A, he second-mos impo an as B, he hi d-mos
impo an as C, and he ou pu a iable as Y (Figu e2.1).
Figu e3.1 displays a e y complex nes ed wha -i e ec . I A is in i s high
o medium s a e, he Y dis ibu ion is na ow, B does no play much ole,
and C has only one s a e p esen in each s a e o A. Con e sely, i A is in i s
low s a e, hen B has a lo i in luence on Y, and in his si ua ion, C a ec s
Y a lo i B is high and only mode a ely i B is low. All he a iables A, B,
and C a e con ollable in he decision con ex , and hei anges ep esen
possible a ia ion. So depending on which po ion o Y he decision-make
wan s o achie e, ei he only A should be manipula ed o medium o high
o A and B i bo h A and B a e low, o all h ee o hem i A is low and B is
high. The co esponding ou pu anges pa ially in e sec , so se e al o he
scena ios can lead o he same anges o Y, he eby c ea ing lexibili y o
he decision-make . The ichness o his iple join he e ogeneous e ec is so
comp ehensi e ha a decision ee was buil o suppo i s eadabili y.
Ano he example o complex he e ogeneous e ec s comes om he supe -
conduc ing 12_Magne model, whe e one o he ou pu s was a ec ed by wo
inpu a iables in a nes ed U-shaped ashion. Again, o illus a ion pu poses,
he con ex is skipped and he a iables ha e been enamed. In Figu e3.2,
one can obse e he U-shape o med by B in he s a es o A. Fo example,
in low A (blue shades), he high and low B esul s in medium alues o Y
(scena ios o he da kes and he ligh es shades o blue a e on op o each
o he ), bu he medium B leads o high and low alues o Y (o he blue sce-
na ios a e loca ed o he sides o he p e iously men ioned ones). While a
BY sca e plo alone ails o e eal his pa e n, SimDec eadily eases ou
a isualiza ion o he nes ed pa e n due o he decomposi ion based on wo
inpu a iables.
Some imes, he e ogenei y p esen s i sel based on de e mining which se s
o inpu a iables a ec which di e en po ions o he ou pu da a. Such
mul idimensionali y can mani es i sel in seemingly unexplained pa e ns on
he SimDec cha and equi es addi ional pa i ionings in he da a in o de o
O e iew o SimDec applica ions 69
ob ain a clea e pic u e (as was done in 8_Ca bon). Decomposing he en i e
da ase e ealed se e al peaks in he ou pu dis ibu ion (Figu e3.3, op).
Clea ly, some o he inpu a iables we e causing hese peaks, bu hei in lu-
ence was no appa en when he en i e da ase was analyzed. The au ho s
ixed he mos in luen ial a iable (mask ype) and examined he decom-
posi ion o only he single-use mask po ion o da a. The peaks s ill con-
ained se e al o e lapping colou s. The mos impo an inpu a iable in ha
Figu e 3.2 SimDec displaying nes ed U-shape e ec , adop ed om 12_Magne ( op
ow), and a sca e plo o he a iable ha causes i B o Y, bu whe e
he U-shape e ec is no isible. (colou image is accessible ia he link)
Sou ce: Pé ez e al. (2024).
Colou A B
Low
Low
Medium
High
Medium
Low
Medium
High
High
Low
Medium
High

DOI: 10.4324/9781003453789-6
This chap e has been made a ailable unde a CC-BY-NC-ND 4.0 license.
Abs ac
The assessmen o in es men p ojec s elies on plen i ul assump ions and com-
bines signi ican unce ain y wi h apidly accumula ing complexi y. Howe e ,
he ools commonly employed in his discipline a e a om ideal and o en ail
o cap u e he equi ed le el o complexi y o adequa ely assis he wide spec-
um o dispa a e needs o he a ious decision-make s. This chap e shows
how Simula ion Decomposi ion (SimDec) can imp o e in es men decisions
by shi ing he ocus om s a ic in es -o -no decision ules owa ds dynamic,
ac ionable p ojec design mindse s. A e in oducing cash low modelling, a
case model is analyzed using SimDec o illus a e he me hod’s con ex -speci ic
capabili ies. SimDec no only cap u es he unce ain ies and e eals which ac-
o s a e mos impo an bu also shows how di e en combina ions o hem
can shape he o e all p o i abili y o he p ojec . The chap e adop s a mul i-
s akeholde pe spec i e, in o mal language, and analogies o cap u e he sho -
alls o adi ional app oaches o in es men app aisal.
1 In oduc ion
Companies a e pe pe ually aced wi h he ine i able challenge o iden i ying
and implemen ing alue-c ea ing in es men p ojec s. I comes as no su p ise
ha inancial s i e (e en bank up cy) awai s hose who a e ine icien o com-
placen in his sea ch o bes p ojec s. On he o he hand, companies capable
o iden i ying good in es men oppo uni ies consis en ly ind hei o unes
g owing. The decisions ha need o be aken a e o en complex because o
he ine i able eliance on u u e es ima es and plen i ul assump ions. A bes ,
he discipline o inance supplies s uc u al amewo ks and decision ules
ha gene ally lead o mo e a ou able ou comes. The compu a ion o Ne
P esen Value (NPV) is widely ega ded as he mos es ablished in es men
app aisal echnique by p o iding a clea -cu decision ule o aluing in es -
men s. The esul o NPV compu a ion is no hing less han a “ o be o no o
Chap e 4
Unlocking ac ionabili y in
inancial modelling wi h
Simula ion Decomposi ion
Roman S epano , Ma iia Kozlo a, and
Julian Sco Yeomans
78 Roman S epano , Ma iia Kozlo a, and Julian Sco Yeomans
be” momen , con enien ly de e mined by he sign o a single numbe (Ross
e al., 2014). I he NPV yields a posi i e numbe , he p ojec is “ o be” and
should be accep ed. Con e sely, i he NPV is nega i e, he p ojec is ejec ed
as a “no o be”. The s aigh o wa d bina y na u e o he decision ule con-
ibu es o i s popula i y due o i s in insic cla i y and simplici y.
Howe e , his ex book NPV ule is no immune om igh ul c i i-
cism usually a ibu able o he s a ic na u e o i s unde lying assump ions.
Namely, a single numbe can ne e cap u e and con ey he ull complexi y
associa ed wi h u u e e en s. Ade e minis ic model can ne e success ully
inco po a e all o he mul iple unce ain ies and con lic ing s akeholde pe -
spec i es. No can i o e su icien insigh o in e ene and edesign any
gi en in es men p ojec . Much mo e ac ionable in o ma ion is needed o
ex ude an e icien business plan ha su icien ly in eg a es all o he di e se
complexi ies ha exis .
While he ask o building he mos de ailed NPV models is ele an
ac oss he boa d, he subsequen app oaches p esen ed below in o de
o use ulness and sophis ica ion, a e also equally impo an (G aham &
Ha ey, 2001; Ryan & Ryan, 2002). The mos pe asi e app oach is o
do no hing mo e han ely simply on he single alue o he NPV calcula-
ion. The o e simpli ica ion in his case is ecklessly p eca ious. The second
app oach is o epea he ini ial o e simpli ica ion absu di y h ee imes
unde he guise o a “scena io analysis”. The hi d app oach amoun s o
an i e a ed “wha -i ” unc ion (ap ly called one-a -a- ime sensi i i y (OAT)
analysis) ha gene a es da a o he c ea ion o a spide cha o a o -
nado diag am. This ep esen s a nex -le el ad ance in analy ical sophis-
ica ion because he a iables can be anked in o de o hei indi idual
e ec on p o i abili y and he mos impac ul ones can be iden i ied. The
ou h app oach is o employ Mon e Ca lo simula ion o examine he like-
lihoods and p obabili y dis ibu ions o he ou comes. Simula ion can be
conside ed an ad anced app oach as i exposes he dynamic links be ween
NPV and simul aneous changes in mul iple a iables. The ou pu s om
his me hod can be displayed as p obabili y dis ibu ions in he o m o a
his og am. One c i icism o he Mon e Ca lo app oach is ha i does no
p o ide a oadmap o wha exac ly needs o be done so ha he p ojec
emains con ined o he a ac i e po ions o i s dis ibu ion while a oid-
ing he nega i e isks. Howe e , his missing ac ionabili y ea u e has been
add essed by he ecen ly de eloped Simula ion Decomposi ion (SimDec)
app oach o Kozlo a and Yeomans (2022). SimDec shows p ecisely how
ce ain combina ions o inpu ac o s need o be changed in o de o s ee
he p ojec in o he desi able po ions o i s p o i abili y dis ibu ion. In
e ec , SimDec p omp s and answe s a se ies o ac ionable ques ions: Can
any hing be done? Wha ? Wha else can be done o achie e he same esul ?
How can i be done? By p o iding hese capabili ies, SimDec aises ye
ano he ques ion. How is i ha he en i e inancial wo ld is s ill sa is ied
Unlocking ac ionabili y in inancial modelling wi h SimDec 79
wi h only he i s ou app oaches o NPV modelling? Consequen ly, his
chap e discusses he nuances o cash low modelling and hen demons a es
how SimDec can elucida e ac ionable in es men oad maps by es ing i in
a numbe o inancial modelling si ua ions.
2 Nuances o cash low modelling
2.1 S akeholde pe spec i e on cash low modelling
The cash low pe spec i e on inancial modelling and decision-making can
be iewed me apho ically as essen ially no hing mo e han he c ea ion o a
mul ilaye ed cake. A i s glance, he cake appea s en i ely non- h ea ening
and s aigh o wa d o make. Howe e , a ho ough knowledge o he ecipe,
an unde s anding o he inhe en in e ac ion be ween he ing edien s, and
he unde lying mul iplici y o he di e en laye s all ep esen challenges
o he ask o success ul baking. Analogously, cash low analysis in ol es
combining nume ous ing edien s, such as e enues, cos s, capi al expendi-
u es, axes, e c., and hen sp eading hei planned in ol emen judiciously
h oughou he li e ime o he gi en in es men p ojec as i hey we e indi-
idual laye s o a inancial cake. Jus like an expe ienced bake , a CEO can
pu sue hei c ea i e ins inc s when combining ing edien s and laye s o
adop a mo e scien i ic app oach o in es men planning. Unde he mo e
echnical app oach, each componen mus ecei e due conside a ion in e ms
o balancing i s o e all con ibu ion and ne alue c ea ion wi h espec o
he o he ing edien s.
People ace in es men decisions all he ime. While some o hese deci-
sions may be mo e s aigh o wa d han o he s, hey all con ain an ine i able
complexi y associa ed wi h u u e unce ain ies. I espec i e o in es men
ype (e.g. he pu chase o a ixed income secu i y, an in es men in eal es a e,
cons uc ion o a p oduc ion acili y, a new se ice, e c.), all decisions can be
cap u ed by he ollowing gene ic NPV alua ion o mula:
CF
NPVI
0
n
=- +i
i (1)
i=1
()
1+
whe e I0 is he amoun o he in es men , CFi is he a e ax di e ence in all
e enues and cos s in he i h pe iod, n is he numbe o ime pe iods, is cos
o capi al, and NPV is he ne p esen alue.
2.1.1 T he pe spec i e o he co po a e inance expe
A pe son ained in inance will be ins an ly d awn o he discoun ac o
1
which o he n h yea is
()
1+ n (see equa ion1). This ac o needs o be
80 Roman S epano , Ma iia Kozlo a, and Julian Sco Yeomans
Figu e 4.1 Me apho o cash low modelling. (colou image is accessible ia he link)
Unlocking ac ionabili y in inancial modelling wi h SimDec 81
applied o all u u e cash lows because, o in es men e alua ion, hey
should be exp essed in e ms o oday’s money. Acco ding o con en ion, he
mos con enien ep esen a ion o he in es men p ojec is a sp eadshee o
he ollowing o ma (Table4.1).
Ha ing pe o med his ans o ma ion, one can ob ain es ima es co e-
sponding o he e ms o he equa ion and demons a e ha i one in es s
200,000 in e u n o an annual cash low o 12,000 and, in i e yea s’ ime,
sells he asse o a highe p ice o 210,000, no alue will be gene a ed, gi en
he 8% cos o capi al (see he las en y in he “Cumula i e DCF” ow,
which is also known as he NPV o he p ojec ). This numbe is no encou -
aging, gi en ha a his s age no main enance, ax, and o he expenses ha e
been ac o ed in o he e alua ion. A able no oo dissimila o he p eceding
one, bu ypically displayed in Excel, is a common ep esen a ion o ma o
equa ion (1) by a co po a e inance expe .
2.1.2 The pe spec i e o he accoun an
The main ocus o an accoun an is he p oduc ion o h ee inancial s a e-
men s: he income s a emen , he cash low s a emen , and he balance shee .
In combina ion, hese s a emen s a e designed o po ay he o e all inancial
posi ion o a company in a ue and ai way. The e o e, he p eceding sce-
na io would be iewed h ough he lens o hei co esponding accoun ing
s anda ds. Accoun an s and in es men app aise s “ alk money” in di e en
e ms, and i is impo an o hem o know he ansla ion ules (see model-
ling aps in Sec ions2.2 and 2.3). Fu he mo e, accoun an s can p o ide
ex ensi e ad ice on a ious axa ion schemes (see Sec ion4.1) and o he
nuances ha migh po en ially imp o e he ou look o a p ojec (Fazza i
e al., 1988).
2.1.3 The pe spec i e o he budge holde
In p inciple, budge holde s ough o be conce ned p ima ily wi h he ea-
sibili y o ini ial in es men s, he quali y o he unde lying asse s, and hei
Table 4.1 Classic cash low model a angemen in a sp eadshee en i onmen
Yea (n) 012345
Capi al –200,000 210,000
expendi u e
CF 12,000 12,000 12,000 12,000 12,000
Ne CF –200,000 12,000 12,000 12,000 12,000 222,000
Discoun ac o 1.00 0.93 0.86 0.79 0.74 0.68
DCF –200,000 11,111 10,288 9,526 8,820 151,089
Cumula i e –200,000 –188,889 –178,601 –169,075 –160,254 –9,165
DCF

82 Roman S epano , Ma iia Kozlo a, and Julian Sco Yeomans
eco e able alue a he end o he p ojec . Since in es men s a e equen ly
made up on as a p econdi ion o gene a ing u u e cash lows, he e is
a na u al emp a ion o ecei e he bene i s as ea ly as possible and incu
he cos s as la e as easible o e he ime ho izon. Howe e , he eali y o
he budge holde s’ posi ion wi hin many o ganiza ions may be di e en .
Alloca ed budge s gene ally need o be ealized wi hin igh ly cons ained
pe iods, and hus, in es men s need o be made a he ea lies possible oppo -
uni y in he p ojec cycle. O he wise, he money si s idle wi hou gene a ing
due e u ns, an o ganiza ion is exposed o po en ially highe axes, o in
cases o public ins i u ions, he en i e budge alloca ions may be d as ically
educed o wi hd awn comple ely.
2.1.4 The pe spec i e o he bank manage
Bank manage s a e na u ally conse a i e since hei p ima y conce n is loan
epaymen in acco dance wi h hei p e-speci ied epaymen schedule. Con-
sequen ly, e alua ions o in es men p ojec s a e pe o med on he basis o
pessimis ic cash lows, longe payback pe iods, and highe cos o capi al
( e lec ing mo e isks) (equa ion (1)). An addi ional conce n is o ensu e ha
he lending a e (which cons i u es he p ima y sou ce o in e es income) is
app op ia ely ma ched o he p oposed in es men p ojec unde he p e ail-
ing economic condi ions.
2.1.5 The pe spec i e o he isk con olle
The isk con olle mus iden i y all possible p ojec isks and measu e
hem in e ms o se e i y o impac and p obabili y o occu ence; his is a
well-known app oach called a isk ma ix. The epo s con aining he isk
ma ix look sophis ica ed and ce ainly con ibu e o a “ eel good” ac o
o mos execu i es. Howe e , i has been shown ha he subjec i e na u e
unde lying his exe cise has li le o do wi h he ac ual p obabili ies o isk
occu ence o hei mone a y damage o he company. Adop ion o mo e
quan i a i e me hods has been s ongly ad oca ed o his c ucial co po a e
unc ion (Hubba d, 2020). This, howe e , equi es addi ional e aining o
he associa ed pe sonnel (Sido enko, 2023).
2.1.6 The pe spec i e o he enginee
Enginee s end o ocus on he p ac icali ies o p ojec implemen a ion as
opposed o any unde lying cos and cash low aspec s. This inancial dis-
connec o en places hem a logge heads wi h inancie s du ing he p ojec
design phase. The challenging job o an in es men commi ee is o balance
a budge ha ensu es ha he enginee s ecei e inancial esou ces su icien
o achie e hei p ojec - ela ed speci ica ions. Lean manu ac u ing (Zhu &
Lin, 2017) and Design o Manu ac u ing and Assembly (DFMA) (Lu e al.,
Unlocking ac ionabili y in inancial modelling wi h SimDec 83
2021) a e inno a i e examples o how on unning o ganiza ions ha e
b idged his gap.
2.1.7 The pe spec i e o he CEO
The ole o he CEO is o iew he in es men p ojec wi hou being o e -
whelmed by he mul iplici y o de ails, pe spec i es, and nuances o he
in es men p ojec . Thei mos alued skill is he holis ic abili y o simul ane-
ously pa se a la ge quan i y o in e disciplina y and in e depa men al in o -
ma ion ha may be incomple e, biased, and con adic o y (Mi chell e al.,
2016). F om a inancial pe spec i e, he pinnacle o such simpli ica ion is
equen ly he single NPV numbe , which ac s as an accep / ejec c i e ion o
he gi en in es men p ojec .
2.2 Modelling ap #1: ac ual s accoun ing cash lows
In p ac ice, co po a ions ep esen he s uc u e o cash lows in a model in
wo di e en ways: (1) ac ual and (2) accoun ing. In a simpli ied o m, ac ual
cash lows (Figu e4.2) include in es men cos (o en e e ed o as CAPEX),
ope a ing p o i (calcula ed by deduc ing ope a ional expenses (OPEX) om
e enues), and axes (compu ed on he basis o accoun ing cash lows). F ee
cash low (FCF) is he summa ion o hese e ms which o ms he basis o
compu ing nume ous p o i abili y indica o s.
Ea nings be o e in e es and axes (EBIT) ep esen he accoun ing alue
used o de e mine he ax base (i.e. he alue ha is hen mul iplied by he ax
a e). EBIT employs accoun ing con en ions ha con e he ini ial in es -
men cos in o a dep ecia ion s eam ha alloca es he cos s h oughou
Figu e 4.2 In e link be ween wo possible s uc u es o a cash low model: ac ual
cash lows (le ) e sus accoun ing cash lows ( igh ). (colou image is
accessible ia he link)
84 Roman S epano , Ma iia Kozlo a, and Julian Sco Yeomans
he li espan o he p ojec . To calcula e ee cash low om EBIT, he ini ial
in es men cos needs o be included (wi h a minus sign) and dep ecia ion
added back (wi h a plus sign). This s ep o adding dep ecia ion (a e p e i-
ously deduc ing i om EBITDA o ge EBIT) is o en a sou ce o con usion
o modelle s unawa e ha dep ecia ion is no a eal cash low i em. This
con usion is easily a oidable i cash lows a e compu ed using only ac ual
lows: in es men cos plus ope a ing p o i minus axes.
2.3 Modelling ap #2: eal s nominal, and cons an s
cu en
Ano he con usion o en a ises in main aining consis ency be ween cash lows
and in e es a es (cos o capi al) when adjus ing he calcula ion o accoun
o in la ion. Figu e4.3 summa izes all possible e ms o he wo ypes o
cash lows and in e es a es. Cash lows and in e es a es need o be exp essed
in he same e ms and ei he adjus ed o in la ion (equi alen ly – excluding
in la ion e ec /cons an dolla s/ eal e ms cash lows) wi h eal in e es a es
o including in la ion (equi alen ly – cu en dolla s/nominal e ms cash
lows) wi h nominal in e es a es.
In e es a es a e no mally epo ed in nominal e ms. Thus, he discoun
a e, usually compu ed as weigh ed a e age o nominal equi y a e and
Figu e 4.3 The connec ion be ween cons an /cu en dolla and eal/nominal in e es a e.
(colou image is accessible ia he link)
Unlocking ac ionabili y in inancial modelling wi h SimDec 85
nominal deb a e, is also nominal. Following he ins uc ion o Figu e4.3,
in o de o s ay consis en , nominal discoun a e should be used wi h cash
lows ha include in la ion. Al e na i ely, he discoun a e should be con-
e ed in o he eal a e, and hen i can be used wi h cash lows ha exclude
in la ion. Bo h ways o compu a ion would esul in he same alue o NPV
in he absence o axes and o he complexi ies (Kozlo a, 2019).
3 SimDec analysis
In his sec ion, SimDec is used o isualize he impac o changes in axa ion,
demand, and p icing on he case model’s o e all p o i abili y. The SimDec
app oach ex ends he unce ain y analysis o classic Mon e Ca lo simula ion
(Me opolis & Ulam, 1949) and simul aneously conduc s a global sensi i i y
analysis (Bo gono o & Pecca i, 2006). The main analysis is pe o med using
he SimDec Excel empla e (Simula ion Decomposi ion, 2023a; Kozlo a &
Yeomans, 2022), while addi ional SimDec Ma lab sc ip s ha e been used o
compu e he sensi i i y indices (Simula ion Decomposi ion, 2023b; Kozlo a
e al., 2024). The no a ion o highligh ing names o a iables wi h bold i alic
and hei s a es wi h i alic is adop ed hence o h.
3.1 Compu a ional model and nume ic assump ions
The classic cash low app oach (Figu e4.1 and equa ion (1)) o modelling in es -
men p o i abili y. The subsequen assump ions a e used o he s ylized model,
which a e u he modi ied o each case condi ion (see Sec ion4) (Table4.2).
The cash low model is simula ed in he nex sec ion unde di e en unce -
ain y assump ions speci ic o each ci cums ance conside ed (Sec ions3.2–3.4).
The simula ion da a is u he used o he sensi i i y analysis wi h SimDec.
Table 4.2 Nume ic assump ions o he s ylized cash low model
Inpu a iable Base case alue
In es men , K$ 30,000
Resale alue 3,000
P ice, K$/pcs 2.5
Volume, pcs/yea 20,000
Fixed cos s, K$/yea 9,000
Va iable cos s, K$/pcs 1.3
O he cos s, K$/yea 5,000
W i ing down allowance 18%
Income ax 25%
Re enue in la ion 3%
Cos in la ion 4%
Cos o capi al ( eal) 5%
Cos o capi al (nominal) 9%
92 Roman S epano , Ma iia Kozlo a, and Julian Sco Yeomans
Re e ences
Bo gono o, E., & Pecca i, L. (2006). Unce ain y and global sensi i i y analysis in he
e alua ion o in es men p ojec s. In e na ional Jou nal o P oduc ion Economics,
104(1), 62–73.
Fazza i, S., Hubba d, R. G., & Pe e sen, B. (1988). In es men , inancing decisions,
and ax policy. The Ame ican Economic Re iew, 78(2), 200–205.
G aham, J. R., & Ha ey, C. R. (2001). The heo y and p ac ice o co po a e inance:
E idence om he ield. Jou nal o Financial Economics, 60(2–3), 187–243.
Hubba d, D. W. (2020). The ailu e o isk managemen : Why i ’s b oken and how o
ix i . John Wiley & Sons.
Kozlo a, M. (2019). Real e sus nominal cash lows. In es men and business analy-
sis wi h excel. h ps://you u.be/E e9jpFxFds?si=11MZd2jVq5elyp84
Kozlo a, M., Moss, R. J., Yeomans, J. S., & Cae s, J. (2024). Unco e ing he e o-
geneous e ec s in compu a ional models o sus ainable decision-making. En i-
onmen al Modelling & So wa e, 171, 105898. h ps://doi.o g/10.1016/j.
en so .2023.105898
Kozlo a, M., & Yeomans, J. S. (2022). Mon e Ca lo enhancemen ia Simula ion
Decomposi ion: A “mus -ha e” inclusion o many disciplines. INFORMS T ans-
ac ions on Educa ion, 22(3), 147–159.
Lu, W., Tan, T., Xu, J., Wang, J., Chen, K., Gao, S., & Xue, F. (2021). Design o
manu ac u e and assembly (D MA) in cons uc ion: The old and he new. A chi ec-
u al Enginee ing and Design Managemen , 17(1–2), 77–91.
Me opolis, N., & Ulam, S. (1949). The Mon e Ca lo me hod. Jou nal o he Ame i-
can S a is ical Associa ion, 44(247), 335–341.
Mi chell, R. K., Wea e , G. R., Agle, B. R., Bailey, A. D., & Ca lson, J. (2016).
S akeholde agency and social wel a e: Plu alism and decision making in he
mul i-objec i e co po a ion. Academy o Managemen Re iew, 41(2), 252–275.
Ross, S. A., Wes e ield, R., & Jo dan, B. D. (2014). Fundamen als o co po a e
inance. I win.
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How ha e hings changed. Jou nal o Business and Managemen , 8(4), 355–364.
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in non- inancial companies, aining and consul ing se ices. Risk-Academy Blog.
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Manu ac u ing Technology Managemen , 28(4), 422–437.

DOI: 10.4324/9781003453789-7
This chap e has been made a ailable unde a CC-BY-NC-ND 4.0 license.
Chap e 5
Unpacking he ole o
con ex ual ac o s in public
suppo o mi iga ing
e enue isk in public–p i a e
pa ne ship p ojec s
Robe a Pelleg ino, Ma iia Kozlo a, Luiz B andao,
and Julian Sco Yeomans
Abs ac
Re enue isk due o demand luc ua ions is one o he majo issues a ec -
ing public in as uc u e p ojec s (building b idges, ai po s, schools, e c.).
I becomes much mo e c i ical when p i a e pa ne s ha e been in ol ed
in he cons uc ion, inancing, and ope a ion o he in as uc u e p ojec s,
as i en e s in o he ealm o Public–P i a e Pa ne ships (PPP). In PPP p o-
jec s, e enue isk impac s he p ojec p o i abili y o he p i a e in es o .
To a ac p i a e inancing in PPP in as uc u e p ojec s, go e nmen s mus
equen ly include supplemen a y public gua an ees o mi iga e his isk.
Howe e , he impac on PPP p ojec s is o en di icul o es ima e, since i
depends bo h on unce ain y and on he ac ual exe cise o he gua an ee. All
hese challenges, along wi h he in insic cha ac e is ic o PPP p ojec s being
pa ne ships among di e en ac o s las ing a long pe iod, complica e he
choice o which o m o gua an ee is mo e sui able o ensu ing p ojec suc-
cess. Such a choice is also s ongly a ec ed by con ex ual ac o s and p ojec
cha ac e is ics. In his chap e , we employ he hyb id sensi i i y–unce ain y
analysis echnique, Simula ion Decomposi ion (SimDec), o in es iga e how
con ex ual ac o s and p ojec cha ac e is ics a ec he choice o he op imal
o m o public subsidy o e enue isk mi iga ion. To his aim, we ocus on
he case o an I alian ai po . Th ough his eal case, we p o ide use ul guide-
lines ha can be used by he go e nmen in he selec ion o public subsidies
o mi iga e e enue isk in PPP p ojec s.
1 In oduc ion
Public–P i a e Pa ne ships (PPP) ha e been used inc easingly o deli e pub-
lic in as uc u e h ough he in ol emen o p i a e expe ise and inancing
in public en e p ise (I ina & Ve onica, 2022). The majo challenges p e en -
ing p i a e pa icipa ion a e equen ly linked o he nume ous unce ain ies
94 Robe a Pelleg ino e al.
which cha ac e ize hese p ojec s. These unce ain y sho comings can
s ongly impede he long- e m p o i abili y o p i a e en i ies (Osei-Kyei &
Chan, 2015). To o e come hese issues and o con inue o a ac ex e nal
p i a e inancing, go e nmen s o en inco po a e public suppo s in ended o
sha e isks wi h he p i a e en i ies (such as e enue isk), he eby gua an ee-
ing an adequa e e u n o he po en ial pa icipan s. While such isk sociali-
za ion incen i es a e equen ly used in PPP p ojec s, assessing hei wo h is
no an easy ask (Pelleg ino, 2021; Hemming, 2006). Al hough he alue o
he gua an ee is no p ese , he payo is exe cised whene e he unce ain y
h esholds igge ing he gua an eed payou condi ions a e me .
Unde a Minimum Re enue Gua an ee (MRG), he go e nmen ag ees o
co e any sho all o e enue up o some p ede ined h eshold. The exac
amoun o be paid o he p i a e en i y canno be de e mined wi h ce -
ain y, a p io i (Ca bona a e al., 2014a, 2014b; Ca bona a and Pelleg ino,
2018). Consequen ly, i is impe a i e ha hese gua an ees be co ec ly
designed so ha all isks a e sha ed mu ually be ween bo h pa ies and
he go e nmen is no o e whelmed by he iscal liabili ies. Fo example,
an excessi e o e paymen occu ed in he case o he Sal ado –I apa ica
b idge sys em when disp opo iona ely gene ous public gua an ees esul ed
in he elimina ion o all isk o he p i a e in es o (San ’Anna e al., 2022).
Con e sely, p i a e en i ies can incu losses when he isk gua an ees a e
no designed p ope ly o su icien ly p o ec hei in e es s. The Leas P e-
sen Value o Re enue (LPVR), which does no in ol e go e nmen pay-
ou s, ep esen s ano he ype o isk-mi iga ing mechanism in which he
go e nmen consen s o ex ending he concession pe iod o ensu e a mini-
mum le el o e u n. The exac ex ension pe iod is no known, a p io i, bu
depends on he e olu ion o e enues (Engel e al., 2001; Xiong & Zhang,
2014; Pelleg ino e al., 2013).
Hence, he issue o p ope choice o public suppo s is c ucial o ensu ing
PPP p ojec s’ success, o bo h public and p i a e pa ies. Al hough se e al
s udies ha e ocused on iden i ying speci ic models o ins umen s o pub-
lic suppo s (B andao & Sa ai a, 2008; Almassi e al., 2013; Ca bona a
e al., 2014b; Ca bona a & Pelleg ino, 2018), only a ew ha e explo ed
he ac ual assessmen and benchma king o he di e en ypes o gua an-
ees (Pelleg ino, 2021; Song e al., 2018; Liu e al., 2017). Pelleg ino (2021)
de eloped a model o compa e gua an ees and o selec he suppo mecha-
nism which op imizes bo h pa ies’ in e es s acco ding o a win–win p inci-
ple. Pelleg ino (2021) concluded ha he choices we e based upon bo h (1)
endogenous ac o s ela ed o he speci ic p ojec o design o he gua an ee
and (2) exogenous ac o s ela ed o he con ex in which he p ojec s a e
de eloped. All sensi i i y analyses pe o med wi hin hese exis ing s udies
ha e examined how each indi idual ac o , aken one-a - ime, in luences he
o e all choice.
Recen esea ch has unde sco ed how impe a i e i is in decision-making
o conside he join beha iou o all ac o s, simul aneously, in o de o
Con ex ual ac o s in mi iga ing e enue isk in PPP p ojec s 95
cap u e how he in e ac ion o di e en inpu ac o s a ec s ou comes
(Kozlo a, Moss, e al , 2024) To ill his gap in he PPP con ex , his chap-
e employs he hyb id sensi i i y–unce ain y analysis echnique, Simula ion
Decomposi ion (SimDec), o examine how he di e en con ex ual ac o s
and p ojec cha ac e is ics concu en ly impac he choice o public subsidy
in PPP e enue isk mi iga ion SimDec has been success ully used p e iously
o se e al ene gy policy con ex s, including enewable ene gy policy design
(Kozlo a e al , 2017), s udying in e ac ion o in es men subsidies and ca -
bon ading (Kozlo a & Yeomans, 2019), and examining he e ec s o bio-
uel suppo ins umen s (Ruponen e al , 2021)
The emainde o he chap e is s uc u ed in he ollowing way Sec ion2
ou lines he compu a ional model o he o e all PPP decision p ocess The
unde lying compu a ional model is desc ibed, including he de ails on he
h ee conside ed suppo ypes (Sec ion2 1); he a ious inpu assump ions
a e desc ibed (Sec ion 2 2); and he ea lie conduc ed sensi i i y analysis
esul s a e eplica ed (Sec ion2 3) Sec ion3 in oduces he SimDec analysis
se -up and he esul s gene a ed Finally, Sec ion4 concludes wi h a discus-
sion on whe he he SimDec analysis has ac ually con ibu ed any signi ican
addi ional insigh in o he mi iga ion p ocess o e enue isk in PPP p ojec s
2 Compu a ional model
2.1 Modelling public suppo
The model o assess and benchma k di e en public suppo s o mi iga e
e enue isk has been designed in o de o mo e equi ably sa is y he in e -
es s o bo h he p i a e and public pa ne s (Pelleg ino, 2021) Fo he p i-
a e sec o , he in en is o enable hem o eco e hei ini ial in es men s
Fo he public sec o , he objec i e is o ensu e ha he in es men s a e
complian wi h accoun ing speci ica ions ega ding e enue gua an ees and
ha hese gua an ee do no p o e o be an one ous bu den on socie y To
achie e hese objec i es, a wo-s age economic app oach has been adop ed
(Pelleg ino, 2021)
In he i s s age, he ne bene i o each pa y is calcula ed using he Ne
P esen Value (NPV) NPV is he di e ence be ween he discoun ed alue o
cash in lows and he discoun ed alue o cash ou lows o p ojec The ne
bene i o he p i a e en i y is compu ed by equa ion (1), while he ne ben-
e i o he public sec o is de e mined using equa ion (2)
NPVI CF
V
CC
Tc
C
R
C
T
cons C
=− ++
()
++
()
=+
1 11
(1)
NPVCF
CF
V
G
G
Tc
G
G
Tc
F
G
R
G
TC
=+
()
++
()
−+
()
−
==+
01
11
1
(2)
96 Robe a Pelleg ino e al.
whe e:
• T
C is he ac ual concession pe iod
• C is he discoun a e o he p i a e en i y
• cons is he cons uc ion pe iod
I
• I= cons
C =0
()
1+ is he p i a e en i y’s in es men in he in as uc-
u e, wi h I being equal o he in es men (capi al expendi u es) in yea
• CF
=−ROC is he cash low in yea , wi h R being he e enue
in yea , OC being he ope a ional expendi u es (including cos o main e-
nance) in yea Cash low is ecei ed by he p i a e en i y du ing he conces-
sion pe iod The in as uc u e is ans e ed o he public en i y a he end o
he concession pe iod Consequen ly, cash low is ecei ed by he public om
he ime o ans e un il he end o he p ojec li e
• VR is he esidual alue o he in as uc u e in he amoun ha he
public pa y ag ees o pay when he in as uc u e is e u ned o he
go e nmen
• CFG
is he cash low ecei ed by he go e nmen du ing he man-
agemen o he p ojec by he p i a e sec o , such as concession ees,
p o i -sha ing, e c
• G is he amoun o gua an ee (de e mined in he nex subsec ions)
• G is he discoun a e o he go e nmen
Acco ding o he NPV c i e ion, he p i a e pa y is sa is ied when NPV is
posi i e (equa ion (3)); he e o e, he isk ha he p i a e en i y is no sa is-
ied is he p obabili y ha NPVC<0 (equa ion (4))
NPVC 0 (3)
P i a eEn i ys’ isk =<P ob
()
NPVC0 (4)
The go e nmen is sa is ied when he alue o he gua an ee G (i e he cos
o he go e nmen ) is economically sus ainable and poli ically accep able
Namely, i should be less han a ixed amoun in o de o be complian
wi h he accoun ing s anda ds speci ying ea men gua an ees (5)
G (5)
The es ima ion o depends upon he c i e ion adop ed in he speci ic
coun y Fo example, he Eu os a ule es ablishes ha asse s should be con-
side ed on-balance shee when he ne cos o gua an ees co e s mo e han
he 50% o he capi al in es men cos s In his case, acco ding o his ule
( =0 5IC), equa ion (5) exp esses he condi ion o sa is ying he public sec-
o ’s iscal managemen in e es s and allows o se ing a le el o G ha keeps
he in es men o -balance shee
Con ex ual ac o s in mi iga ing e enue isk in PPP p ojec s 97
The isk o he public sec o may be exp essed as he p obabili y ha i s NPV
(conside ing he alue o eleased gua an ee) is lowe han 0 (equa ion (6))
Go e nmen ’s iskP=< obN
()
PVG0 (6)
Once he in e es s o he wo pa ies a e compu ed, he public suppo s
a e benchma ked and chosen in he second s age To be complian wi h he
win–win condi ion, he o m o gua an ee minimizing he di e ence be ween
he ne p o i s (NPV) gained by he con ac ual pa ies and he isk bo ne by
he wo pa ies is selec ed
The ollowing sec ions illus a e how o calcula e he e ec o h ee sup-
po ins umen s on PPP p ojec s and he co esponding logic o selec ing
he op imal one Mon e Ca lo simula ion is employed o accoun o he
a iabili y o ac o s a ec ed by he con ac ing unce ain y Bo h his o ical
da a and expe opinion a e used o de ine he unce ain y o di e en inpu
dis ibu ions Mon e Ca lo simula ions p o ide “mo e ealis ic” p obabilis-
ic ep esen a ions o he ou pu s, in con as o he mo e commonly used,
single “de e minis ic” alues ob ained h ough mo e adi ional echniques
2.1.1 Minimum e enue gua an ee (MRG)
Unde he MRG, he go e nmen ag ees o pay he p i a e company all pos-
sible e enue sho alls up o some p ede ined le el (Rg) MRGs mi iga e he
inhe en isks and make hese in es men ypes a ac i e o p i a e in es o s
The e enue R ecei ed by he p i a e company while ope a ing he in a-
s uc u e is calcula ed by equa ion (7)
Rm
=ax
()
PR ,Rg (7)
whe e PR is he p ojec e enue in yea wi hou gua an ee
The o al amoun o gua an ee G is de e mined by equa ion (8)
maxR
()
−PR
GTc
g
;0
= (8)
=cons
()
1+ G
whe e he ac ual concession pe iod T
C coincides wi h he con ac ual one
TC, ha is, TT
CC
=
2.1.2 L eas p esen alue o e enue (LPVR)
Unde an LPVR schema, he go e nmen ag ees o ex end he concession
pe iod when he p esen alue o e enues equals he minimum p ede ined
h eshold (LPVR) in equa ion (9)

98 Robe a Pelleg ino e al.
Tc
C R
T
LPVR wi h TT
>
=cons
()
1+CC
(9)
G
whe e he ac ual e enue coincides wi h he p ojec e enue, ha is, R =PR
I equa ion (9) is sa is ied o TT
CC
, hen he concession will end a TC as
con ac ually es ablished Unde his schema, he gua an ee is he alue o he
cash lows enounced by he go e nmen due o he lexible e m con ac , as
in equa ion (10)
CF
G= Tc
i T
C > TC (10)
T=c
()
1+ G
2.1.3 P ice cap egula ion (PCR)
The p ice cap egula ion (PCR) p o ides a mechanism aimed a p e en ing
monopolis ic in as uc u e i ms om ea ning excessi e e u ns Unde such
a angemen s, he p i a e company mus deli e a se ice o p oduc subjec
o a maximum p ice ceiling ha is nego ia ed wi h he go e nmen I he
i m’s cos s all below his ceiling, he i m ea ns a p o i while socie y expe i-
ences a “loss” O he wise, when he i m’s cos s ise abo e he p ice ceiling,
he p ice does no exceed he limi and he i m will be penalized o he ine -
iciency (Pelleg ino, 2021; Pelleg ino e al , 2011)
Acco ding o PCR, he p i a e company de elops an in es men plan ha
is sha ed wi h he egula o y agency The expec ed annual dep ecia ion is
dependen upon he p og ammed in es men s, he expec ed ope a ing cos s
o managing he in as uc u e, and he expec ed p o i s Based on hese
da a, he egula o y agency es ima es a “calcula ed” ee o each yea , which
is he ee o ecouping ope a ing cos s and dep ecia ion o new in es men s
This app oach ensu es an adequa e e u n on in es men s, as calcula ed in
equa ion (11)
VT
exp C
=
()
CA++RC
(11)
whe e CC ep esen s he calcula ed ope a ing cos s (calcula ed opex ),
including main enance cos ; AC is he calcula ed dep ecia ion acco ding o
he in es men plan; RC is he calcula ed emune a ion as a pe cen age (se by
he egula o a p io i) o he in es ed capi al; and Vexp is he expec ed alue
a o he p ojec ed a ic olume
Gi en “ eal-wo ld” unce ain ies, he ac ual si ua ion may be di e en
om he expec ed (o calcula ed) one, ei he in e ms o ac ual cos o in
Con ex ual ac o s in mi iga ing e enue isk in PPP p ojec s 99
e ms o a ic olume I he ac ual cos s
()
CA++Rac ual
a e lowe han he
calcula ed ones, he ex a p o i will be sha ed be ween he public and p i a e
sec o s O he wise, i ep esen s a loss o he p i a e i m
I w is he p ea anged pe cen age o ex a p o i ecognized
by he egula o y agency, he ex a p o i o he public is de e mined in
equa ion (12)
w
P o i sha ing
=
()
CC
C−ac ual
(12)
100
whe e CC
a e he calcula ed ope a ing cos s, and Cac ual
a e he ac ual
ope a ing cos s Addi ionally, pa e ns may de ia e om ini ial p ojec ions,
p o iding excess e enues o he p i a e i m i hey u n ou o be highe
han expec ed
2.2 Case bac kg ound and nume ic assump ions
To illus a e he use ulness o he PPP model de eloped in he p e ious sec-
ion, we applied i o he case o an I alian ai po The p ojec is be ween he
Na ional Ci il A ia ion Au ho i y (ENAC)1 and a p i a e con ac o manag-
ing he ai po
F om an ope a ions pe spec i e, he e enues a ise om bo h a ia ion
and non-a ia ion ac i i ies A ia ion e enues a e di ec ly a ibu able o any
ae onau ically- ela ed ac i i ies ca ied ou a he ai po , including ai po
cha ges, secu i y se ices, cen alized in as uc u es, and o he ela ed ac i -
i ies Non-a ia ion e enues include comme cial ac i i ies (sub-concessions,
u ili ies, pa king, ad e ising), eal es a e, and o he hi d-pa y ancilla y
ac i i ies The ope a ional cos s consis o se ice cos s, pe sonnel cos s, and
consump ions cos s
The es ima ion o he ope a ing e enues and cos s has been based on
his o ical da a and expe opinion The inpu a iables a e ca ego ized in o
de e minis ic and unce ain a iables
The de e minis ic a iables a e:
• The concession pe iod co esponds o he ime when he in as uc u e is
ope a ed by he p i a e and is ixed a 33yea s
• The p ojec li e ime co e s he en i e li espan o he p ojec and is se a
67yea s
• The o al in es men cos s o e 33yea s is 11,470M€
• The discoun a e is assumed o be equal o he isk- ee a e o bo h pa -
ies ( G= C=5%)
100 Robe a Pelleg ino e al.
Table 5.1 Unce ain y assump ions o inpu a iables
G oup Inpu andom a iables P obabili y Sou ce
dis ibu ion1,2
Re enues Real es a e subconcession, € PERT(50, 56, 60) Expe
Comme cial subconcession, € PERT(96, 99, 105) opinion
Pa king (in subconcession), € U(9.73, 11.90)
Ad e isemen , € U(11, 15)
O he e enues om a ia ion U(27, 34)
ac i i ies, €
O he e enues om non- U(16, 20)
a ia ion ac i i ies, €
Cos s Cos o se ices, € PERT(182, 300, 600) Expe
Cos o pe sonnel, € PERT(72, 100, 150) opinion
Cos o uel and lub ican , € PERT(1.42, 3.3, 8)
Consump ion ma e ials, € PERT(2, 6, 15)
T a ic T a ic – passenge s GBM(0.0332, His o ical
0.0385) da a
T a ic – eigh GBM(0.0.25, 0.0.80)
O he Elec ic ene gy p ice, €/MWh MR(21.10, 0.08167, His o ical
0.1774) da a
1 Pa ame e alues a e in millions.
2 PERT s ands o Be aPERT dis ibu ion; U, uni o m; GBM, Geome ic B ownian Mo ion;
and MR, mean e e ing.
Sou ce: Based on Pelleg ino (2021) (h ps://ascelib a y.o g/doi/10.1061/%28ASCE%2
9CO.1943–7862.0002098), Table1, p.6.
The unce ain a iables a e:
• A ia ion e enues a ise om secu i y se ices, cen alized in as uc u es,
and o he ela ed mino ac i i ies (a ia ion e enues) His o ical da a and
expe opinion we e used o es ima e hem (see Table5 1)
• Non-a ia ion e enues include subconcessions and u ili ies, pa king, and
ad e ising (see Table5 1)
• T a ic is modelled as a andom a iable ollowing a Geome ic B own-
ian Mo ion (Pichayapan e al , 2003; Ga in & Cheah, 2004; B andao &
Sa ai a, 2008; Iye & Saghee , 2011) (equa ion (13))
2
−Q
+
=
Q2 Q
QQ
1e
+ (13)
whe e Q is he a ic g ow h a e, Q is he annual ola ili y o he a ic,
and ~N(0,1) is he s anda d Wiene p ocess Table5 1 epo s he pa am-
e e alues used in he case The uni a y p ice cha ged o he use s has been
calcula ed based on his o ical da a (ai po cha ges: landings and depa u e
igh s: €3 30; pa king and hospi aliza ion igh s: €0 17; passenge boa ding
ee: €13 85; eigh loading and unloading axes: €0 04)
• Ope a ions cos s, such as se ice cos s, pe sonnel cos s, and consump-
ions cos s, a e based on his o ical da a We model he elec ici y p ice
Con ex ual ac o s in mi iga ing e enue isk in PPP p ojec s 101
as a andom a iable acco ding o a Mean Re e ing P ocess (Blanco &
So onow, 2001a, 2001b; Blanco e al , 2001; Deng, 2000), acco ding o he
equa ion:
dS
=
()
sS
−d +dW
whe e s is he long un mean ( he mean e e sion le el), is he annual ola-
ili y o he p ice, is he mean e e sion a e, and dW is a B ownian mo ion
(so dW Nd
()
0 )
Table5 1 epo s he assump ions used o modelling he s a is ical dis i-
bu ions o unce ain a iables
The inpu a iables o g oups C and D a e s ochas ic p ocesses, whe e he
alue a each ime depends on he alue in he p e ious yea All o he inpu
a iables a e assumed o independen ly ollow he dis ibu ions speci ied in
Table5 1, each yea
The model is implemen ed in a sp eadshee , and he unce ain y handling,
simula ion, and sensi i i y analysis a e pe o med using he C ys al Ball so -
wa e package
2.3 P e ious sensi i i y analysis s udies
Pelleg ino (2021) pe o med an ex ensi e unce ain y and sensi i i y s udy
o he case In pa icula , a Mon e Ca lo simula ion was un, and he esul -
ing p obabili y dis ibu ion examined in he absence o suppo Subsequen
simula ion expe imen s we e epea ed o each suppo ype, and he desc ip-
i e s a is ics a e p o ided in Sec ion2 3 1 In addi ion, one-a -a- ime (OAT)
sensi i i y analyses we e conduc ed o he di e en le els o suppo and o
di e en alues o he unce ain inpu s (see Sec ion2 3 2)
2.3.1 M on e Ca lo simula ion
E alua ing he p ojec wi hou any o m o gua an ee, we ob ain he ne ben-
e i s (NPV) o he public and p i a e pa ies, as shown in Figu e5 1
As seen in he igu es, he p ojec is posi i e o he go e nmen and nega-
i e o he p i a e pa y in he absence o go e nmen suppo While he
isk o loss is negligible o he go e nmen , i is high o he p i a e en i y
Clea ly, any in as uc u e p ojec exhibi ing such cha ac e is ics would no
be appealing o p i a e in es o s and would, he e o e, equi e addi ional
go e nmen suppo gua an ees o become mo e a ac i e
Table5 2 shows he ne p o i s a is ics o he wo ac o s (p i a e pa y
and go e nmen ) o he p ojec when conside ed unde each o he h ee
o ms o public suppo (MRG, LPVR, and PCR)
I is clea ha in oducing go e nmen suppo inc eases he p ojec p o i -
abili y o he p i a e en i y and educes he isk ha he p i a e in e es s a e
no sa is ied F om he go e nmen pe spec i e, i can be no iced ha unde
LPVR, he NPV emains he same as he case wi hou suppo s, while MRG
108 Robe a Pelleg ino e al.
single annual alue o he same a iable, such inpu a iables we e ans o med
in o mean and a iance alues. This in oduces 26 pa ame e s in o he analysis
om he 13 inpu a iables speci ied in Table5.1. Th ee addi ional a iables
ep esen ing he suppo le el o each o he h ee ypes a e also eco ded.
Consequen ly, he o e all da ase consis ed o 1,000 i e a ions o 12 ou pu s
and 29 inpu pa ame e s. Fu he mo e, a combined da ase was c ea ed o he
h ee main ou pu alues using an ex a a i icial disc e e inpu a iable o ep-
esen he suppo case. This combined da ase enables a di ec compa ison o
all policy op ions simul aneously using a single g aph by employing he ex a
suppo inpu o designa e di e en suppo ypes in he decomposi ion.
3.2 Sensi i i y indices
This case poses wo signi ican compu a ional challenges o he e ec i e
de e mina ion o sensi i i y indices. Fi s ly, he highly unce ain condi ions
a e no comple ely e lec ed by he selec ed inpu pa ame e s (i.e. he agg e-
ga ion o indi idual annual inpu s in o summa ized means and a iances).
Secondly, he numbe o inpu s is qui e high compa ed o he ela i ely low
numbe o simula ed i e a ions. Fo hese easons, only i s -o de indices (i.e.
sensi i i y alues o indi idual inpu a iables) a e compu ed as he es ima-
ion o second-o de e ec s becomes oo noisy (see Table5.4). In Table5.4,
he no able sensi i i y indices a e highligh ed wi h g een shading; all index
alues below 2% a e g eyed ou , as a e he ac ual names o he inpu s ha
ha e all sensi i i y index alues below 2% o each ou pu .
Table5.4 indica es ha he Suppo ype is he mos in luen ial a iable
in he me ged da ase . The co esponding suppo le els appea in luen ial in
co esponding suppo ypes, o Ta i in P ice Cap, LPVR in LPVR, and Rg
in MRG. Howe e , he impac s o hese e ec s a e no symme ic o he di e -
en pa ies. The a i a ec s NPV o he p i a e in es o bu has only a mino
in luence on he p o i abili y o he go e nmen . LPVR has modes e ec on
he go e nmen NPV, bu none o he p i a e in es o , and exhibi s a consid-
e able di e ence be ween he wo. Rg plays a signi ican ole o NPV o p i-
a e in es o and he di e ence be ween he wo bu has only a modes e ec
on he go e nmen NPV. Besides he suppo -le el a iables, he mean a ic
o passenge s is he only o he a iable ha con ibu es a no iceable i s -o de
in luence o e all cases. The i s -o de e ec s o all o he inpu a iables a e
negligible. A inal in luence obse a ion is ha he sum o all indices is consid-
e ably below 100% in he no suppo case. This obse a ion is cha ac e is ic o
a highly unce ain sys em con aining many comple ely andom inpu s.
3.3 Decomposi ion
Figu e5.3 displays he dis ibu ions o each o he h ee ou pu s o he me ged
da ase , NPVG – NPVC, NPVC, and NPVG, decomposed by Suppo ype ( he
mos in luen ial pa ame e iden i ied in Sec ion3.2). The decomposed g aphs

Con ex ual ac o s in mi iga ing e enue isk in PPP p ojec s 109
Table 5.4 Sensi i i y indices ( i s -o de e ec s) o inpu pa ame e s o model ou pu s
Inpu s P ice Cap LPVR MRG No suppo
Bo h NPVCNPVGBo h NPVCNPVGBo h NPVCNPVGBo h NPVCNPVG
Suppo
Mean Elec ici y P ice (no mal) 1% 1% 1% 1% 1% 1% 1% 1% 1% 0% 1% 1%
Va iance Elec ici y P ice (no mal) 0% 1% 0% 1% 0% 1% 2% 2% 1% 1% 1% 0%
Mean T a ic – eigh (no mal) 1% 0% 1% 0% 1% 1% 1% 1% 1% 1% 0% 1%
Va iance T a ic – eigh (no mal) 1% 1% 0% 1% 1% 1% 1% 1% 0% 1% 1% 0%
Ta i 4% 29% 1% 1% 1% 1% 1% 1% 1% 1% 1% 1%
Mean Ad e isemen 0% 2% 1% 1% 1% 1% 1% 2% 1% 1% 1% 1%
Va iance Ad e isemen 1% 1% 1% 1% 1% 1% 0% 1% 1% 0% 1% 1%
Mean Comme cial subconcession 0% 0% 0% 0% 0% 0% 1% 1% 1% 1% 0% 0%
Va iance Comme cial subconcession 1% 0% 0% 1% 0% 1% 0% 1% 0% 1% 0% 0%
Mean Consump ion ma e ials 0% 0% 0% 1% 0% 0% 0% 0% 0% 0% 0% 0%
Va iance Consump ion ma e ials 1% 1% 1% 0% 1% 1% 1% 1% 1% 1% 1% 1%
Mean Cos o uel and lub ican 2% 1% 2% 1% 1% 2% 1% 1% 1% 1% 1% 2%
Va iance Cos o uel and lub ican 1% 1% 1% 0% 1% 2% 1% 1% 1% 1% 1% 1%
Mean Cos o pe sonnel 1% 1% 2% 0% 1% 1% 1% 2% 1% 1% 1% 2%
Va iance Cos o pe sonnel 2% 1% 1% 1% 1% 1% % 1% 2% 2% 1% 1%
Mean Cos s o se ices 0% 1% 1% 3% 1% 0% 2% 3% 1% 2% 2% 1%
Va iance Cos s o se ices 1% 1% 1% 2% 1% 1% 0% 1% 1% 1% 1% 1%
LPVR 1% 1% 1% 85% 0% 14% 1% 0% 1% 2% 0% 1%
Mean O he e enues om a ia ion 1% 1% 0% 0% 1% 0% 1% 1% 1% 1% 1% 0%
Va iance O he e enues om a ia ion 1% 1% 1% 2% 1% 1% 0% 1% 0% 1% 1% 1%
Mean O he e enues om non-a ia ion 0% 0% 0% 1% 0% 1% 1% 1% 1% 1% 1% 0%
Va iance O he e enues om non-a ia ion 1% 0% 1% 0% 1% 1% 1% 1% 0% 1% 1% 1%
Mean Pa king (in subconcession) 1% 1% 1% 0% 1% 1% 0% 1% 1% 1% 1% 1%
Va iance Pa king (in subconcession) 1% 1% 1% 1% 1% 1% 1% 1% 1% 1% 1% 1%
(Con inued)
110 Robe a Pelleg ino e al.
Inpu s P ice Cap LPVR MRG No suppo
Bo h NPVCNPVGBo h NPVCNPVGBo h NPVCNPVGBo h NPVCNPVG
Mean Real es a e subconcession 0% 1% 0% 1% 1% 1% 1% 1% 1% 1% 1% 0%
Va iance Real es a e subconcession 1% 1% 1% 2% 1% 1% 1% 1% 1% 1% 1% 1%
Rg 1% 0% 1% 1% 1% 1% 82% 82% 38% 1% 1% 1%
Mean T a ic – passenge s 44% 25% 48% 6% 45% 36% 7% 7% 27% 19% 35% 48%
Va iance T a ic – passenge s 1% 1% 1% 1% 1% 1% 1% 1% 1% 1% 1% 1%
Sum o i s -o de indices 71% 76% 72% 117% 69% 72% 113% 116% 88% 46% 61% 71%
No e: “Bo h” s ands o NPVG – NPVC.
Table 5.4 (Con inued)
Con ex ual ac o s in mi iga ing e enue isk in PPP p ojec s 111
Figu e 5.3 Simula ion Decomposi ion o p o i abili y dis ibu ions o he go e nmen ( igh ), p i a e pa y (middle), and hei
di e ence (le ) by he policy ype. (colou image is accessible ia he link)
112 Robe a Pelleg ino e al.
isibly indica e ha he p o i abili y dis ibu ion o he go e nmen and he
dis ibu ion o he di e ence wi h he p i a e pa y p o i abili y a e clea ly
di e en ia ed by he ou policy cases. Because he p o i abili y dis ibu ion
o he p i a e in es o appea s mo e condensed, i has been decomposed u -
he by including he mode a ely in luencing (7%) Mean a ic a iable o
p o ide addi ional explana o y cla i y.
Fo he p i a e in es o (Figu e5.3, middle), P ice cap appea s o be he
mos a ac i e suppo ype because i always p o ides gua an eed p o i -
abili y ( he en i e ed sub-dis ibu ion is in he posi i e NPV ange). MRG
is also always p o i able, bu wi h less upside compa ed o P ice cap. LPVR
has a negligible, bu non-ze o, p obabili y o losses. In con as , No suppo
makes he p ojec look una ac i e, wi h an expec ed mean below ze o. The
inc eased passenge a ic sligh ly shi s p o i abili y upwa ds, bu does no
show any majo in luence. This con i ms i s non-ze o, bu low, sensi i i y
index o 7%.
The go e nmen (Figu e 5.3, igh ) bene i s he mos om P ice cap,
whe eas he dis ibu ions o he o he suppo ypes gene ally emain g ouped
oge he . No suppo and LPVR occupy almos he same p o i abili y ange
as LPVR, hough hey ex end mo e in o lowe - alue egions. Howe e , nei-
he a iable p oduces esul s in he nega i e p o i abili y ange. MRG has a
non-ze o p obabili y o loss o he go e nmen .
The di e ence o he wo NPVs (Figu e5.3, le ) compa es he ela i e
economic posi ions o he wo pa ies by showing how much highe he p o -
i abili y is o he go e nmen in compa ison o he p i a e in es o . The
P ice cap sub-dis ibu ion is high in he posi i e ange, e en hough i is
also he mos p o i able scheme o he p i a e in es o . This occu s because,
o his suppo ype, he consume pays he p o i s di ec ly o bo h pa ies.
Unde LPVR, he go e nmen bene i s mo e han he p i a e in es o mos o
he ime, bu no by as much as unde P ice cap. This e ec can be obse ed
in he igu e because he yellow sub-dis ibu ion occupies a na owe ange
close o ze o, hough i occasionally en e s in o he nega i e zone. Con e sely,
unde MRG, he p i a e in es o p o i s mo e han he go e nmen mos o
he ime. Finally, he decomposi ions o each indi idual suppo ype do no
unco e any in e es ing pa e ns. All indi idual e ec s epo ed in Table5.4
assume a a he mono onic appea ance, and hus, hese g aphs ha e been
omi ed om he chap e .
In summa y, he SimDec app oach has conside ably eased he o e all com-
plexi y o he analysis p ocess o he isk mi iga ion decision-make . While he
p e iously conduc ed sensi i i y analysis app oaches all equi ed mul iple simu-
la ion expe imen s o p oduce hei esul s (Figu es5.1–5.2 and Tables5.2–5.3),
only a single simula ion was necessa y o p oduce all o he SimDec esul s. Sim-
Dec au oma ically inco po a es an analysis o all o he a iables ha had o be
gene a ed indi idually in he p io app oaches. The h ee g aphs in Figu e5.3
Con ex ual ac o s in mi iga ing e enue isk in PPP p ojec s 113
combine he in o ma ion con en om Figu e5.1 (p obabili y dis ibu ions),
Table5.2 ( ha o e s 72 di e en alues o analysis), and Table5.3 ( ha u -
he unco e s he de ails wi h 315 mo e alues). SimDec gene a es p o i abili y
dis ibu ions o all o he policy op ions simul aneously on a single g aph. This
isualiza ion enables all he in o ma ion o be di ec ly compa able and all o
he compa a i e insigh s o become eadily ob ious. Fu he mo e, while he
ea lie model exhibi ed only mono onic beha iou , he SimDec isualiza ion
has unco e ed a mo e complex nonlinea ela ionships, including signi ican
unde lying he e ogeneous beha iou . Consequen ly, SimDec should become an
essen ial analysis suppo app oach o any well-in o med isk mi iga ion in
PPP decision-making (Kozlo a, Moss, e al., 2024).
4 Discussion and conclusions
This chap e has ou lined a SimDec analysis o mi iga ing he e enue isks
o a ious public in as uc u e suppo ypes. In gene al, he PPP model is
challenging due o he signi ican le els o unce ain y inhe en wi hin he
model, he combina ion o nume ous inpu a iables ha change concu -
en ly, and he limi ed numbe o simula ion uns. Fu he mo e, he e has
been a need o in eg a e ex ensi e p io unce ain y and sensi i i y analy-
ses in o he decision p ocess. Ne e heless, i has been shown ha SimDec
pe o ms admi ably by con ibu ing se e al addi ional analy ical bene i s
oge he wi h nume ous supplemen a y insigh s.
Fo he PPP mi iga ion case conside ed, SimDec p o ided global insigh s
in o he economic balancing o di e en policy op ions, e ealed he mos
impo an ac o s, and di ec ly highligh ed he e ec s o se e al modelling
choices. The global sensi i i y analysis om SimDec e ealed ha , in con-
as o he ea lie one-a -a- ime analysis (Figu e5.2), only passenge a ic
olume is impo an o he ai po in es men p o i when all unce ain con-
di ions a e conside ed simul aneously (Table5.4). Mo eo e , in he absence
o suppo , he a iabili y o he ou pu canno be su icien ly explained by
he agg ega ed inpu pa ame e s due o he conside able andomness o he
mul iple inpu a iables.
In conclusion, o he gene al case, i can be ecommended ha SimDec
should be b oadly applied o he analysis o public in as uc u e in es men s
o in es iga ing pa ne ship a angemen s, o examining policy op ions,
and o conduc ing in es men isk mi iga ion analysis.
Acknowledgemen s
The wo k is suppo ed by g an 220178 om he Finnish Founda ion o
Economic Educa ion and by g an OGP0155871 om he Na u al Sciences
and Enginee ing Resea ch Council.

114 Robe a Pelleg ino e al.
No es
1 The Na ional Ci il A ia ion Au ho i y (ENAC) is a non-economic public body wi h
egula o y, o ganiza ional, adminis a i e, pa imonial, accoun ing, and inancial
au onomy.
2 h ps://gi hub.com/Simula ion-Decomposi ion.
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DOI: 10.4324/9781003453789-8
This chap e has been made a ailable unde a CC-BY-NC-ND 4.0 license.
Abs ac
Applying Addi i e Manu ac u ing (AM) me hodologies, such as 3D p in ing
o conc e e, migh p o ide a mechanism o e olu ionize he cons uc ion sec-
o . Howe e , he ambiguous na u e o uni economics has de e ed i s mo e
ex ensi e in eg a ion. As such, his s udy i s p esen s a de e minis ic model
o es ima ing di ec and indi ec cos s in AM and hen ad ances a s ochas-
ic uni cos model by in eg a ing unce ain y anges. Using (Mon e Ca lo)
Simula ion Decomposi ion, his model is analyzed ega ding p obabilis ic
scena ios, he sensi i i y o inpu ac o s, and unce ain y e ec s. The esul s
con i m he exis ence o economies o scale and highligh AM’s po en ial
o cons uc ion ac oss a di e se ange o scena ios. Manage s, esea che s,
in es o s, and policymake s alike can use his model o in e ac i ely na iga e
he complexi ies o AM in he cons uc ion indus y o in o m decisions and
d i e echnology de elopmen . As AM echnology ad ances, he models can
be i e a i ely e ined and expanded, e en ually imp o ing uni economics,
p oduc i i y, and p o i abili y. Fu u e esea ch can hen le e age such models
o explo e AM’s po en ial impac in cons uc ion, in as uc u e, and housing
p ojec s.
1 In oduc ion
The cons uc ion indus y may ele a e p oduc i i y by adop ing ad anced
manu ac u ing echniques om o he sec o s, such as au oma ion om au o-
mo i e (Gann, 1996). Howe e , he ongoing in oduc ion o no el echnolo-
gies in cons uc ion p esen s se e al challenges, o example, unclea use
pe cep ion o obo s (Walze e al., 2023). Beyond unde s anding echno-
logical ba ie s and use needs, he economic implica ions o no el echnol-
ogy in he sec o ha e d awn u he a en ion in cons uc ion managemen
schola ship (Kanga i & Halpin, 1990; Ta um, 1986). A guably, he eme -
gence o Addi i e Manu ac u ing (AM) he alds a ans o ma i e phase in he
Chap e 6
P in ing homes
Uni cos es ima ion o addi i e
manu ac u ing in cons uc ion
Alexande N. Walze , Ma iia Kozlo a, and
Julian Sco Yeomans
P in ing homes 117
cons uc ion indus y by ad ancing no el me hods o p oduc ion ha ex end
he bounda ies o inno a ion (Be man, 2012).
A he hea o his cu ing-edge echnology lies a digi ally d i en ab-
ica ion p ocess which, h ough he laye -by-laye deposi ion o ma e-
ial – anging om cemen i ious pas e o s eel, plas ics, esins, o a blend
o hese – accu a ely maps he desi ed elemen s along a pa h dic a ed by a
p e-app o ed 3D model (Gibson e al., 2015). The po en ial adop ion o his
echnology wi hin he cons uc ion indus y is gaining in e es , as i p omises
an a ay o unp eceden ed possibili ies. I s o e ings ex end om enhanced
design lexibili y o po en ial cos e iciency and, pe haps, mos signi ican ly,
a clea pa h owa d sus ainabili y (Wohle s & Ca ey, 2015; Zunino, 2023).
The cu en inno a ion landscape in his ield e eals a mix o pilo p ojec s
spea headed by academia and indus y wo ldwide. La ge mul ina ional co -
po a ions and well- unded s a -ups a e inc easingly s epping in o he a ena,
indica ing a g owing commi men o his echnological e olu ion (Fo d &
Despeisse, 2016).
Howe e , close examina ion is necessa y o comp ehend he p o i abili y
o AM in he cons uc ion indus y. Es ima ing uni cos s is a c i ical s a -
ing poin o such analysis (Tucke , 1986) o e alua e whe he AM could
yield economies o scale, whe e inc eased p oduc ion dec eases pe -uni
cos s (Besanko e al., 2009). “I ’s eally impo an o be p o i able a he uni
le el – and ake ha as a i s p io i y” (Eisenha d , 2023, 19:40).
Figu e6.1 depic s a ecen indus y example o AM using 3D p in ing o
cemen i ious ma e ials (o en e e ed o as 3D conc e e p in ing, “3DCP”)
by using an indus ial obo ic a m o p oduce in as uc u e ounda ions ( is-
ible on he le ).
1.1 Poin o depa u e
While p e ious in es iga ions in o p oduc i i y in eme ging cons uc ion
echnologies exis (e.g. Ga cia de So o e al., 2018), he analysis ends o
ha e been ela i ely simpli ied by neglec ing nume ous c i ical aspec s in e-
g al o a comp ehensi e cos e alua ion. Gene ally, p oduc i i y deno es
he ou pu olume an o ganiza ion can gene a e pe uni o inpu – labou ,
capi al, and ma e ials, among o he s (Sy e son, 2011). Se ing as a ba om-
e e o e iciency, i gauges how e ec i ely a i m, an indus y, o e en an
en i e economy deploys i s esou ces. Fo ins ance, a company migh assess
i s p oduc i i y based on he numbe o uni s i manu ac u es pe labou
hou . Assuming o he ac o s emain cons an , heigh ened p oduc i i y
could pa e he way o educed cos s and augmen ed p o i s (Bloom & Van
Reenen, 2010).
Con e sely, cos e iciency sc u inizes he ela ionship be ween inpu
expenses and he alue o quali y o ou pu s. Ap ocess can be classi ied as
220 Robe J. Moss, Ma iia Kozlo a, An hony Co so, and Je Cae s
5.6 Accu acy analysis
Fo POMDP p oblems ha make a inal decision, he accu acy is de ined as
how close he inal decision was o he co ec decision. Fo bina y decisions,
his is simply whe he he agen ook he co ec ac ion o no . Fo con inu-
ous decisions, his could be he di e ence be ween he inal decision and he
co ec decision (e.g. dis ance o an unknown goal). Fo he mine al explo a-
ion POMDP, we ea he inal decision as a classi ica ion ask (i.e. whe he
o classi y he o ebody as a esou ce o mine o abandon). Based on he inal
decision, he accu acy is compu ed as:
numbe o co ec decisions
accu acy =numbe o decisions
The numbe o decisions is equi alen o he numbe o episodes (i.e.
seeds) pe model con igu a ion. Fo a se o economical o ebody s a es E, he
numbe o co ec decisions is:
11(|as=Îmine Ea)(+=abandon |)sEÏ
The con ou map analysis o he accu acy in Figu e9.17 indica es ha
e e y model- ideli y con igu a ion has accu acy abo e abou 0.69 (whe e
an accu acy o 0.5 would co espond o a andom policy). Also e iden in
he con ou s is ha he g id dimensions ha e he la ges e ec and ha he
medium- and low- ideli y s a e shapes ha e simila accu acy. Unsu p isingly,
he highes - ideli y model con igu a ion p oduces he highes accu acy.
The sensi i i y analysis in Table9.7 con i ms ha he model ideli ies ha e
li le e ec on he accu acy, all less han 1%. Table9.8 de ails he decompo-
si ion o accu acy based on he model ideli ies wi h an explained a iance
o he decomposed ou pu o 0.009. These esul s show ha he accu acy
anges om 0.69 o 0.84 (whe e he la e co esponds o he highes ideli y
case), ma ching he con ou map analysis. This sugges s ha ega dless o he
choice o model ideli y, ela i ely high accu acy can be achie ed.
Table 9. 7 Sensi i i y indices o accu acy
Inpu Fi s -o de Second-o de e ec Combined
e ec sensi i i y
S a e shape Planning G id index
i e a ions dimensions
S a e shape 0.002 —0.001 0.0002 0.002
Planning i e a ions 0.001 — — 0.0001 0.001
G id dimensions 0.006 — — — 0.006

Model ideli y analysis using Simula ion Decomposi ion 221
Figu e 9.17 Con ou maps o he accu acy in he inal mine o abandon decision. (colou image is accessible ia he link)
222 Robe J. Moss, Ma iia Kozlo a, An hony Co so, and Je Cae s
Table 9. 8 Decomposi ion o accu acy by s a e shape, planning i e a ions, and g id
dimensions
S a e shape Planning G id Accu acy
i e a ions dimensions Min Mean Max P obabili y
Ci cle Low Low 0.00 0.76 1.00 7%
High 0.00 0.81 1.00 15%
High Low 0.00 0.74 1.00 4%
High 0.00 0.79 1.00 7%
Ellipse Low Low 0.00 0.74 1.00 7%
High 0.00 0.79 1.00 15%
High Low 0.00 0.69 1.00 4%
High 0.00 0.79 1.00 7%
Blob Low Low 0.00 0.75 1.00 7%
High 0.00 0.83 1.00 15%
High Low 0.00 0.80 1.00 4%
High 0.00 0.84 1.00 7%
5.7 Seed s . andom sampling
As desc ibed in Sec ion4.2, wo ypes o Mon e Ca lo da a gene a ion we e
s udied: sampling seeds o a disc e e se o inpu con igu a ions and andom
sampling o e a ange o inpu s. Resul s in Table9.9 sugges ha he o e all
model ideli y sensi i i y analysis conclusions a e una ec ed by he sampling
scheme. The e o e, we chose o sample based on he seed s a egy o allow
us o isualize accu acy using con ou s. Figu e9.18 compa es wo ou pu s
( eg e and un ime) using he di e en sampling schemes. The eg e dis-
ibu ions a e an example whe e he his og ams (and suppo ing sensi i i y
indices) a e nea ly equi alen , and he un imes a e an example whe e he his-
og ams a e isually di e en (despi e he sensi i i y analysis closely ma ch-
ing). The un ime his og ams o he andom sampling scheme (Figu e18b2)
a e smoo he as hey a e compu ed o e a ine ange (i.e. de ined by he x–y
ange in he con ou plo s).
6 Discussion
The analysis p esen ed in his chap e highligh s he use o SimDec o model
ideli y sensi i i y o sequen ial planning pe o mance. We in oduced he
POMDP model- ideli y amewo k (PMFF) and applied i o a eal-wo ld
case s udy o c i ical mine al explo a ion. The esul s o his case s udy sug-
ges ha complex s a e modelling o accu a ely ep esen he subsu ace may
be less impo an han ocusing on planning ideli y and en i onmen idel-
i y, as shown in he sensi i i y indices mean in Table9.10 (also shown in he
o e all esul s in Table9.1). The s a e shape model (i.e. s a e ideli y) had he
la ges sensi i i y o he numbe o ac ions planning pe o mance me ic wi h
Model ideli y analysis using Simula ion Decomposi ion 223
Table 9. 9 Combined sensi i i y indices o all ou pu s o he wo sampling s a egies
ions
Sampling
0.006
0.042
0.008
No. o ac
Seed
0.008
0.052
0.003
Sampling
0.011
0.006
0.009
Bias
Seed
0.001
0.002
0.007
Sampling
0.006
0.229
0.201
Run ime
Seed
0.005
0.248
0.203
Simple andom sampling b.
Sampling
0.001
0.004
0.006
e geR
Seed
0.003
0.002
0.010
n u e
Sampling
0.001
0.005
0.005
scoun ed
Seed
0.0003
0.0002
0.0010
i.e. his analysis)
DiInpu /ou pu
hapeS a e s
lanning i e a ions
id dimensions
Seed sampling (
P
G
a.
224 Robe J. Moss, Ma iia Kozlo a, An hony Co so, and Je Cae s
Figu e 9.18 Compa ison o his og ams ob ained wi h seed sampling (a1 & a2) and andom sampling (b1 & b2e simila esul s a ). R
o eg e (a1 & b1) and di e en o un ime (a2 & b2). (colou image is accessible ia he link)
Model ideli y analysis using Simula ion Decomposi ion 225
a sensi i i y index o 0.008. Al hough ela i ely low, his ideli y esul ed in
educed in o ma ion ga he ing o con e ge he simple belie , hus leading o
ewe ac ions pe episode. Bo h he planning i e a ions (i.e. planning ideli y)
and he g id dimensions (i.e. en i onmen ideli y) had he la ges sensi i i ies
o un ime wi h sensi i i y indices o 0.248 and 0.203, espec i ely. This un -
ime sensi i i y is unde s ood o come om wo componen s o he planne :
(1) he size o he ac ion space is he size o he g id dimensions, hus leading
o mo e ac ions o explo e du ing planning, and (2) he pa icle il e belie
upda e uses impo ance esampling wi h condi ional Gaussian simula ions
o condi ion he subsu ace ield on he o e measu emen s. The e o e, when
he g id dimensions a e la ge , he e a e mo e ac ions and a la ge subsu ace
o gene a e based on he obse a ions. Also, one would expec he un ime
o inc ease as a unc ion o planning i e a ions. All h ee inpu ideli ies had
he lowes sensi i i ies o he discoun ed e u n wi h sensi i i y indices o
0.0003, 0.0002, and 0.001, espec i ely. In POMDP planning and ein o ce-
men lea ning, he discoun ed e u n is he p ima y me ic used o de e mine
he pe o mance o a decision-making agen . This sugges s ha , ac oss all
inpu ideli ies, he planning pe o mance is no sensi i e o model ideli y.
6.1 Applicabili y
Demons a ing he use o SimDec o s udy he sensi i i y o model choices in
a POMDP has b oade applicabili y ou side he case s udy o mine al explo-
a ion. PMFF p o ides a gene al amewo k o be applicable o any POMDP.
O he applica ion a eas could ocus on he sa e y o POMDP planning algo-
i hms, including s udying POMDPs o au onomous d i ing (Sunbe g &
Kochende e , 2022) and ca bon cap u e and s o age (Wang e al., 2023).
The sensi i i y analysis could u he analyze he sys em beha iou in e ms
o how he sensi i i y in he inpu s a ec s decision-making based on he
ac ions aken. The combina ion o SimDec and PMFF could also be used no
only o model pe o mance analysis bu also o model selec ion: ine- uning
he model beha iou o op imal decision-making based on he balance o
mul iple pe o mance objec i es.
6.2 Open-sou ce code
The sou ce code o he gene al PMFF amewo k and he in e ace and
expe imen code used in his case s udy o he mine al explo a ion POMDP
Table 9.10 Sensi i i y index o als
Inpu /ou pu Sensi i i y indices mean
S a e shape 0.019
Planning i e a ions 0.305
G id dimensions 0.230

226 Robe J. Moss, Ma iia Kozlo a, An hony Co so, and Je Cae s
a e a ailable online.1 Open-sou ce packages o un SimDec o o he ypes
o sys ems (using Mon e Ca lo da a om simula ed o eal-measu ed si ua-
ions) a e a ailable in Ma lab, Py hon, Julia, R, and Excel.2
Acknowledgemen s
This wo k is suppo ed by g an 220178 om he Finnish Founda ion o
Economic Educa ion, by g an OGP0155871 om he Na u al Science and
Enginee ing Resea ch Council o Canada, and by he S an o d Ins i u e o
Human-Cen e ed AI.
No es
1 h ps://gi hub.com/sisl/POMDPModelFideli yF amewo k.jl.
2 h ps://gi hub.com/Simula ion-Decomposi ion.
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i hm and SimDec isualiza ion o comp ehensi e sensi i i y analysis o complex
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pd /2310.13446
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DOI: 10.4324/9781003453789-13
This chap e has been made a ailable unde a CC-BY-NC-ND 4.0 license.
Chap e 10
Upg ading he oolbox o
echno-economic assessmen
wi h SimDec
Powe - o-X case
Hannu Ka junen, Sini-Kaisu Kinnunen,
A o Laa i, An e o Te onen, Pe e i Laaksonen,
Ma iia Kozlo a, and Julian Sco Yeomans
Abs ac
Powe - o-X (P2X) echnology holds g ea po en ial o deca boniza ion and
sees an ac i e g ow h o R&D, pilo p ojec s, and scaling ini ia i es. Such
p ojec s a e su ounded by emendous unce ain y due o hei long li es-
pan, dependency on ma ke and policy e olu ion, and high up on cos s.
Thus, he usage o adequa e analy ical ools is o pa amoun impo ance o
design, e alua e, and execu e P2X p ojec s. In his chap e , we ook one such
echno-economic epo o a P2X p ojec and eplica ed i s one-a -a- ime
sensi i i y analysis and scena io analysis wi h he mo e powe ul SimDec
app oach. The b ead h o he newly acqui ed insigh s inspi ed he au ho s o
upg ade he analysis o e lec p esen -day ci cums ances in o de o de e -
mine wha indings SimDec could con ibu e o he e ol ing si ua ion. In all
analyzed cases, SimDec showed an excellen capabili y o combining unce -
ain y and sensi i i y analysis o de i ing comp ehensi e ac ionable insigh s
o in es men p ojec s.
Keywo ds: P2X, powe - o-X, SimDec, simula ion, easibili y, capi al in es -
men , discoun ed cash low model, ne p esen alue, global sensi i i y analy-
sis, unce ain y analysis
1 In oduc ion
P2X (powe - o-X) is an umb ella e m o pa hways which con e elec ici y
in o a ious commodi ies, such as uels, chemicals, gases, hea , o e en ood.
One subse o P2X is ep esen ed by elec o uels, also known as e- uels. This
class o uels unc ions as a di ec d op-in eplacemen o ehicles and o he
de ices elying on in e nal combus ion engines and liquid uels. Ins ead o
using ossil c ude oil as he eeds ock, e- uels a e syn he ized om ca bon
dioxide and hyd ogen. No ably, he hyd ogen may be ob ained om wa e
The oolbox o echno-economic assessmen wi h SimDec 229
elec olysis, which, in u n, is ope a ed using enewable elec ici y. Syn hesis
p ocesses o P2X p oduc s and e- uels may ake many o ms and di e en
eac ion s eps, such as he Saba ie eac ion, hyd ogena ion using he e oge-
neous ca alys s, and biosyn hesis (Laaksonen e al., 2021).
Feasibili y s udies ela ed o P2X p ojec s a e highly ele an and in e es
is inc easing ega ding he p o i abili y o hese p ojec s (Dahi u e al., 2022).
Howe e , he a ailabili y o eliable da a using eal cases is limi ed. This
is pa ly because o con iden iali y issues, bu also because o unce ain ies
ela ed o he key ac o s a ec ing he economic easibili y o P2X in es -
men s, such as end p oduc p ice, expec ed dec ease in p oduc ion cos s due
o echnological and manu ac u ing inno a ions, o gene al unce ain ies in
p ocess design a p elimina y design s age. Modelling he echnical and eco-
nomic easibili y o he new ene gy solu ions is c i ical in o de o p omo e
he ene gy ansi ion in a sus ainable manne . Because p e ious cases wi h
eal da a a e limi ed, sensi i i y analysis and simula ions a e impo an when
e alua ing he p o i abili y o his kind o in es men .
This s udy aims o eplica e and imp o e a p e iously conduc ed
p e- easibili y s udy o an e- uel plan (Laaksonen e al., 2021). Some o he
challenges ela ing o he p e- easibili y s udy include (1) unce ain y in he
p oduc ma ke p ices and inpu elec ici y p ice, (2) nume ous echnical
pa hways p oducing a a ie y o p oduc s wi h di e en olumes, and (3)
limi ed ce ain y in equipmen cos es ima es. The numbe o ac o s ha
need o be conside ed can quickly inc ease o such le els ha i is ha d o
g asp which ac o s a e ele an and which a e no .
In cos –bene i analysis and in es men app aisal, usually only limi ed
sensi i i y analysis app oaches a e used, such as one-a -a- ime sensi i i y
analysis (Bo chway e al., 2023; Rahmanzadeh e al., 2023; Fang e  al.,
2023), when each inpu a iable is changed indi idually, and nei he syne -
ge ic manage ial capabili ies no join e ec s o mul iple unce ain y sou ces
can be cap u ed (Kozlo a, Lo Piano, e al., 2024). In a SCOPUS da abase
sea ch, ou o o e 200,000 esul s wi h he “cos –bene i ” keywo d, only
7% men ion “sensi i i y analysis” (in ei he i le, keywo ds, o abs ac ),
and only 0.05% con ain “global sensi i i y analysis”,1 a mo e sophis i-
ca ed ype whe e all inpu s a e a ied a he same ime (Kozlo a, Lo Piano,
e al., 2024). In addi ion o one-a -a- ime analysis, some esea che s pe -
o m unce ain y analysis by means o Mon e Ca lo simula ion and display
he dis ibu ion o esul ing p o i abili y indica o s (Mombello e al., 2023;
Gill-Wiehl e al., 2023). This ype o analysis, howe e , lacks he knowledge
o which inpu ac o s a e mo e impo an and d i e he ou pu dis ibu ion
one way o ano he .
A ecen me hodological de elopmen , Simula ion Decomposi ion (Sim-
Dec), combines he bene i s o sophis ica ed sensi i i y analysis and unce -
ain y analysis by e ealing which inpu s a e impo an and how di e en
combina ions o hem ansla e on o he ou pu dis ibu ion (Kozlo a &
236 Hannu Ka junen e al.
whe e is ime index, n is he las yea o analysis, i is yea ly in e es a e,
and CF is cash low. The ini ial in es men cos (I) o echnical ins alla ion,
including enginee ing, occu s a he alue poin in ime 0. The NPV is he
di e ence be ween he p esen alue o cash in lows and he p esen alue
o cash ou lows om he yea 1 o 20 (PV) less he p esen alue o ini ial
in es men (I).
NPVP=-VI (2)
Nume ic assump ions o he inpu a iables o he model a e p esen ed
in Appendix 1. Annual cash in lows a e based on e enues om selling
end-p oduc s (and by-p oduc s) and depend upon he annual p oduc ion
amoun s, ope a ion ime, and he p oduc ion a io. The ini ial in es men
cos s consis o echnical in es men cos s, ese e, and wo king capi al.
Cash ou lows o he model consis o expenses du ing ope a ion. Aweigh ed
a e age cos o capi al (WACC) in e es a e is employed and he cos o
equi y in luences he in e es a e. These inpu a iables di ec ly impac he
discoun ed cash low and he calcula ion o NPV.
The model also compu es speci ic in es o cash lows when de e mining
he in es men IRR. In es o cash low is calcula ed om he annual ope a -
ing ma gin (equi alen o ne cash low) dec eased by bo h deb amo iza ion
and deb in e es cos s. As cash low depends on he p o i , in es o cash
low co esponds o he in es men e u n om equi y. The appo ionmen
o subsidy, deb , and equi y all impac he in es o cash low.
CF
=-ope a ingma gin deb amo iza ion -deb in e es cos s (3)
2.3 P e ious sensi i i y analysis s udies
Laaksonen e al. (2021) p e iously pe o med wo o ms o sensi i i y analy-
sis on he model: (1) a one-a -a- ime sensi i i y analysis o he base scena io,
and (2) a selec ed scena io analysis ha compu ed de e minis ic p o i abili y
indica o s.
2.3.1 One -a -a- ime sensi i i y analysis
The key a iables oge he wi h hei ealis ic anges, we e es ablished by
he pa icipa ing esea che s and expe s (Table 10.1). The mos c i ical
ac o s we e iden i ied o be end p oduc p ice (Gasoline p ice in Base sce-
na io), Hyd ogen p ice, Ope a ion ime, and In es men ese e. The a i-
ous impac s on p o i abili y o he unce ain y and isks we e analyzed by
examining changes o he model om a ying one inpu a ime. Table10.1
p esen s he esul s wi h s a ing alues in he Base scena io.

The oolbox o echno-economic assessmen wi h SimDec 237
Table 10.1 One-a -a- ime sensi i i y analysis
Base
scena io
Elec ici y p ice,
€/MWh 20 30 40 50
IRR (in es o ) 18.0% 16.9% 15.8% 14.7%
Hyd ogen p ice,
€/MWh 10 15 20 25 30
IRR (in es o ) 20.3% 15.8% 11.2% 6.3% 1.0%
In es men
ese e −30% −15% 0% 15% 30%
IRR (in es o ) 52.0% 33.1% 22.6% 15.8% 10.9%
Gasoline, €/ 1000 1200 1300 1400 1600 1800
IRR (in es o ) −3.3% 7.1% 11.5% 15.8% 24.0% 31.9%
Deb in e es
a e 1% 2% 3% 4% 5%
IRR (in es o ) 17.2% 15.8% 14.5% 13.2% 12.0%
O&M 2% & 3% 3% & 4% 4% & 5%
IRR (in es o ) 15.8% 11.6% 7.2%
Ope a ion ime 6000 7000 8000
IRR (in es o ) 5.4% 10.8% 15.8%
In es men sub-
sidy (TEM) 30% 40% 50%
IRR (in es o ) 12.4% 15.8% 20.1%
Sou ce: Upda ed om Laaksonen e al. (2021) (h ps://lu pub.lu . i/bi s eam/handle/10024/
162597/P2X%20Jou seno%20Final%20Repo .pd ?sequence=1&isAllowed=y), Figu e4.5, p.66.
2.3.2 Scena io analysis
Laaksonen e al. (2021) c ea ed i e di e en scena ios o compa e di e en s a -
egies and al e na i es (Table10.2). The i s scena io is speci ied as he base sce-
na io. The second scena io ep esen s a a ia ion in which elec olysis-sou ced
hyd ogen is used ins ead o pu chased by-p oduc hyd ogen. Since bo h o hese
scena ios employ an MTG-pa hway app oach, he inal p oduc is gasoline.
The hi d scena io, named MTG, is a a ia ion o he base scena io pos-
sessing mo e de ailed cos pa ame e s and o he e ised assump ions. The
inal wo scena ios employ non-MTG echnological app oaches. In he
MeOH case, p oduc ion is hal ed a he me hanol s age. The MTO-MOGD
case ini ially con e s me hanol o ole ins and hen in o gasoline and dis-
illa es. The MTG, MeOH, MTO-MOGD scena ios all equi e pu chased
hyd ogen as opposed o hyd ogen p oduced elec oly ically.
3 SimDec analysis
SimDec is i s used o eplica e he ea lie sensi i i y analysis, ollowed by a
es uc u ed sensi i i y analysis wi h upda ed assump ions.
238 Hannu Ka junen e al.
Table 10. 2 Scena io analysis
Scena io Desc ip ion To al In es men In es o IRR NPV, M€
in es men , subsidy,
M€ M€
Base scena io Ini ial i s d a o 76.5 26.4 15.8% 30.1
plan p o i abili y
analysis.
Base scena io Ini ial i s d a o 116.0 40.2 --144.0
elec olysis plan p o i abili y
analysis using elec-
olyse -sou ced
hyd ogen.
MTG Basic ou e o d op- 82.8 28.6 24.7% 53.0
in- uels. Compa ed
o he base sce-
na io, mos c i ical
changes a e:
• Upg aded p od-
uc p ices and
in es men s
• U ili y consump-
ions e ised
• Ca alys enewal
cos included
MeOH Final p oduc is 62.1 21.4 9.0% 7.2
me hanol.
• No d op-in- uel
syn hesis in in es -
men and ca alys
cos
• P oduc p ice
assumed o be
€400/
MTO-MOGD Al e na i e syn hesis 99.3 34.4 23.0% 56.9
pa hway including
ke osene and
diesel as end
p oduc .
Sou ce: Upda ed om Laaksonen e al. (2021). (h ps://lu pub.lu . i/bi s eam/handle/10024/
162597/P2X%20Jou seno%20Final%20Repo .pd ?sequence=1&isAllowed=y), Table4.3, p.67.
3.1 Mon e Ca lo simula ion
In Table10.3, he inpu a iables o he SimDec Mon e Ca lo simula ion a e
assumed o be uni o mly dis ibu ed wi hin he anges o he alues used in
he p e ious sensi i i y analysis s udy (i.e. Table10.1). The a ia ion in all
p oduc p ices is assumed o be he same as o he Gasoline p ice, anging
om 63% o 114%.
The oolbox o echno-economic assessmen wi h SimDec 239
om esidual hea and oxygen we e no s udied in de ail, as hei in luence
would no elimina e he dominance o end p oduc p ice, hyd ogen p ice,
and in es men on p o i abili y. Using hese assump ions, he model was sim-
ula ed 50,000 imes, and he da ase was analyzed using he SimDec Ma lab
package.2
3.2 Simula ion Decomposi ion
The ou pu was analyzed using bo h he simple binning app oach o sensi-
i i y indices compu a ion and SimDec isualiza ion (see Chap e 2 o his
book, Kozlo a, Roy, e al. (2024)).
The analysis was pe o med in ou i e a ions:
1. Base scena io only (ex ension o ea lie OAT analysis, Sec ion2.3.1)
2. All scena ios (ex ension o ea lie scena io analysis, Sec ion2.3.2)
3. Cu en ly ealis ic scena ios (upda ed unce ain y assump ions and new
se o scena ios)
4. Me hanol elec olysis scena io (cu en ly unde conside a ion as a
pilo case)
Table 10.3 Va ia ion in inpu pa ame e s
Inpu a iable Range Dis ibu ion
Elec ici y p ice, €/MWh [20, 50] Uni o m
Hyd ogen pu chase p ice, €/MWh [10, 30] Uni o m
P oduc selling p ices [63%, 114%] Uni o m
Me hanol p ice, €/ n [253, 455] Uni o m
Gasoline p ice, €/ n [1000, 1800] Uni o m
Ke osine p ice, €/ n [1059, 1907] Uni o m
Diesel p ice, €/ n [1081, 1947] Uni o m
LPG, €/ n [323, 582] Uni o m
To al in es men ese e Uni o m
Deb in e es a e [1%, 5%] Uni o m
O&M cos s
Ope a ions, % o ac ual e enue [2%, 4%] Uni o m
Main enance, % o echnical e enue [3%, 5%] Uni o m
Ope a ion ime, h/a [6000, 8000] Uni o m
In es men subsidy, sha e o [30%, 50%] Uni o m
echnical in es men
Scena io {1} – Base scena io Disc e e
{2} – Base scena io
elec olysis
{3} – MTG 2.0
{4} – MeOH
{5} – MTO-MOGD
NPV was chosen as he ou pu a iable ins ead o IRR. The con ibu ions
240 Hannu Ka junen e al.
3.2.1 Base scena io only (ex ension o OAT, Sec ion2.3.1)
The Base scena io is il e ed om he simula ed da ase , esul ing in he
ex ac ion o 9,922 co esponding ou pu s om he 50,000 da a poin s.
Table10.4 shows he i s -o de sensi i i y indices (indi idual in luence o
each inpu a iable) o enable a anking o he inpu a iables by hei ela i e
impo ance. The sensi i i y indices indica e ha Gasoline p ice is he mos
in luen ial a iable, ollowed by Hyd ogen p ice, and hen by he In es men
ese e. The second-o de e ec s a e all negligible. This inding implies ha
he model is addi i e and ha hese esul s a e consis en wi h he p e ious
OAT analysis (Table10.2).
Fo he decomposi ion, he wo mos in luen ial inpu a iables, Gasoline
p ice and Hyd ogen p ice, a e chosen. The esul ing SimDec g aph is shown
in Figu e10.3.
Figu e10.3 exhibi s a mono onic ela ionship be ween he mos in luen-
ial inpu a iables and he ou pu . NPV inc eases wi h inc easing Gasoline
p ice, since i a ec s e enues, and dec eases wi h Hyd ogen p ice, since his
con ibu es o cos s. Mos o he High sub-dis ibu ion po ion o he Gaso-
line p ice lies in he posi i e NPV ange, signi ying he o e all g ea po en ial
o his echnology. Howe e , mos o he in luence o e p o i abili y esides
in ex e nal ma ke ac o s beyond he con ol o managemen .
3.2.2 All scena ios (ex ension o scena io analysis, Sec ion2.3.2)
Table10.5 shows he sensi i i y indices compu ed o he indi idual scena -
ios o e he en i e da ase (wi h he new Scena io a iable included as a
sepa a e inpu ).
Table 10.4 Sensi i i y indices o Base scena io
Inpu a iable Sensi i i y index
Gasoline p ice 55%
Hyd ogen p ice 16%
In es men ese e 16%
Ope a ion ime 5%
O&M 4%
In es men subsidy 2%
Deb in e es a e 1%
Elec ici y p ice 0%
LPG P ice 0%
Ke osine P ice 0%
Diesel P ice 0%
Me hanol P ice 0%
To al 100%
The oolbox o echno-economic assessmen wi h SimDec 241
Figu e 10.3 Simula ion Decomposi ion o NPV (Base scena io) by Gasoline p ice
(55%) and Hyd ogen p ice (16%). (colou image is accessible ia he link)
Colou Gasoline p ice, €/ Hyd ogen p ice, €/MWh NPV, M€
Min Mean Max P obabili y
Low
[1,000, 1,267] Low [10, 17] −56 −11 45 11%
Medium [17, 23] −70 −24 29 11%
High [23, 30] −83 −37 13 11%
Medium
[1,267, 1,533] Low [10, 17] −39 15 83 11%
Medium [17, 23] −47 157 11%
High [23, 30] −67 −13 54 11%
High
[1,533, 1,800] Low [10, 17] −19 41 104 11%
Medium [17, 23] −34 28 89 11%
High [23, 30] −44 14 73 11%
Table10.5 clea ly indica es ha he Scena io a iable is he mos in luen-
ial pa ame e o e he en i e da ase . Howe e , each scena io demons a es
i s own ela i ely unique sensi i i y p o ile and ha p oduc p ice has a sig-
ni ican e ec on p o i abili y o each scena io. In he Base elec olysis sce-
na io, Elec ici y p ice is he mos impo an ac o , since he hyd ogen is
p oduced in-house and equi es elec ici y. In es men ese e appea s sig-
ni ican in he MTO-MOGD scena io, which can be pa ially explained by
he la ge absolu e in es men .

242 Hannu Ka junen e al.
Figu e10.4 decomposes he en i e da ase by Scena io and Gasoline p ice.
The co esponding sensi i i y indices appea in he legend.
The decomposi ion shows ha he Base scena io elec olysis (yellow) is
associa ed wi h a g ea e unce ain y (as i is wide ) han o he scena ios and
is conside ably shi ed in o he nega i e NPV ange wi h only a negligible
posi i e po ion. All o he scena ios essen ially lie on op o each o he wi h
a simila p o i abili y p o ile. The MeOH scena io exhibi s a much lowe
upside po en ial han Base scena io, MTG, and MTO-MOGD, oge he wi h
a nega i e expec ed mean (see mean NPV o he Medium Gasoline p ice in
each scena io). The in luence o Gasoline p ice p o ides a no iceable ho i-
zon al shi o shades in he Base scena io and MTG, while also possessing
he highes sensi i i y indices. The shi is no iceable in he Base scena io elec-
olysis, al hough less p onounced, gi en he alue o i s sensi i i y index. In
he MeOH and MTO-MOGD scena ios, he shaded sub-dis ibu ions clea ly
lie on op o each o he , which p o ides a isual con i ma ion o hei negli-
gible sensi i i y indices.
The SimDec analysis isually inc eases he amoun o insigh o e he
ea lie de e minis ic scena io analysis. Fi s ly, a e y di e en impo ance
p o ile o inpu a iables is e ealed in each scena io. Secondly, he dis ibu-
ions o he SimDec cha s ein o ce a dis inc isual sense o he unce ain y
exposu e om each p ojec . Thi dly, he decomposi ion u he guides he
decision-make by p o iding a deepe comp ehensi e unde s anding o how
di e en ac o s in e ac , he eby a ec ing he o e all p o i abili y o he
in es men .
Table 10.5 Sensi i i y indices o all scena ios and he en i e da ase
Scena io Base case Base case
elec olysis MTG MeOH MTO-MOGD Al oge he
Elec ici y p ice30% 52% 1% 1% 0% 2%
Hyd ogen p ice416% 0% 15% 27% 17% 5%
In es men ese e 16% 15% 16% 17% 27% 6%
Gasoline p ice555% 24% 56% 0% 2% 7%
Me hanol P ice 0% 0% 0% 46% 0% 8%
Ke osine P ice 0% 0% 0% 0% 8% 0%
Diesel P ice 0% 0% 0% 0% 21% 0%
LPG P ice 0% 0% 0% 0% 0% 0%
Deb in e es a e 1% 1% 1% 0% 1% 0%
O&M 4% 4% 4% 4% 7% 2%
Ope a ion ime 5% 0% 5% 2% 9% 1%
In es men subsidy 2% 2% 2% 2% 3% 1%
Scena io - - - - - 66%
Sum 100% 97% 99% 99% 96% 97%
The oolbox o echno-economic assessmen wi h SimDec 243
3.2.3 Cu en ly ealis ic scena ios
A e he sensi i i y analysis eplica ion, he model assump ions we e
upda ed o e lec cu en condi ions. The ollowing scena io upda es we e
implemen ed:
Figu e 10.4 Simula ion Decomposi ion o NPV by Scena io (66%) and Gasoline
p ice (7%). (colou image is accessible ia he link)
Colou Scena io Gasoline p ice, €/
(sensi i i y indices and
s a es)
NPV, M€
Min Mean Max P obabili y
Base
scena io
elec olysis
24% Low [1,000, 1,267] −260 −143 −33 7%
Medium (1,267, 1,533] −242 −119 −8 7%
High (1,533, 1,800] −214 −92 22 7%
MeOH 0% Low [1,000, 1,267] −95 −29 40 7%
Medium (1,267, 1,533] −101 −29 42 6%
High (1,533, 1,800] −99 −28 42 7%
MTO-MOGD 2% Low [1,000, 1,267] −85 −6 94 7%
Medium (1,267, 1,533] −91 −3 91 7%
High (1,533, 1,800] −83 396 7%
MTG 56% Low [1,000, 1,267] −100 −30 39 7%
Medium (1,267, 1,533] −67 −1 77 6%
High (1,533, 1,800] −41 26 101 7%
Base
scena io 55% Low [1,000, 1,267] −83 −24 45 7%
Medium (1,267, 1,533] −64 183 6%
High (1,533, 1,800] −44 28 104 7%
244 Hannu Ka junen e al.
• Only elec olysis scena ios we e conside ed. This assump ion is ela ed
pa ly o local de elopmen s and also o e lec he iew ha hyd ogen
canno be sou ced eliably and in signi ican scale as a by-p oduc om
exis ing p ocesses. Consequen ly, P2X p ocesses mus independen ly
secu e any hyd ogen equi ed.
• One addi ional scena io is in oduced. The MTG Elec olysis specula i e
scena io assumes a mo e e icien and less cos ly elec olyse . In addi ion,
he oxygen ob ained as a by-p oduc om elec olysis is assumed o ha e
a alue o €20/MWh.
• The a ia ion o p oduc selling p ices is upda ed – o [400, 1000] €/ n o
me hanol and ±50% o e e y hing else.
• Elec ici y p ice is upda ed o a ange o [30, 60] €/MWh.
• The a ia ion in In es men ese e is d opped and ixed a 15%. The a i-
a ion o To al In es men cos is in oduced ins ead wi hin he ange ±30%.
• The In es men subsidy is changed o a bina y a iable wi h alues [0,
40%] ha ep esen he unce ain y in ecei ing he subsidy.
Table10.6 p o ides he sensi i i y indices calcula ed, as be o e, o he
indi idual scena ios o e he en i e da ase . Once again, he Scena io a i-
able is conside ed as a sepa a e inpu .
A numbe o di e ences can be obse ed in compa ison wi h he p e i-
ous case (Table10.5). Because only elec olysis cases ha e been conside ed,
he Elec ici y p ice is uni o mly in luen ial ac oss all scena ios, while, con-
e sely, Hyd ogen p ice is ne e impo an . Howe e , he In es men subsidy
becomes mo e in luen ial a e i s bina y a iable modi ica ion. The scena io
wi h he highes impac on To al in es men , MTO-MOGD elec olysis,
e eals he la ges sensi i i y o In es men subsidy. P oduc p ices emain
he mos impo an p o i abili y ac o h oughou .
Figu e10.5 shows he decomposi ion o in es men p o i abili y esul ing
om a iables Scena io and Gasoline p ice.
All elec olysis scena ios exhibi poo p o i abili y p o iles, wi h he majo -
i y o hei sub-dis ibu ions alling in o he nega i e NPV ange. The consid-
e ably lowe ed sensi i i y index o Scena io (12% he e as opposed o 66%
p e iously) is due o he a he -s acked appea ances o he sub-dis ibu ions.
The MTG Elec olysis specula i e and MeOH Elec olysis demons a e he
highes upside po en ials o all he scena ios.
3.2.4 Me hanol elec olysis scena io
In his sec ion, he MeOH elec olysis case is sc u inized mo e closely. MeOH
elec olysis ep esen s he ac ual scena io chosen o he P2X cons uc ion
p ojec a Lappeen an a. Acco ding o Table10.6, he mos in luen ial inpu
a iables behind i s p o i abili y a e Me hanol p ice (56%) and Elec ici y
p ice (25%). Consequen ly, Figu e10.6 illus a es a decomposi ion based
upon hese wo ac o s.
The oolbox o echno-economic assessmen wi h SimDec 245
Table 10.6 Sensi i i y indices o he upda ed model wi h elec olysis-only scena ios
Scena io Base case
elec olysis MTG Elec olysis MeOH Elec olysis MTO-MOGD
Elec olysis MTG Elec olysis
specula i e Al oge he
Elec ici y p ice 26% 24% 25% 29% 22% 22%
Hyd ogen p ice60% 0% 0% 0% 0% 0%
To al in es men 12% 10% 8% 17% 9% 13%
Gasoline p ice 48% 51% 1% 3% 57% 27%
Me hanol p ice 0% 0% 56% 0% 0% 13%
Ke osine p ice 0% 0% 1% 8% 0% 1%
Diesel p ice 0% 0% 0% 23% 0% 3%
LPG p ice 1% 0% 0% 1% 0% 0%
Deb in e es a e 1% 1% 1% 1% 1% 1%
O&M 3% 2% 2% 3% 2% 2%
Ope a ion ime 1% 0% 1% 0% 1% 0%
In es men subsidy 10% 11% 8% 18% 9% 10%
Scena io - - - - - 12%
Sum 102% 101% 103% 103% 103% 103%
252 Hannu Ka junen e al.
Appendix 1: Inpu a iables o
he DCF model (base scena io/
MTG) (Laaksonen e al., 2021)
Inpu a iable Nume ic alue Uni Sou ce o in o
(assump ion)
Ope a ion ime 8,000 h/a
P oduc quan i ies
• Me hanol 25,000 /a Aspen modelling and
• Gasoline 8,750/9,500 /a case desc ip ion
• Diesel 0 /a (me hanol quan i y
• Ke osine 0 /a ixed).
• LPG 2,000/1,000 /a
• Pu ge s eam 300/500 /a
• Oxygen 0 /a
• Wa e 0 /a
• Hea 0MWh/a
P oduc selling p ices
• Me hanol 0€/ Selling p ices o end
• Gasoline 1,400/1,583 €/ p oduc s a e based
• Diesel 1,500/1,677 €/ on ma ke analysis
• Ke osene 1,500/1,712 €/ and he knowledge
• LPG 512 €/ o expe s in he
p ojec .
P oduc ion a io (plan a ailabili y)
• Fi s yea 50 %
• Yea s 2–20 100 %
Technical in es men
cos s
• Hyd ogen 2.3/5.2 M€ Technical in es men
• Ca bon dioxide 18.5 M€ cos s a e based on
• MeOH syn hesis 16.7 M€ budge a y o e s and
• MTG syn hesis 19.3/17.6 M€ knowledge o expe
• Auxilia y sys ems 1.0/2.0 M€ in
• O he in es men 4.5/6.6 M€ p ojec eam.
cos s*
Rese e (%) 15 %
Wo king capi al addi ion 0.5 M€
(cash ese e)
Financing
• In es men subsidy 40 %
• Deb 70 %
• Equi y 30 %
Cos s and expenses du ing ope a ion
(Con inued)

The oolbox o echno-economic assessmen wi h SimDec 253
Inpu a iable Nume ic alue Uni Sou ce o in o
(assump ion)
• Ope a ion cos s (as 2 % Annual p oduc ion
pe cen age o ac ual amoun s and annual
e enue) consump ions o
• Main enance cos s (as 3 % elec ici y, s eam,
pe cen age o echni-hyd ogen, and ca bon
cal in es men ) dioxide a e based on
• Elec ici y 22,470/29,920 MWh Aspen modelling.
consump ion P ices o aw ma e-
• Elec ici y p ice 40 €/ ials (elec ici y,
(including ans e ee) MWh s eam, hyd ogen,
• S eam consump ion 60,312/33,200 MWh and CO2) a e based
• S eam p ice 20 €/ on he knowledge o
MWh expe s in he p ojec
• H2 consump ion 182,000 MWh and exis ing ma ke
• H2 p ice 15 €/ p ices.
MWh
• Real es a e ax (pe -1.43 %
cen age o building
in es men , excluding
equipmen )
• Insu ance cos s (as 0.25 %
pe cen age o deb )
• Adminis a ion cos s 2 %
(pe cen age o ac ual
e enue)
O he sou ce da a
• Deb a e 2 %
• Cos o equi y 6 %
• Change % o WACC 0%/a
(weigh ed a e age
cos o capi al)
• Ra e o in la ion 0 %
• Income ax % 0 %
• Numbe o yea s o 20
deb amo iza ion
• S aigh -line dep ecia-20
ion (yea s)
• Residual alue 0 €
No e: LPG, liquid pe oleum gas; WACC, weigh ed a e age cos o capi al.
*O he cos s include elec ici y connec ion ees, in as uc u e ( oads, e c.), buildings,
enginee ing, in e es and expenses du ing cons uc ion, bank ees, land lease be o e he
s a -up, and pe mi ing.
Pa IV
Applica ions: Enginee ing
DOI: 10.4324/9781003453789-15
This chap e has been made a ailable unde a CC-BY-NC-ND 4.0 license.
Abs ac
The eliabili y o s eel s uc u es is a complex nonlinea phenomenon ha
depends on mul iple ex e nal and echnological ac o s. Accumula ed a igue
can lead o a sudden collapse o cons uc ion, esul ing in los epu a ions,
sunk in es men s, and e en loss o li es. Thus, accu a e models ha cap-
u e a igue damage accumula ion a e o pa amoun impo ance, as a e he
adequa e me hods ha explain and communica e he complex inpu –ou pu
ela ionships o he model.
In his s udy, we apply Simula ion Decomposi ion (SimDec) o a a igue
assessmen model de eloped o welded join s. SimDec exposed and com-
munica ed a h ee-dimensional he e ogeneous e ec in he model. The h ee
inpu a iables in e ac pai wise and a ec he ou pu in a nonlinea ashion
condi ioned o each o he . Iden i ying such e ec s is c i ical when designing
eliable s eel s uc u es.
1 In oduc ion
Mechanical sys em componen s, such as ha ound in indus y p ocess
equipmen , b idges and in as uc u es, ehicles and anspo a ion equip-
men , machine y, and c anes, play an impo an ole in he unc ioning o
a ious indus ies. The mechanical design o hese sys ems needs o sa is y
he echnical equi emen s (i.e. he unc ions o ope a ions needed by an
end-p oduc ). These unc ions can in ol e ene gy con e sions, load-bea ing
capaci ies, and/o accessibili y and dimensions o ce ain space. In addi ion
o he echnical equi emen s, he mechanical sys em mus ul il he s uc-
u al sa e y and in eg i y du ing he se ice load ac ions. This is necessa y in
o de o a oid loss o expensi e s uc u al asse s and in as uc u e o loss
o human li es due o he sudden collapse o up u es o mechanical com-
ponen s in he wo s case. In he con ex o s uc u al design and analysis,
mechanical indus ies ely hea ily on modelling and simula ions o add ess
Chap e 11
Cap u ing mul i-dimensional
nonlinea beha iou o a s eel
s uc u e eliabili y model –
global sensi i i y analysis
An i Ahola, Ma iia Kozlo a, and
Julian Sco Yeomans

258 An i Ahola, Ma iia Kozlo a, and Julian Sco Yeomans
such hings as s uc u al beha iou (s eng h, de lec ions, s abili y), use
expe ience and con ol sys ems, and e i ica ion o a ious unc ionali ies.
Due o he inc eased compu a ional esou ces, nowadays, hese models a e
mo e equen ly buil on a nume ical basis using comme cially a ailable so -
wa e. I espec i e, i emains c ucial o unde s and he unde lying beha iou
o hose models in o de o make e ec i e decisions abou he design o mo e
esilien s uc u es.
In he con ex o s uc u al applica ions, s eel ma e ials a e widely used
due o hei excellen mechanical-pe o mance- o-weigh a io, widesp ead
a ailabili y, economical p o i abili y, and manu ac u abili y. Because o
his, s eel ma e ials ha e been employed in many o he a o emen ioned
ields. Amongs di e en ailu e c i e ia, a igue is o pa amoun impo -
ance, pa icula ly o hose componen s subjec ed o cyclic and/o dynamic
load condi ions. Fa igue is a phenomenon in which a s uc u al elemen
expe iences c acking unde cyclic o luc ua ing s ess load condi ions ha
a e lowe han he yield o , ul ima ely, s eng h o he ma e ial. Ahigh
ac ion o epo ed ailu es in s eel componen s can be a ibu ed o he
a igue phenomenon (Hobbache , 2020). Se e al s udies ha e e en epo ed
ha mo e han 50% o ailu es in me allic componen s esul om a igue
(S ephens e  al., 2000). Some o hese a igue-o igina ing ailu es ha e
caused se e e consequences: he c ash o he i s comme cial passenge je
plane (De Ha illand, 1954, US), he capsizing o he Alexande L. Kielland
oil pla o m (1980, No way), and he de ailmen o a high-speed ain in
Eschede (1998, Ge many) claimed 21, 123, and 101 human li es, espec-
i ely. Compa ed o many o he ailu e mechanisms, a igue phenomenon
can be complica ed by mul iple in luencing ac o s. In addi ion, he unce -
ain y ela ed o he p edic ed ope a ing load condi ions gene ally p e en s
an accu a e assessmen o a igue and s uc u al li e cycle in enginee ing
(Hul g en e al., 2021). Taking in o accoun he ac ha s eel p oduc ion
cu en ly gene a es mo e han 7% o he global CO2 emissions (Wo ld S eel
Associa ion, 2021), he e is an escala ing need o c ea e mo e sus ainable,
high-pe o ming s uc u al s eel applica ions.
S eel s uc u es usually inco po a e welding as he joining me hod o c e-
a e pe manen connec ions. Welded connec ions a e suscep ible o a igue
ailu es as he p ocess in oduces geome ical discon inui ies, ensile esidual
s esses, and po en ial laws in o he ma e ial. O e he pas ew decades,
g ea e o s ha e been employed o es ablish design and analysis me hodolo-
gies o a igue assessmen s o welded connec ions. Ac ing s ess, o s ain
ampli ude, has been iden i ied as one key pa ame e (B aun e al., 2022).
Consequen ly, he as majo i y o a igue assessmen app oaches u ilize
applied s ess-based me hods ha ha e also been documen ed in in e na-
ional p oduc and (s eel) s uc u e s anda ds (EN 1993-1-9, 2005). These
me hods ha e clea ly es ablished co ela ion be ween applied s ess and li e
(S-N cu es), o example, using Basquin o equi alen equa ions (Dowling,
2013). The model pa ame e s o such equa ions a e usually de e mined ia
Mul i-dimensional nonlinea beha iou o a s eel s uc u e 259
expe imen al es ing, i.e. a igue es ing is ca ied ou on componen s. F om
empi ical obse a ions (applied s ess e sus li e da a), he model pa ame e s
a e hen s a is ically e alua ed. E en hough local s esses would be used, he
pa ame e s ob ained a e based on he s ochas ic models. A he high-cycle
a igue (HCF) egime, usually a Gaussian dis ibu ion o expe imen ally
de e mined a igue li es (a a ce ain load le el) is ob ained om which he
cha ac e is ic design cu es a e hen de e mined a he decided su i al p ob-
abili y. Due o his, mos a igue app oaches conside ac o s con ibu ing
o a igue in a s a is ical manne , i.e. co ec ion ac o s and di e en design
cu es a e ob ained o ce ain ep esen a i e da ase s. To adop addi ional
pa ame e s go e ning a igue pe o mance o welded connec ions, such as
ma e ial s eng h and esidual s esses, a mul ipa ame ic 4R me hod has
been p oposed. Use o he me hod enables a conside a ion o he combined
e ec s o he a o emen ioned pa ame e s o imp o e he accu acy o a igue
assessmen s, pa icula ly in he con ex s o combined pos -weld ea men s
(Ahola e al., 2021) and/o a iable ampli ude loads (Lipiäinen e al., 2023;
G önlund e al., 2024; Rohani Ra a e al., 2024).
Sensi i i y analysis o such complex models is an essen ial componen o
hei design, analysis, and decision-making p ocesses (Iooss e al., 2022).
Howe e , e en ad anced global sensi i i y analysis echniques lack he means
o iden i ying he shapes o he in e ac ions in a model and o communica ing
hei impo ance o decision-make s (Kozlo a, Moss, e al., 2024). Simula-
ion Decomposi ion (SimDec) is an app oach ha builds on global sensi i i y
analysis and ex ends i in o a isualiza ion o he mos c i ical sys em beha -
iou (Kozlo a, Roy, e al., 2024). In his chap e , we explo e he added alue
o SimDec con as ed wi h p e iously done se ies o one-a -a- ime sensi i i y
analyses o he 4R model.
In he nex sec ion, he 4R me hod, i s compu a ional model, and a
desc ip ion o p e iously conduc ed sensi i i y s udies a e summa ized.
Sec ion3 desc ibes he se -up o he Mon e Ca lo simula ion, he compu-
a ion o sensi i i y indices, and he co esponding se ies o isualiza ions.
The SimDec app oach indica es a single main decomposi ion in ol ing he
h ee mos in luen ial a iables, which in e ac pai wise, p oducing nes ed
he e ogeneous e ec s. Fu he mo e, he single-inpu decomposi ions a e ana-
lyzed in conjunc ion wi h in e ac ion decomposi ions using each pai o inpu
a iables. The chap e concludes wi h a compa ison o he esul s o ea lie
sensi i i y analysis s udies and wi h a discussion o he added alue p o ided
by SimDec o his speci ic case.
2 Compu a ional model
2.1 4R me hod
The 4R me hod has been de eloped o cons uc mo e accu a e assessmen s
o e ec i e s ess in a igue s eng h p edic ions. I is a mul ipa ame ic model
260 An i Ahola, Ma iia Kozlo a, and Julian Sco Yeomans
Figu e 11.1 4R model desc ip ion. Inpu pa ame e s: (a) esidual s ess, (b) ma e i-
al’s ul ima e s eng h a he hea -a ec ed zone (HAZ), (c) applied s ess
a io, and (d) weld oe adius, and cyclic beha iou a no ch.
(colou
image is accessible ia he link)
ha accoun s o nume ous pa ame e s associa ed wi h he a igue pe o -
mance o welded connec ions. The 4R me hod conside s esidual s esses (
s
es
,
Figu e11.1a), ma e ial ul ima e ensile s eng h (R
m
, Figu e11.1b), applied
s ess a io (R, Figu e11.1c) o ex e nal loading, as well as geome ical weld
quali y ia he weld oe adius (
ue
, Figu e11.1d). Due o he applied ou
(bolded) “R”- ela ed pa ame e s, he app oach was named he 4R me hod.
The local s ess a io is applied in he mean s ess-co ec ion using he
well-known Smi h-Wa son-Toppe (SWT) equa ion (Smi h e al., 1970). As a
esul , he mean s ess-co ec ed e ec i e s ess is applied in he a igue assess-
men s using a con en ional S-N (s ess–li e)–based co ela ion. Sec ion2.2
desc ibes he compu a ion o cyclic s ess beha iou in de ail.
2.2 Compu a ional model
This sec ion ou lines he de ails o he compu a ional model applied in he 4R
me hod. The essence o he 4R me hod is o compu e he local (cyclic) elas ic–
plas ic beha iou a a a igue-c i ical no ch. The cyclic beha iou can be
simula ed based on he nume ical model (e.g. using ini e elemen s), bu i is
usually mo e easible o conduc such analyses using analy ical equa ions due
Mul i-dimensional nonlinea beha iou o a s eel s uc u e 261
o hei complexi y. As an ou pu alue, he mean s ess-co ec ed e e ence
e ec i e no ch s ess ange is compu ed as:
∆∆
k e k uelocal ue m es
R R R
,
/,
,,=
()
−
()
1 (1)
whe e
k e , is he mean s ess-co ec ed ( e e ence) local s ess,
k
is
linea -elas ic no ch s ess ob ained using an e ec i e s ess concep (i.e. ei he
using a ic i ious adius concep o heo y o c i ical dis ance).
Fu he de ini ions o he applicable s ess concep s o welded connec-
ions and cu edges ha e been in oduced in he p e ious wo ks unde aken
by Ahola e al. (2021) and Lipiäinen e al. (2023). The Rlocal alue is ob ained
om he local cyclic beha iou based on he minimum and maximum s ess
as ollows (see also Figu e11.1):
Rlocalmin max
= /
. (2)
Fo a de e mina ion o local beha iou , bo h maximum and minimum
s ess is de e mined. The ma e ial beha iou is desc ibed using an elas ic–
plas ic model. In his con ex , he well-known Rambe g–Osgood model can
be employed (Dowling, 2013). Fo he mono onic load ( i s peak load o a
i s cycle), he ma e ial beha iou is o mula ed as:
=+=
()
+
()
ep
n
EH//
/1 , (3)
whe e
is he ( o al) s ain,
e is he elas ic s ain,
p is he plas ic s ain,
is he s ess,
E
is he modulus o elas ici y, and
H
and
n
a e, espec i ely,
he s eng h coe icien and s ain ha dening exponen o he ma e ial plas ic
beha iou .
Fo he cyclic ma e ial beha iou , he kinema ic ha dening ule is assumed,
and he cyclic ma e ial beha iou is o mula ed as:
=+=
()
+
()
ep
n
EH//
/
22
1, (4)
whe e he a iables a e simila o equa ion (3) bu desc ibed by he ange (
).
To analy ically compu e he elas ic–plas ic beha iou , Neube ’s no ch he-
o y is applied o ob ain plas ic beha iou om elas ic s esses (see Dowling
(2013)). The uppe bound (mono onic load) can be o mula ed as:
max eskmax
max
esk
max
E
R
E
=+
()
=+−
()
()
()
() /
,
22
1 (5)
268 An i Ahola, Ma iia Kozlo a, and Julian Sco Yeomans
Figu e11.3 depic s he dis ibu ion o he ou pu s ess, s e ching om
nea ze o o 900 MPa. The mos in luen ial inpu , esidual s ess, b eaks
down he ou pu dis ibu ion in o h ee pa s acco ding o i s s a es, com-
p essi e & negligible (blue), medium (yellow), and high (g een). In e es ingly
enough, whe eas comp essi e & negligible esidual s ess esul s in a wide
ange o ou pu alues, medium and high esidual s ess ocus he co e-
sponding ou pu alues on a ela i ely cons ained space.
The in luence o he second-impo an inpu a iable, s ess a io, depends
on he s a e o he i s inpu a iable, esidual s ess. I esidual s ess is
medium o high, he s ess a io has a limi ed e ec , which can be seen om
he mino ho izon al shi o shades o yellow and g een. I esidual s ess is
comp essi e & negligible, howe e , he s ess a io plays a signi ican ole.
The hi d impo an inpu a iable, s eel g ade, di ides he ou pu a ib-
u ed o comp essi e & negligible esidual s ess in o wo well-de ined
sub-dis ibu ions (da k-blue scena ios e sus ligh -blue ones). Medium and
high esidual s ess, howe e , is a ibu ed o only a single s eel g ade, mild
o he o me and UHSS o he la e .
Ou pu s ess alues abo e 630 MPa can esul only om h ee combi-
na ions o inpu ac o s: (1) comp essi e & negligible esidual s ess wi h
medium & high s ess a io and UHSS s eel g ade, o (2, 3) high esidual
s ess wi h bo h s ess a io le els and wi h only UHSS s eel g ade possible
in such combina ion. The ou pu s ess alues below 530 MPa can only be
achie ed when s ess a io is e e sed and esidual s ess is ei he comp es-
si e & negligible o medium, no ma e he s eel g ade. Mid alues o he
ou pu s ess a e mos ly comp ised o he h ee scena ios, wo wi h medium
esidual s ess and one comp essi e & negligible one wi h low & high s ess
a io and mild s eel g ade. The mos unce ain (unp edic able o leas unde
con ol) scena io is he one wi h comp essi e & negligible esidual s ess,
low & high s ess a io, and UHSS s eel g ade (ligh -blue); i s e ches o e
90% o he ange o he ou pu .
The decision-making implica ions u n ou o be ela i ely s aigh o -
wa d. When he s uc u al design in ol es high o medium esidual s esses,
he s ess a io does no play an impo an ole in he es ima ion o he ou pu
s ess. This is also in line wi h he gene al unde s anding o he esidual s ess
e ec s on he a igue beha iou o welded connec ions (Hobbache , 2016).
Howe e , o s uc u es wi h comp essi e and low esidual s ess, he accu a e
es ima ion o s ess a io o , i possible, he design o he ope a ing condi ions
is c i ical. I he s ess a io appea s o be high (o he ope a ing condi ions
canno be so ened), he g ade o s eel becomes he nex mos impo an
design pa ame e . Such decision logic is buil based on he isually mos
p ominen he e ogenei ies and illus a ed by he decision ee in Figu e11.4.
To acili a e he pe cep ion o p o essionals, in he decision ee, no malized
alues a e used. These a e ob ained by di iding he ou pu e e ence s ess
k ,e (equa ion (1)) by he applied nominal s ess o
no m=200 MPa.

Mul i-dimensional nonlinea beha iou o a s eel s uc u e 269
Figu e 11.3 Main decomposi ion o he s uc u al eliabili y model ou pu by he mos
in luen ial h ee inpu pa ame e s, explaining 96% o he a iance o he ou -
pu (sum o hei sensi i i y indices) and po aying h ee second-o de e ec s
causing he e ogeneous inpu –ou pu ela ionship. The his og am is s acked and
exposes he en i e simula ion da a wi hou o e lapping. The sha e o da a in
each scena io (o he p obabili y o scena io) is displayed in he igh mos col-
umn o he legend. (colou image is accessible ia he link)
Colou Residual s ess,
σ es
S ess
a io, R S eel
g ade, Rp0.2
Ou pu s ess, Δσk, e Sha e
o da a
Min Mean Max
Comp essi e &
negligible Re e sed Mild 107 332 475 11%
UHSS 11 264 515 11%
Low &
high Mild 320 467 591 22%
UHSS 68 543 819 22%
Medium Re e sed Mild 383 456 524 6%
UHSS NaN NaN NaN NaN
Low &
high Mild 422 499 622 12%
UHSS NaN NaN NaN NaN
High Re e sed Mild NaN NaN NaN NaN
UHSS 630 704 795 6%
Low &
high Mild NaN NaN NaN NaN
UHSS 656 746 851 12%
270 An i Ahola, Ma iia Kozlo a, and Julian Sco Yeomans
Figu e 11.4 Decision ee cons uc ed based on he mos p ominen he e ogenei y in he e ec s o inpu a iables on he ou -
pu s ess (deno ed wi h s ess concen a ion ac o K
, e
). (colou image is accessible ia he link)
Mul i-dimensional nonlinea beha iou o a s eel s uc u e 271
By doing his, a e e ence no ch s ess concen a ion ac o is ob ained. This
ac o di ec ly implies he e ec s on he a igue s eng h capaci y.
K ,,e =
k e /, no m (9)
The decision ee p esen ed in Figu e11.4 should be aken wi h a g ain
o sal , howe e . Fi s ly, he esul ing anges o he ou pu s ess in e sec , so
he di e en b anches o he ee do no lead o exclusi e solu ions, and as
men ioned while discussing Figu e11.3, di e en anges o he ou pu can
be achie ed wi h se e al scena ios. Secondly, he ee nodes a e cons uc ed
om he mos p ominen he e ogeneous e ec s ac oss he en i e ange o he
ou pu . I one, howe e , would p e e o ocus on a subse ange o conside
a limi ed se o applicable solu ions (i.e. ce ain ma e ial s eng h), he deci-
sion logic needs o be econs uc ed om Figu e11.3 again and he esul ing
decision ee migh change i s s uc u e.
3.3.2 Con ibu ion o indi idual inpu s
In his subsec ion, he decomposi ions c ea ed o each inpu a e shown o
illus a e hei indi idual con ibu ion o he a iance o he model ou pu .
P oceeding in o de o signi icance (Table11.2), he i s decomposi ion by
esidual s ess is shown in Figu e11.5. The ange o he inpu a iable is
di ided in o ou s a es; nega i e alues all in o he comp essi e s a e, al-
ues up o 100 cons i u e he Negligible s a e, ollowed by medium and high,
a ibu ed o he di e en s eel g ade le els (Table11.1).
F om Figu e 11.5, one can obse e a a he peculia e ec . While he
comp essi e and negligible s a es co e he majo i y o he model ou pu
alue ange, wi h Comp essi e s e ching u he in o he lowes alues, he
medium and high s a es c ea e na ow, dis inc sub-dis ibu ions ha explain
he wo peaks o he o e all dis ibu ion o he model ou pu . Such ocused
concen a ion o alues in he medium and high s a es explains he high sen-
si i i y index o 51%.
The decomposi ion by s ess a io is depic ed in Figu e11.6. The ange o
he a io alues is di ided in o h ee s a es wi h all nega i e alues cons i u -
ing he e e sed s a e, and he emainde di ided acco ding o he equal ange
p inciple.
Figu e11.6 demons a es a g adual shi o he scena ios o he igh , wi h
he minimums o each scena io s aying u he apa han he maximums.
Such a g adien e ec signi ies he mono onic ype o he inpu ’s e ec .
The decomposi ion by s eel g ade is opposi e o mono onic (Figu e11.7).
Al hough he ange o he s eel g ade alues is di ided in o h ee s a es o
equal sub- anges, only he lowe and he highe ac ually exis in he model,
which cons i u e mild and UHSS s eel g ade, co espondingly.
272 An i Ahola, Ma iia Kozlo a, and Julian Sco Yeomans
Al hough s eel g ade ecei es a ela i ely low combined e ec (only 10%
acco ding o Table11.2), he isualiza ion in Figu e11.7 e eals a clea dis-
inc ion be ween he wo s eel g ades. The mild s eel g ade occupies a ela-
i ely na ow a ea sligh ly shi ed o he le on he g aph, while he UHSS
s eel g ade peaks in he igh pa o he dis ibu ion wi h i s ail co e ing he
en i e ange o he mild s eel g ade scena ios (and going e en lowe beyond
hem). Such an e ec ype ha causes he di e ence in a ia ion o he ou pu
bu less so in he mean is poo ly cap u ed by a iance-based sensi i i y indi-
ces, since hey a e compu ed based on a e ages. SimDec isualiza ion b ings
cla i y and allows in-dep h analysis o such e ec s based on he desc ip i e
s a is ics o he co esponding scena ios (legend).
Colou Residual s ess, σ es Ou pu s ess, Δσk, e Sha e o
da a
S a e Value, MPa Min Mean Max
Comp essi e [−400, 0) 11 413 819 49%
Negligible [0, 100) 322 503 819 16%
Medium [100, 650) 383 481 622 17%
High [650, 950] 630 732 851 17%
Figu e 11.5 Con ibu ion o esidual s ess o he a iance o he ou pu : 51% o
he a iance is explained by he inpu a iable. (colou image is acces-
sible ia he link)
Mul i-dimensional nonlinea beha iou o a s eel s uc u e 273
The ac o wi h he leas signi icance, a igue no ch ac o , demons a es
app op ia ely li le in luence on he SimDec isualiza ion as well (Figu e11.8),
whe e all h ee equally spaced s a es o his inpu la gely in e sec and lie on
op o each o he .
Only a sligh shi on he igh edge o he dis ibu ion explains he com-
pu ed 4% sensi i i y index.
3.3.3 In e ac ion be ween esidual s ess and s ess a io
Residual s ess and s ess a io ha e he s onges in e ac ion e ec and
oge he explain o e 85% o he a iance o he ou pu . Each o he wo
a iables is b oken down in o h ee s a es ( he same as be o e o he esidual
Colou S ess a io, R Ou pu s ess, Δσk, e Sha e o
da a
S a e Value Min Mean Max
Re e sed [−1.2, 0) 11 420 817 50%
Low [0, 0.4) 219 522 825 21%
High [0.4, 0.7] 393 602 851 29%
Figu e 11.6 Con ibu ion o s ess a io o he a iance o he ou pu : 35% o
he a iance is explained by he inpu a iable. (colou image is acces-
sible ia he link)

274 An i Ahola, Ma iia Kozlo a, and Julian Sco Yeomans
s ess) and o equal anges o he s ess a io (Table11.4). The esul ing
decomposi ion is shown in Figu e11.9.
Figu e11.9 is e y simila o Figu e11.3 since he decomposi ion is
cons uc ed om he same wo a iables. Figu e11.9 con i ms he clea
he e ogeneous e ec , which was also obse ed in Figu e11.3. The e ec
o he second impo an a iable, s ess a io, depends on he s a e o
esidual s ess. When esidual s ess is medium o high, he s ess a io
does no a ec he ou pu e y much (sligh ho izon al shi o he shaded
sub-dis ibu ions wi hin he g een and yellow pa s). When he esidual
s ess is comp essi e & negligible, howe e , he s ess a io has a much
mo e p onounced impac (subs an ial ho izon al shi o he blue-shaded
sub-dis ibu ions).
Colou S eel g ade, Rp0.2 Ou pu s ess, Δσk, e Sha e o
da a
S a e Value, MPa Min Mean Max
Mild [255, 523) 107 441 622 50%
-[523, 792) NaN NaN NaN NaN
UHSS [792, 1060] 11 548 851 50%
Figu e 11.7 Con ibu ion o s eel g ade o he a iance o he ou pu : 10% o
he a iance is explained by he inpu a iable. (colou image is acces-
sible ia he link)
Mul i-dimensional nonlinea beha iou o a s eel s uc u e 275
3.3.4 In e ac ion be ween s eel g ade and s ess a io
The nex s ong in e ac ion occu s be ween s eel g ade and s ess a io. The
modelling o he s eel g ade alues is done o he wo case ma e ials, S355
and S950 (Table11.1). Thus, he wo ea lie s a es a e used o his inpu
(Table11.5) and, o cla i y o isualiza ion, is chosen i s o decomposi ion
(Figu e11.10).
F om Figu e11.10, i can be obse ed ha ou pu alues a ibu ed o
mild s eel g ade a e concen a ed in he middle (peaking a a ound 450 MPa),
while he ones a ibu ed o he UHSS s eel g ade a e sp ead o e he en i e
ange o he ou pu and o m ano he peak a ound 700 MPa. The s ess a io
has a isible mono onic impac in mild s eel g ade, and a messy e ec in he
UHSS s eel g ade. This appea s as i mono onici y is epea ed wice, which,
Colou Fa igue no ch ac o , K Ou pu s ess, Δσk, e Sha e o
da a
S a e Value Min Mean Max
Low [2.3, 2.6) 11 467 777 47%
Medium [2.6, 2.8) 12 504 828 30%
High [2.8, 3.1] 17 538 851 23%
Figu e 11.8 Con ibu ion o a igue no ch ac o o he a iance o he ou pu :
4% o he a iance is explained by he inpu a iable. (colou image is
accessible ia he link)
276 An i Ahola, Ma iia Kozlo a, and Julian Sco Yeomans
Table 11. 4 S a es o ma ion o inpu a iables o he supplemen a y
decomposi ion by esidual s ess and s ess a io
Residual s ess S ess a io
S a e Min Max S a e Min Max
Comp essi e & negligible −400 100 Re e se −1.2 −0.6
Medium 100 650 Low −0.6 0.1
High 650 950 High 0.1 0.7
Colou Residual
s ess, σ es
S ess
a io, R Ou pu s ess, Δσk, e Sha e o
da a
Min Mean Max
Comp essi e &
negligible Re e se 11 299 515 22%
Low 68 417 650 13%
High 237 541 819 30%
Medium Re e se 383 446 524 6%
Low 421 476 548 3%
High 428 508 621 8%
High Re e se 630 704 795 6%
Low 656 724 816 3%
High 669 754 851 8%
Figu e 11.9 Supplemen a y decomposi ion o he s uc u al eliabili y model
po aying he in e ac ion e ec be ween esidual s ess and s ess
a io. Thei combina ion explains 86% o he a iance o he ou pu .
(colou image is accessible ia he link)
Mul i-dimensional nonlinea beha iou o a s eel s uc u e 277
Table 11. 5 S a es o ma ion o inpu a iables o he supplemen a y
decomposi ion by s eel g ade and s ess a io
S eel g ade S ess a io
Min Max Min Max
Mild 255 657 Re e se −1.2 −0.6
UHSS 657 1,060 Low −0.6 0.1
- - - High 0.1 0.7
Colou S eel g ade,
Rp0.2
S ess
a io, R Ou pu s ess, Δσk, e Sha e o
da a
Min Mean Max
Mild Re e se 107 370 524 17%
Low 320 446 548 11%
High 366 493 621 23%
UHSS Re e se 11 413 795 16%
Low 67 516 816 11%
High 237 663 851 22%
Figu e 11.10 Supplemen a y decomposi ion o he s uc u al eliabili y model
po aying he weak 4% in e ac ion e ec be ween s eel g ade and
s ess a io. Thei combina ion explains 43% o he a iance o he
ou pu . (colou image is accessible ia he link)
284 Manuel Ga cía Pé ez e al.
The cha ged pa icles achie e ci cula ajec o ies hanks o dipola mag-
ne ic ields ha exe he necessa y Lo en z o ces ha bend hei pa hs
acco ding o he desi ed cu a u e. The a ge magne ic ield is hus a unc-
ion o he desi ed cu a u e ( ixed by he leng h o he accele a o i sel ) and
he mass o he pa icles (Fe acin, 2014). The La ge Had on Collide (LHC)
a CERN has been using dipola ields o abou 8.33 T since 2008. The p o-
posed Fu u e Ci cula Collide (FCC), cu en ly in iabili y s udy, aims o
100 TeV collisions wi h a 100km ing accele a o . Gi en his design choice,
he necessa y (dipola ) magne ic ield is 16 T (Tommasini e al., 2017).
1.1.1 Basics o supe conduc ing Nb3Sn
Some ma e ials/me als may exhibi supe conduc ing beha iou unde he
igh condi ions. This beha iou is cha ac e ized by he absolu e absence o
elec ical esis i i y, he eby enabling la ge cu en densi ies (o he o de o
a ew kA/mm2) o low wi hou any ol age d op o hea losses (Fe acin,
2014). Fo his condi ion o occu , cables o he ma e ial need o be main-
ained below a c i ical empe a u e (usually c yogenic, on he o de o a ew
kel in) and below a maximum ex e nal magne ic ield.
The supe conduc ing dipole magne s in he LHC and many o he pa icle
accele a o s cu en ly use NbTi as supe conduc ing ma e ial. Howe e , his
alloy is no capable o beha ing as a supe conduc o a he magne ic ields
equi ed o he FCC ope a ion. The e o e, Nb3Sn has been selec ed as he
p e e ed supe conduc ing ma e ial o he FCC (Schoe ling e al., 2015), as
i is capable o being supe conduc i e o e wide anges o magne ic ields
and empe a u es (Figu e12.1). In Figu e12.1, he su aces di ide he space
o magne ic ield, empe a u e, cu en densi y in o wo egions. The ma e ial
is supe conduc ing i he wo king condi ions all in he egion on he oppo-
si e side o his su ace.
F om he obse ed da a, i is clea ha NbTi canno gene a e magne ic
ields o 16 T, as i s peak ield (a 0 K and no cu en ) is 14.5 T.
1.1.2 Applica ion on supe conduc ing coils and magne s
Some ypes o supe conduc ing cables consis o mul iple wis ed s ands
(a ound 40) in he o m o a ape. Such a shape, e e ed o as a Ru he -
o d cable, p o es especially p ac ical o winding double-pancake coil. Each
s and (o o de 1mm in diame e ) con ains a a iable numbe ( om ens o
hund eds depending upon he ma e ial and manu ac u ing p ocess) o much
smalle ilamen s wi h he supe conduc ing ma e ial embedded in a s abiliz-
ing ma ix o coppe (see Figu e12.2).
The Ru he o d cable is wound a ound a cen al piece e e ed o as he
pole. Dedica ed space s, wedges, o ille s a e o en added o con ol and
adjus he posi ion o he windings. All o his ensemble (pole, cable wind-
ings, space s/wedges, and ille s) is usually e e ed o as a coil (Figu e12.3).

Sensi i i y analysis o a supe conduc ing magne design model 285
Figu e 12.1 C i ical su aces o supe conduc ing alloys app oxima ed by he co ela ion o Bo u a (1999) and i ed o da a
poin s o Godeke e al. (2007) and Fe acin (2017). (colou image is accessible ia he link)
286 Manuel Ga cía Pé ez e al.
Figu e 12.2 (a) View o an Nb
3
Sn Ru he o d cable showing he s ands and ibe glass insula ion. (b) Close-up o he s ands. (c)
C oss-sec ion o he eRMC/RMM Ru he o d ape consis ing o 40 s ands. (d) De ailed iew o one s and c oss sec-
ion showing he Cu ma ix and he 120 ilamen s in a honeycomb pa e n. (e) An eRMC coil being wound wi h he
cable; he bo om pancake laye has been comple ed.
(colou image is accessible ia he link)
Sou ce: Izquie do Be múdez e al. (2018); cou esy o CERN.
Sensi i i y analysis o a supe conduc ing magne design model 287
Figu e 12.3 CAD iew o an eRMC ( op) and RMM- ype (bo om) coils. (colou image is accessible ia he link)
Sou ce: Izquie do Be múdez e al. (2018); cou esy o CERN.
288 Manuel Ga cía Pé ez e al.
Supe conduc ing coils a e placed su ounding he egion o in e es , he
bo e. The elec ical cu en passing h ough hese coils gene a es he desi ed
magne ic ield. Su ounding he coils, a suppo s uc u e ensu es he neces-
sa y mechanical p e-s ess and s abili y o he coils (Fe acin, 2017). This
combina ion o supe conduc ing coils and suppo s uc u e is usually
e e ed o as a supe conduc ing magne . Synch o ons equi e a numbe o
supe conduc ing magne s in se ies o achie e he ajec o y cu a u e o a
beam passing h ough he bo es. Fo ins ance, he FCC is expec ed o equi e
a ound 4,600 14.3m long 16T dipole magne s (Schoe ling & Zlobin, 2019),
whe eas he LHC u ilizes 1,232 8.33T magne s.
1.2 The eRMC and RMM magne s
1.2.1 Coils and suppo s uc u e
The Enhanced Race ack Model Coil (eRMC) and Race ack Model Mag-
ne (RMM) ep esen wo supe conduc ing magne s designed by he CERN
R&D p og am. They we e concei ed o es he Nb3Sn supe conduc ing alloy
and i s capabili ies/challenges o he FCC as a pa o a i e-yea (2016 o
2021) p og am (Tommasini e al., 2017). The eRMC magne ea u es wo
1240mm long block double-pancake coils si ing on op o each o he . The
RMM magne adds a hi d coil, ea u ing he 50mm bo e inside i s cen al
pole ha i s be ween he wo eRMC coils (Izquie do Be múdez e al., 2017;
Rochepaul e al., 2018). Dedica ed pads o pushe s a e used o comp ess he
coils e ically and ho izon ally. These pads a e bol ed oge he , su ounding
he coils, and G10 ibe glass pla es se e as cushions. The en i e ensemble is
usually e e ed o as he coil pack (Figu e12.4 and Figu e12.5).
Su ounding he coil pack a e e i ic yokes which con ibu e o he
a ge magne ic ield. An aluminium ex e nal shell encloses he ensemble
(Figu e12.6 and Figu e12.7).
The suppo s uc u e was analyzed and alida ed i s wi h he use o
dummy coils made o aluminium blocks (Ga cía Pé ez e al., 2020). The
inal ope a ion o bo h eRMC and RMM success ully achie ed he 16.5T in
he cen al pole and in a 50mm bo e ( espec i ely), as in ended (Pe ez e al.,
2022; Gau he on e al., 2023).
1.2.2 Magne mechanical s eps and powe up
The b i leness o he Nb3Sn supe conduc ing ma e ial makes i s applica-
ion a majo enginee ing challenge. The sel -induced Lo en z o ces end o
open any coil ho izon ally. These o ces a e o he o m
JB
(whe e hese
ec o s ep esen he cu en densi y in A/m² and he magne ic ield in T,
espec i ely). Since he magne ic ield scales up wi h he cu en I, his c oss
p oduc scales up wi h I². This esul s in e y high in e nal o ces ying o
Sensi i i y analysis o a supe conduc ing magne design model 289
Figu e 12.4 CAD iew o c oss sec ion o he eRMC coil pack, ea u ing he coils and he comp essing pushe s. (colou image is
accessible ia he link)

290 Manuel Ga cía Pé ez e al.
Figu e 12.5 CAD iew o c oss sec ion o he RMM coil pack ea u ing he RMM- ype coil be ween wo
eRMC- ype coils, wi h he bo e in he cen e, whe e he 16.5 T ield is a ge ed. (colou
image is accessible ia he link)
Sensi i i y analysis o a supe conduc ing magne design model 291
Figu e 12.6 oke and he shell held in placey he younded bwing he coil pack su
ion. (colou image is accessible ia he link)
Le : Pic u e o he end o he eRMC magne sho
by some shims. Righ : CAD ans e sal c oss-sec
Sou ce: Cou esy o CERN.
292 Manuel Ga cía Pé ez e al.
. (colou image is accessible ia wing 3/8 o he magne iew sho. Righ : Cu o ull assembly
esy o CERN.
: e
); cou
. L RMM magne
he link).
on e al. (2022
12.7
Gau he
e
ce:
uigF
Sou
Sensi i i y analysis o a supe conduc ing magne design model 293
open he coil, since he supe conduc ing cu en densi ies o he cables is o
he o de o 400–600 A/mm². The suppo s uc u e mus ensu e ha he
coils a e comp essed enough in o de o limi he displacemen s caused by
hese o ces, bu no o such an ex en ha he low ma e ial yield limi s a e
eached.
The comp ession is ypically achie ed in he ollowing way. Fi s ly, dedi-
ca ed bladde s illed wi h p essu ized wa e ac upon he gaps in be ween he
yoke hal es and he pushe s o he coil pack. This widens he gap su icien ly
o allow shims o a speci ic wid h o be inse ed manually. These shims a e
wide han he nominal slo gaps (Caspi e al., 2001). Once he bladde wa e
p essu e is elie ed, hese bladde s can be ex ac ed as he coil pack emains
locked and comp essed wi hin he s uc u e by he shims. Secondly, when
he en i e magne is cooled down o c yogenic wo king empe a u es, he
ex e nal aluminium shell sh inks mo e han he es o he ma e ials, u he
aising he o al comp ession. The magne can hen be powe ed o ca y he
cu en h ough he coils and gene a e he ield, as he coils ha e been su -
icien ly p eloaded (comp essed) be o ehand.
2 Compu a ional model
The magne mechanical and magne ic beha iou a e simula ed by s uc u al
and magne ic ini e-elemen models. These models p o ide use ul pa ame-
e s, a iables, and condi ions, such as he necessa y ho izon al in e e ence
(shimming) o a gi en a ge ield, he ma e ial s ess si ua ion, o he neces-
sa y bladde p essu e o inse he keys (shims). Th oughou his ex , he
wo ds keys/shims and in e e ence/shimming a e used in e changeably.
Fini e-elemen models wo k by c ea ing a ( ypically simpli ied) geom-
e y o some en i y ha is unde s udy (Figu e12.8). This geome y is hen
sub-di ided in o much smalle pa s, e e ed o as elemen s (Figu e12.9).
Ma e ial p ope ies and loads (such as weigh , o ces, ic ions, con ac s,
cu en s, mo emen cons ain s) a e de ined on hese elemen s. Thus, i is
possible o app oxima e he solu ion o pa ial-di e en ial equa ions on he
whole domain assuming simpli ied a ia ions (usually linea o quad a ic)
ac oss each elemen . I he esolu ion is ine enough, he model can accu a ely
cap u e he necessa y de ails, a ia ions, and g adien s o he magni udes in
he mo e complex geome y. Figu es12.8 o 12.10 show he buildup o he
FEM model geome y, he disc e iza ion (mesh), and an example o ou pu
solu ion, espec i ely.
In Figu e12.8, he symme ies enable he calcula ion o only 1/4 o a
ans e sal slice o he magne . This is also why o he RMM, only one o
he laye s o he middle coil is modelled. The di e en pa s ha e been col-
ou ed by ma e ial.
An ANSYS Mechanical 2D ini e-elemen model ep esen ing one
c oss-sec ion o he RMM magne is used o his s udy. Only 1/4 o he
300 Manuel Ga cía Pé ez e al.
Figu e 12.11 BH cu es o he e i ic ma e ials u ilized in he model (i on yoke
and e ical pushe , and eRMC pole). (colou image is accessible ia
he link)
3 SimDec analysis
SimDec combines he compu a ion o global sensi i i y indices (Kozlo a e al.,
2023) wi h a isualiza ion echnique based on he mul i a iable decomposi-
ion o a da ase (Kozlo a, Moss, e al., 2024). Ade ailed desc ip ion o he
algo i hm, nuances o i s usage, and ins uc ions o in e p e ing i s esul s
can be ound in Chap e 2 (Kozlo a, Roy, e al., 2024). In his sec ion, he
names o inpu and ou pu a iables appea in bold i alic, and he s a es o
inpu a iables a e shown in i alic.
3.1 Sensi i i y pa ame e s
Ce ain geome ic aspec s o he magne ha e been pa ame ized and will be
a ied in a sensi i i y s udy. The se en pa ame e s a e shown in Table12.2.
The model a ia ions we e simula ed on he CSC1 Puh i supe com-
pu e , whe e each e alua ion cycle equi ed 13 minu es on a e age. Se -
e al po en ial e alua ion le els we e selec ed o each inpu a iable (see
Table12.1) leading o 15,360 possible da a combina ions analysis. A ull
ac o ial expe imen al design, o g id sea ch, was conduc ed o e all he
combina ions o he da a poin s. Howe e , a ious inpu combina ions
esul in degene a i e geome ies due o he yoke adius being oo small
o he size o he coil pack being oo la ge. A e disca ding hese cases
po aying un ealis ic geome ies (Table12.3), 8,261 da a poin s emained
o u he analysis.

Sensi i i y analysis o a supe conduc ing magne design model 301
Table 12. 2 Inpu pa ame e s, hei e alua ion poin s, and physical meaning
Inpu a iables E alua ion poin s De aul (design) alue Aspec compa ison o min and max alues
Cable heigh , cable_heigh {20.25, 21.75,
23.25, 24.75} 21.75mm
To al numbe o cable
windings, n_windings {240, 252, 264,
276, 288,} 264
Thickness o he shell,
shell_ hickness {40, 80, 120} 70mm
(Con inued)
302 Manuel Ga cía Pé ez e al.
Inpu a iables E alua ion poin s De aul (design) alue Aspec compa ison o min and max alues
Radius o he yoke, yoke_ {240, 280,
320, 360} 330mm
Heigh o he e ical
pushe , pad_heigh {534, 539,
544, 549} 539mm
Size o he ho izon al shim,
hkey_size {21, 23,
25, 27} 24mm
Ve ical loca ion o
he ho izon al shim,
hkey_posi ion
{18, 20, 22, 24} 22mm
Table 12.2 (Con inued)
Sensi i i y analysis o a supe conduc ing magne design model 303
Inpu a iables E alua ion poin s De aul (design) alue Aspec compa ison o min and max alues
Radius o he yoke, yoke_ {240, 280,
320, 360} 330mm
Heigh o he e ical
pushe , pad_heigh {534, 539,
544, 549} 539mm
Size o he ho izon al shim,
hkey_size {21, 23,
25, 27} 24mm
Ve ical loca ion o
he ho izon al shim,
hkey_posi ion
{18, 20, 22, 24} 22mm
3.2 Ou pu pa ame e s
The model eco ds 11 ou pu alues o ope a ion iabili y, wi h 7 o hem
selec ed o u he SimDec analysis (Table12.3).
Cu en e lec s he ope a ing physical elec ical cu en lowing h ough
each o he windings. Limi a ions o hese cu en s exis ela ed o he supe -
conduc i i y capabili ies o Nb3Sn (see Figu e12.1).
The conduc o a ea co esponds o he ans e sal c oss sec ion o he
coil. I is p opo ional o he o al numbe o windings and he cable heigh .
The ho izon al in e e ence is he o al alue o he shimming wi h which
he magne is loaded a oom empe a u e. The alue e lec s how much
wide he ho izon al key is han i s gap.
The maximum on Mises s ess in he coil is one o he main ou pu s a
each o he h ee s eps o he mechanical submodel. This s ess should s ay
below he coil deg ada ion limi s (see Table12.1) o 150 and 200 MPa.
The bladde p essu e equi ed o inse he a ge shimming (ho izon al
in e e ence) is also moni o ed. An excessi e p essu e can lead o bladde
ailu es ha ende he oom- empe a u e p eload (shim inse ion) un iable.
These ou pu a iable conside a ions a e summed up in Table12.3.
Typically, he design pa ame e s and p opo ions o hese magne s en ail
complex mul i a iable op imiza ions in ol ing magne ic ield in ensi y, uni-
o mi y, easibili y, e c. Fo SimDec demons a ion pu poses, he design a -
ge s ha e been simpli ied o minimize he coil conduc o a ea (one o main
economic cos componen s o he magne s) while main aining he mechanical
s ess le els below ma e ial ailu e a 16.5T ope a ion and wi h a easible
ho izon al shimming and bladde p essu e.
Table 12. 3 Ou pu a iables expec ed/ iable anges and conside a ion wi hin he
sensi i i y s udy
Ou pu a iable Adequa e ange Sha e o cases wi h
ul illed c i e ion
Cu en , IUnde 14,000 [A] 100%
Conduc o ans e sal a ea (mm ) –
(o 1/4 magne due o symme ies)
Ho izon al in e e ence, hin Be ween 200 and 97%
2000 [ m]
Coil on Mises s ess oom- empe a-Unde 150 [MPa] 98%
u e p eload (1), coil_s ees_1
Coil on Mises s ess a cooldown (2), Unde 200 [MPa] 100%
coil_s ees_2
Coil on Mises s ess a powe ing (3), Unde 200 [MPa] 92%
coil_s ees_3
P essu e o bladde , bladde _P Unde 50 [MPa] 91%
304 Manuel Ga cía Pé ez e al.
3.3 Sensi i i y Indices
Sensi i i y indices a e compu ed using he simple binning app oach (Kozlo a,
Moss, e al., 2024) wi h open-sou ce code a ailable in Py hon, R, Julia, and
Ma lab. The combined sensi i i y indices compu ed appea in Table12.4.
These sensi i i y indices cap u e he inhe en complexi y o he model in which
each ou pu is a ec ed by di e en se s o he inpu a iables. Table12.4 dem-
ons a es ha mos o he ou pu s possess e y di e en sensi i i y p o ile.2
3.4 SimDec analysis o each model ou pu
This sec ion p esen s a de ailed analysis o he sensi i i y indices o each
model ou pu supplemen ed wi h i s co esponding SimDec isualiza ions.
3.4.1 Cu en
The cu en necessa y o achie e he design choice o 16.5 T a he bo e na u-
ally depends upon he coil su ace a ea, which a ies p opo ionally o he
numbe o windings and he cable heigh .
Sensi i i y indices o cu en a e p esen ed in Table12.5. Inpu s cable
heigh and numbe o windings oge he explain 96% o he ou pu a iabil-
i y, while he second-o de e ec s a e negligible. The nega i e alues indica e
co ela ion, which could a ise om he absence o model ou pu o ce ain
combina ions o hese wo inpu s.
The wo mos impo an inpu a iables, numbe o windings and cable
heigh , in he o de o hei impo ance, a e chosen o he isual decomposi-
ion (Figu e12.12).
Table 12. 4 Sensi i i y indices o selec ed model ou pu s
Ou pu s
Inpu s cu en conduc o
a ea hin coil_
s ess_1 coil_
s ess_2 coil_
s ess_3 bladde _P
cable_heigh 42% 57% 2% 15% 43% 55% 3%
n_windings 54% 41% 3% 20% 5% 1% 1%
shell_ hickness 1% 1% 82% 19% 39% 12% 11%
yoke_ 5% 1% 12% 43% 6% 18% 76%
pad_heigh 0% 0% 0% 1% 4% 2% 1%
hkey_size 0% 0% 0% 0% 0% 1% 0%
hkey_posi ion 0% 0% 1% 0% 5% 14% 0%
To al 103% 101% 100% 98% 102% 103% 92%
No e: Values below 0.01 ha e been g eyed ou . The es ima es a e gene ally
wi hin 2–3% con idence in e al.
Sensi i i y analysis o a supe conduc ing magne design model 305
Table 12. 5 Sensi i i y indices o cu en
Inpu a iable Fi s -o de
e ec Second-o de e ec Combined
sensi i i y index
cable_
heigh n_windings shell_
hickness yoke_ pad
_heigh hkey_
size hkey_
posi ion
cable_heigh 43% −3% 0% 2% 0% 0% 0% 42%
n_windings 56% 0% −1% 0% 0% 0% 54%
shell_ hickness 1% 0% 0% 0% 0% 1%
yoke_ 5% 0% 0% 0% 5%
pad_heigh 0% 0% 0% 0%
hkey_size 0% 0% 0%
hkey_posi ion 0% 0%
To al 105% 103%

306 Manuel Ga cía Pé ez e al.
Figu e 12.12 Simula ion Decomposi ion o he RMM supe conduc ing magne
model o ou pu a iable cu en . (colou image is accessible ia
he link)
Colou Numbe o
windings Cable heigh
[mm] Cu en [A]
Min Mean Max P obabili y
240–252 20.25, 21.75 11,858 12,443 13,081 21%
23.25, 24.75 12,712 13,328 14,019 20%
264–288 20.25, 21.75 10,899 11,563 12,287 32%
23.25, 24.75 11,650 12,343 13,142 27%
The g aph appea s dissec ed and ba ely esembles he mo e amilia -looking
con inuous his og am no mally associa ed wi h p obabili y dis ibu ions.
This can be explained by he majo in luence o only wo inpu s on his
ou pu and by he disc e e g id sampling ha e alua es he model o e only
a limi ed se o poin s. Ne e heless, he decomposi ion s ill p o ides isual
insigh and is suppo ed u he by he desc ip i e s a is ics p esen ed in he
legend accompanying he SimDec g aph. The pa e n displayed in Figu e12
Sensi i i y analysis o a supe conduc ing magne design model 307
appea s mono onic, wi h he cable cu en dec easing in numbe o windings
and inc easing in cable heigh .
3.4.2 Conduc o a ea
As he Conduc o a ea is simply he p oduc o cable heigh and numbe o
windings, hese wo inpu s should, in heo y, ully explain he a iabili y
o his ou pu . Howe e , he me hod o compu ing sensi i i y indices om
simula ed da a is only an app oxima e one and can esul in sligh nume ic
noise. Some noise de ia ions can be obse ed in Table12.6, whe e he cable
heigh and numbe o windings accoun o only 98% o he ou pu a i-
ance (wi h he di e ence om 100% co esponding o nume ical noise). The
second-o de e ec s o he conduc o a ea a e negligible, al hough a small
in e ac ion be ween he wo inpu s o 4% can be obse ed, which esul s om
hei mul iplica ion in he model. Shell hickness exhibi s a small co ela ion
wi h cable heigh and numbe o windings. Howe e , since hese inpu s a e
independen , his obse ed co ela ion is a esul o he sample cleaning.
The cable heigh and numbe o windings ully explain conduc o a ea.
The e o e, he co esponding SimDec his og am would consis o e en ewe
dis inc alues han o cu en in Figu e12.12. Consequen ly, he need o
a isualiza ion is elinquished, and he abula ep esen a ion o he disc e e
ou pu is p esen ed in Table12.7, ins ead.
The de aul RMM magne ea u es numbe o windings = 264, wi h
21.75mm cable heigh , esul ing in 6,088mm² conduc o a ea (Izquie do
Be múdez, 2017).
3.4.3 Ho izon al in e e ence
The ho izon al in e e ence is mos ly a ec ed by shell hickness, wi h a
combined sensi i i y index o 82%. The yoke adius shows a 12% in lu-
ence, while all o he inpu a iables ha e a negligible e ec on he ou pu
(see Table12.8). No p onounced second-o de e ec s a e de ec ed, which is
expec ed since an inc eased shell hickness ensu es a much s onge cooldown
comp ession. Consequen ly, less ho izon al shimming is necessa y o main-
ain he pole-coil con ac p essu e o 10 MPa.
The shell hickness and yoke adius oge he explain 94% o he a ia ion
in he ho izon al in e e ence and a e used o decompose i s dis ibu ion in
Figu e12.13.
Figu e 12.13 demons a es ano he mono onic ela ionship pa e n in
which he ho izon al in e e ence dec eases in bo h shell hickness and
yoke adius. This dec ease is no linea . The di e ence o ou pu a e ages
o 80mm and 120mm (yellow and g een) shell hicknesses is 188mm,
whe eas o 40mm and 80mm (blue and yellow), i is 589mm. Apa om
he means, he ou pu a iance dec eases wi h highe shell hickness. This
308 Manuel Ga cía Pé ez e al.
Table 12. 6 Sensi i i y indices o conduc o a ea
Inpu a iable Fi s -o de e ec Second-o de e ec Combined
sensi i i y
index
cable_
heigh n_windings shell_
hickness yoke_ pad
_heigh hkey_
size hkey_
posi ion
cable_heigh 56% 4% −2% 0% 0% 0% 0% 57%
n_windings 39% −1% 0% 0% 0% 0% 41%
shell_ hickness 3% 0% 0% 0% 0% 1%
yoke_ 1% 0% 0% 0% 1%
pad_heigh 0% 0% 0% 0%
hkey_size 0% 0% 0%
hkey_posi ion 0% 0%
To al 99% 101%
Sensi i i y analysis o a supe conduc ing magne design model 309
Table 12. 7 Resul ing conduc o a ea om di e en combina ions o cable
heigh and numbe o windings
n_windings
240 252 264 276 288
cable_heigh ,
[mm]
20.25 5143 5401 5658 5916 6174
21.75 5534 5811 6088 6365 6643
23.25 5924 6221 6518 6815 7112
24.25 6315 6631 6948 7264 7581
causes a la ge o e lap o he yellow and g een scena ios wi h shell hickness
80mm and 120mm, espec i ely, and less wi h he blue one o shell hick-
ness 40mm. These wo pa e ns cause he blue scena io o s ay u he apa
om he es and o ms a so o ca i y in he dis ibu ion.
3.4.4 on Mises coil s ess a s age 1 ( oom- empe a u e p eload)
The on Mises coil s ess a s age 1 is a ec ed by se e al inpu a iables,
including yoke adius (43%), numbe o windings (20%), shell hickness
(19%), and cable heigh (15%) (see Table12.9).
The decomposi ion shown in Figu e12.14 is done o he h ee mos in lu-
en ial inpu a iables ha oge he explain 82% o a iabili y o he ou pu .
Examining he SimDec g aph, one can obse e ha coil s ess a s age 1
dec eases wi h yoke adius and shell hickness, bu inc eases wi h he num-
be o windings.
In e es ingly, he combina ion o shell hickness o 40mm and yoke adius
o 280mm esul s in no iceably dissec ed sub-dis ibu ions o he ou pu .
This obse a ion can be explained by he cable heigh inpu a iable being
excluded om he decomposi ion. I he designe wished o na iga e in o a
dispa a e pa o he sub-dis ibu ions, he decomposi ion analysis could be
easily epea ed o ha espec i e pa o he da ase .
3.4.5 on Mises coil s ess a s age 2 (cooldown)
The on Mises coil s ess a s age 2 exhibi s a di e en sensi i i y p o ile
compa ed o ha o s age 1. A s age 2, cable heigh and shell hickness play
he impo an ole, whe eas he in luence o o he inpu a iables is negligible
(see Table12.10).
The decomposi ion by hese wo mos impo an inpu a iables explains
82% o he ou pu a iabili y and shows non-mono onic pa e ns o ela-
ionships (Figu e 12.15). The lowes shell hickness (40 mm) esul s in
316 Manuel Ga cía Pé ez e al.
Figu e 12.15 Simula ion Decomposi ion o he RMM supe conduc ing magne
model o ou pu a iable coil s ess a s age 2. (colou image is
accessible ia he link)
Colou Cable
heigh
[mm]
Shell
hickness
[mm]
Coil s ess 2 [MPa]
Min Mean Max P obabili y
20.25 40 165.0 169.6 173.5 9%
80 170.1 175.1 179.3 9%
120 172.5 176.5 180.9 9%
21.75 40 158.8 164.2 169.4 9%
80 165.5 169.7 174.6 10%
120 166.9 171.2 175.8 8%
23.25 40 157.3 162.4 167.3 6%
80 163.2 167.9 177.8 10%
120 163.7 169.0 177.5 9%
24.75
40 160.6 164.3 167.2 3%
80 165.0 171.8 184.0 9%
120 166.7 173.2 184.6 9%

Sensi i i y analysis o a supe conduc ing magne design model 317
Table 12.1 1 Sensi i i y indices o coil s ess a s age 3
Inpu a iable Fi s -o de
e ec Second-o de e ec Combined
sensi i i y
index
cable_
heigh n_
windings shell_
hickness yoke_ pad
_heigh hkey_
size hkey_
posi ion
cable_heigh 39% 1% 6% 1% 2% 0% 22% 55%
n_windings 0% 0% 0% 0% 0% 0% 1%
shell_ hickness 9% 0% 0% 0% 1% 12%
yoke_ 17% 0% 0% 1% 18%
pad_heigh 1% 0% 0% 2%
hkey_size 0% 0% 1%
hkey_posi ion 2% 14%
To al 68% 103%
318 Manuel Ga cía Pé ez e al.
Table 12.1 2 E ec s o he hkey posi ion and cable heigh on maximum on Mises s esses in he coil
Si ua ion Aspec Coil s ess a cooldown (2) Coil s ess a powe ing (3) Legend [MPa]
a) de aul
b) alle cable by 2mm pe
laye ; posi ion o he
ho izon al shim lowe ed
c) alle cable, posi ion o he
ho izon al shim main ained
a he cen e o he coil
No e: The maps o he s ess highligh he posi ion and alue (in MPa) o he maximum. No e how when he shim is no well cen ed (si ua ion
b), he s ess ocuses and peaks on he co ne o he bo om laye o windings. (colou image is accessible ia he link)
Sensi i i y analysis o a supe conduc ing magne design model 319
Figu e 12.16 Simula ion Decomposi ion o he RMM supe conduc ing magne
model o ou pu a iable coil s ess a s age 3. (colou image is
accessible ia he link)
Colou Cable
heigh [mm] Yoke adius
[mm] Coil s ess a s age 3 [MPa]
Min Mean Max P obabili y
20.25 280 142.6 150.1 158.0 9%
320 144.8 152.2 160.3 8%
360 147.3 154.3 162.3 10%
21.75 280 137.7 143.7 149.8 8%
320 139.8 146.2 151.8 9%
360 141.5 148.4 155.1 9%
23.25 280 136.3 141.7 146.9 8%
320 138.2 144.5 151.0 9%
360 139.9 147.0 155.8 9%
24.75 280 137.8 143.3 150.5 5%
320 137.8 145.8 156.6 8%
360 139.7 149.2 159.9 8%
320 Manuel Ga cía Pé ez e al.
Table 12.1 3 Sensi i i y indices o bladde p essu e
Inpu a iable Fi s -o de
e ec Second-o de e ec Combined
sensi i i y
index
cable_
heigh n_
windings shell_
hickness yoke_ pad
_heigh hkey_
size hkey_
posi ion
cable_heigh 1% 1% 1% 1% 0% 0% 0% 3%
n_windings 0% 0% 1% 0% 0% 0% 1%
shell_ hickness 9% 2% 0% 0% 0% 11%
yoke_ 74% 0% 0% 0% 76%
pad_heigh 1% 0% 0% 1%
hkey_size 0% 0% 0%
hkey_posi ion 0% 0%
To al 85% 92%
No e: Values below 0.01 a e g eyed ou .
Sensi i i y analysis o a supe conduc ing magne design model 321
Figu e 12.17 Simula ion Decomposi ion o he RMM supe conduc ing magne
model o ou pu a iable bladde p essu e.
Colou Yoke_
[mm] Shell_
hickness
[mm]
Bladde p essu e [MPa]
Min Mean Max P obabili y
280 40 28.2 54.5 62.4 8%
80 42.2 49.5 70.0 11%
120 48.9 55.8 69.5 10%
320 40 20.5 37.3 45.0 9%
80 30.5 35.1 49.4 13%
120 36.8 42.8 53.6 12%
360 40 15.9 25.3 33.1 9%
80 23.2 27.0 36.3 14%
120 25.1 35.2 37.1 13%

322 Manuel Ga cía Pé ez e al.
ness kshell hico oups coded g
)
-colou bladde p essu e wi h
(colou image is accessible ia he link
o e ence on al in e zho i
pai s consis en o Figu e12.17.
o plo
e adius
e
yok
Sca
and
12.18 euigF
Sensi i i y analysis o a supe conduc ing magne design model 323
due o he ac ha a smalle yoke o e s less bladde a ea, he eby equi ing
a highe p essu e in o de o exe a gi en o ce. The shell hickness, howe e ,
po ays a diamond-shape ela ionship wi h bladde p essu e, wi h high and
low shell hickness alues esul ing in in e media e alues o bladde p es-
su e and he medium alue o shell hickness leading o high and low bladde
p essu e. This pa e n occu s o each alue o yoke adius and would no be
isible wi hou u he decomposi ion.
Figu e12.18 highligh s an in es iga ion o he ela ionship be ween blad-
de p essu e and ho izon al in e e ence while p ese ing he decomposi ion
and colou ing logic om Figu e12.17.
Some ends in Figu e12.18 e eal a pa e n ha shows he equi ed p es-
su e g owing linea ly wi h he in e e ence ( he diagonally-s e ched clus e s
o poin s). As in ui i ely expec ed, he wide he a ge ed gap, he highe
he equi ed p essu e o open ha gap. This linea dependency possesses a
slope ha g ows in conjunc ion wi h he shell hickness due o inhe en igid-
i y. Con e sely, o he pa e ns exhibi no p essu e dependence (ho izon ally
s e ched clus e s), mo e o en han no wi hin he same colou ( ep esen ing
a ixed alue o yoke and shell sizes).
Due o he nes ed na u e o he e ec s (pa e ns occu ing inside he
g oups o di e en combina ions o inpu a iables), only one g oup is ana-
lyzed sepa a ely. This analysis is pe o med by ixing he yoke adius a
360mm, he shell hickness a 40mm, and he numbe o windings a
264. The esul ing se o 152 da a poin s was examined using SimDec. The
sensi i i y indices indica e ha cable heigh now explains 86% o blad-
de p essu e a ia ion (compa ed wi h a negligible 3% o he ull da ase ,
Table12.13), hkey posi ion explains 8.5%, hkey size explains 6%, pad
heigh explains 3%, and all o he a iables ha e no in luence (i.e. 0%). The
decomposi ion o bladde p essu e is pe o med by ano he ou pu o in e -
es , ho izon al in e e ence, and he mos in luencing inpu , cable heigh
(see Figu e12.19).
Figu e12.19 shows ha he ho izon al in e e ence and cable heigh o
he selec ed po ion o da a a e highly co ela ed (obse e he many missing
scena ios in he legend). Low in e e ence wi h low cable heigh esul s in
low alues o bladde p essu e, and ice e sa. Mo eo e , lowe alues o
he in e e ence esul in mo e compac anges o bladde p essu e, indi-
ca ing ha hose poin s in which inc easing in e e ence does no seem o
inc ease he bladde p essu e end o occu mo e equen ly wi h he lowes
alues o cable heigh – e ec i ely making he coil pack smalle and less
igid. Un o una ely, no physical explana ion o explain his end has ye
been es ablished.
324 Manuel Ga cía Pé ez e al.
Figu e 12.19 Decomposi ion o bladde p essu e on a limi ed da ase (yoke
adius=360mm, shell hickness=40mm, and numbe o wind-
ings=264) by cable heigh ha explains 86% o a ia ion o he
bladde p essu e, and by ano he ou pu o in e es – ho izon al
in e e ence. Absen due o co ela ion and a ely occu ing sce-
na ios a e ma ked wi h g ey on colou . (colou image is accessible ia
he link)
Colou Hin [μm] Cable_
heigh
[mm]
Bladde p essu e [MPa]
Min Mean Max P obabili y
[1.35, 1.45] 20.25 35.3 36.3 37.5 29%
21.75 37.0 37.6 38.2 3%
23.25
24.75
(1.45. 1.55] 20.25 36.5 36.5 36.5 1%
21.75 36.6 37.4 38.3 26%
23.25 38.7 39.0 39.3 4%
24.75
(1.55, 1.70] 20.25
21.75
23.25 38.0 39.2 40.3 23%
24.75 40.2 41.0 41.8 15%
Sensi i i y analysis o a supe conduc ing magne design model 325
4 Conclusions
This chap e has p esen ed an applica ion o SimDec o a compu a ionally
complex magne ic and mechanical, ini e-elemen model o a supe conduc ing
magne . This model possesses nume ous ou pu s o in e es and SimDec has
been used o show ha he sensi i i y p o iles o hese a iables di e qui e
conside ably. SimDec p o ided a con enien way o exhaus i ely analyze he
mechanical beha iou o he magne s and hei suppo s uc u e. Among o he
esul s, he indings con i med ha he aluminium shell hickness is a majo
con ibu o o he cooldown comp ession wi h espec o necessa y shimming
and coil s esses, and ha he ela i e heigh o he e ical pushe ac ually
has li le e ec on mos pa ame e s, in line wi h he exis ing knowledge in his
ield. One unexpec ed and ye unexplained pa e n be ween bladde p essu e,
in e e ence, and cable heigh is e ealed by SimDec. Consequen ly, SimDec
could be conside ed a powe ul ancilla y ool o de e mining in e depend-
encies and syne gies o he pa ame e s in supe conduc ing magne . F om a
b oade pe spec i e, SimDec has demons a ed a no el way o conduc ing a
sensi i i y analysis on a complex sys em wi h mul iple ou pu s o in e es and
has led o he exposu e o p e iously concealed he e ogeneous e ec s.
Acknowledgemen s
The wo k is suppo ed by g an 220178 om he Finnish Founda ion o
Economic Educa ion and by g an OGP0155871 om he Na u al Sciences
and Enginee ing Resea ch Council o Canada. The au ho s a e g a e ul o
s a o he Magne Design and Technology o he Depa men o Technology
o CERN o he aluable eedback and he ini e-elemen mAPDL models o
he RMM magne .
No es
1 CSC (IT Cen e o Science) is a Finnish cen e o expe ise in in o ma ion echnol-
ogy owned by he Finnish s a e and highe educa ion ins i u ions (h ps://csc. i/web/
gues ).
2 h ps://gi hub.com/Simula ion-Decomposi ion.
Re e ences
Bo u a, L. (1999, Sep embe 26–Oc obe 2). A p ac ical i o he c i ical su ace
o NbTi. P oceedings o 16 h In e na ional Con e ence on Magne ic Technology,
Pon e Ved a Beach, USA.
Caspi, S., Gou lay, S., Ha alia, R., Lie zke, A., ONeill, J., Taylo , C., & Jackson, A.
(2001, Ma ch). The use o p essu ized bladde s o s ess con ol o supe conduc -
ing magne s. IEEE T ansac ions o Applied Supe conduc i i y, 11(1), 2272–2275.
Fe acin, P. (2014). Supe conduc i i y and supe conduc ing magne s o he
LHC upg ade. Cou se Lec u es. h ps://indico.ce n.ch/e en /318566/a ach-
men s/612965/843302/140824_summe -s uden s_I_ inal.pd
332 Anna Sido enko e al.
(Klein, 2015; Walczak, e al., 2012; Klein, 2008). Consequen ly, his unde ly-
ing le el o du ess leads o a high chance o nega i ely impac ing he o e all
quali y o he decision-making p ocess (Keinan, 1987, p.639). As a esul , a
“sa e ” op ion is commonly op ed o ins ead o he op imal o mos s a egi-
cally bene icial one (Wagne & Mo isi, 2019; Bad e e al., 2012).
Humans a e bo h limi ed by hei cogni i e s uc u es (i.e. men al p o-
cessing abili ies) and, a he same ime, o e whelmed by mul i ace ed and
o en disco dan ac o s. All o he condi ions men ioned can induce s ess
(Phillips-W en & Adya, 2020; Ma sden e al., 2006; Le ch & Ha e , 2001;
Hwang & Lin, 1999). In u n, s ess con ibu es o c i ical in o ma ion
being o e looked and disca ded when c i ical decisions mus be aken (Van
B uggen e al., 1998). Technological suppo and da a isualiza ion ools can
help in o e coming s ess- ela ed cogni i e laws and boos he a ionali y o
he decision-making p ocess (Walczak e al., 2012). People encoun e com-
plex dilemmas a bo h o ganiza ional and indi idual le els. Manage s decide
on he s a egic de elopmen o a company and, ou side o hei wo k oles,
indi iduals also mus make choices. While some decisions a e i ial, o he
decisions will shape majo u u e li e ajec o ies. Unde ei he scena io, he
c i e ia ha we need o conside make i challenging o g asp he ull pic u e
o eaching a comp ehensi e solu ion. Accessible and use - iendly model-
ling and isualiza ion ha e he po en ial o assis he decision-making p ocess
and o educe/mi iga e he nega i e impac om inhibi ing ac o s.
In his chap e , we examine six si ua ions based on eal e en s whe e he
speed o he decision-making is no p essing. Thei g a i y and complexi y,
none heless, hinde he abili y o de i e s aigh o wa d solu ions wi hou
employing analy ical ools o suppo he p ocess. The con ex o indi idual
decision-making implies a di e gen quali y o isk ac o s in compa ison o
o ganiza ional ones. This is no he same hing as acing he nega i e epe -
cussions a ising om poo decision-making. To coun e ac po en ial isks,
SimDec is used o aid in he p oblem analysis and solu ion disco e y ha he
six p o agonis s emba ked upon (Kozlo a, Moss, Cae s, e al., 2024).
2 Cases
We conside six decision-making si ua ions ha we e ecen ly encoun-
e ed ei he di ec ly by he au ho s o indi ec ly by hei iends/ amily (see
Table13.1).
The Sa ings case demons a es how he annui y unc ion ansla es a small
mon hly deposi in o a u u e signi ican gain. Simila ly, he Language lea n-
ing case is based on a powe cu e ha ans o ms hou s o s udying in o a
u u e mas e y le el. These wo cases demons a e ha e en a e y basic, sim-
ple unc ion can be s udied wi h SimDec. The SimDec analysis p o ides alu-
able insigh s o decision-making ha can p o e indispensable when e en
mo e sou ces o a ia ion o unce ain y a e included.

New le el o pe sonal decision-making 333
The Mo gage and Fa pe cen age cases ep esen si ua ions whe e wo di -
e en model ou pu s a e analyzed: loan e m in yea s and in e es expenses in
eu os in he o me case, and body weigh in kilos and a pe cen ages in he
la e . The wo ou pu s in he Mo gage case display he exac same depend-
ency s uc u e and he dis ibu ion shape, so one can use he same policy o
a ec bo h ou pu s equally. Con e sely, he a pe cen age case demons a es
how a model can p oduce wo di e en ou pu dis ibu ions wi h di e en
dependency p o iles om he same inpu s. As a esul , a comp omise s a -
egy should be conside ed o pu suing he wo con lic ing objec i es, o he
objec i es hemsel es may need o be econside ed.
The Coun y and Ca choice cases show how mul i-c i e ia decision-making
p oblems, ei he based on objec i e da a o subjec i e a ing scales, can be
ad anced om simple o de ing asks o a mo e in-dep h in es iga ion o
he unce ain y behind each al e na i e and an unde s anding o he d i ing
o ces behind i .
All o he models a e publicly a ailable, oge he wi h he SimDec imple-
men a ion in a ious languages (Kozlo a, Moss, Roy, e al., 2024).1
2.1 Sa ings
Timo leads a ugal li es yle and wan s o con ince his oomma e o i s ben-
e i s. E e y penny ma e s and e en small, bu egula sa ings, can make a
di e ence. The powe o egula sa ings lies in he “mi acle” o compound
in e es . Compound in e es akes in o accoun no only he sum o all p e-
ious sa ings, bu also he in e es al eady acc ued on hem (i.e. in e es is
ea ned on he in e es ). The mo e money ha is sa ed, he as e he g ow h
o he o al balance. Fu he mo e, he longe he money has been sa ed, he
Table 13.1 Modelling cons uc o he six cases conside ed
Case Model Desc ip ion
Sa ings Annui y Deciding on mon hly sa ing amoun by examining
he u u e alue o sa ings
Coun y MCDM wi h a Choosing a coun y o esidence based on pe -
choice a ing scale sonal pe cep ions o di e en c i e ia
Mo gage Cash low model Compu ing he loan du a ion and in e es
expenses unde unce ain in e es a e
Language Powe unc ion Explo ing how much ime should be commi ed
lea ning o language lea ning based on expe imen ally
de i ed lea ning cu e unc ion
Ca choice MCDM wi h Deciding on whe he o buy a ca , and which,
measu ed da a based on hei cos and echnical cha ac e is ics
Fa pe -Addi ion & Unde s anding he e ec o lean and a issue
cen age mul iplica ion educ ion on body a pe cen age
No e: MCDM s ands o mul i-c i e ia decision-making.
334 Anna Sido enko e al.
mo e p ominen he esul s o he accele a ing g ow h The u u e alue o
sa ings ha compound can be de e mined by he ollowing annui y o mula:
()
n
11+ −
FV =P
(1)
whe e FV is he u u e alue o he balance, P is a egula sa ings paymen ,
is he in e es a e, and n is a numbe o ime pe iods The in e es a e should
ma ch he uni s o he numbe o pe iods (i e annual o yea s, mon hly o
mon hs)
The ques ion o in e es is how much di e ence would mon hly ins al-
men s o €100, €200, o €300 make o e a i e-yea sa ings challenge in
which he unce ain in e es a e a ies uni o mly be ween 0% and 10%
To add ess his ques ion, he simple annui y o mula (1) wi h he disc e e
mon hly sa ings amoun and uni o mly dis ibu ed in e es a e was simu-
la ed 3,000 imes o p oduce he dis ibu ion o u u e (in i e yea s) alue o
sa ings2 (see Figu e13 1)
Figu e13 1 shows ha mon hly ins almen s o €300 esul in nea ly ou
imes mo e capi al a e i e yea s in compa ison o ins almen s o €100 (see
da ke po ion o he dis ibu ion on he igh compa ed o he ligh -colou ed
po ion on he le ) The highe sa ings a e na u ally mo e sensi i e o he
Figu e 13.1 Dis ibu ion o u u e sa ings o di e en mon hly sa ing amoun
(ma ked wi h di e en colou s) and unce ain in e es a e. (colou
image is accessible ia he link)
New le el o pe sonal decision-making 335
a ia ions in he in e es a e, which esul s in he wide dis ibu ion along
he X-axis. Highe a es in he €300 scena io gene a e much mo e luc a i e
ou comes in compa ison o he lowe mon hly sa ings scena ios. The heigh s
o he h ee dis inc dis ibu ion pa s do no hold much meaning and a e
only di e en because he same numbe o obse a ions (same a ea) a e dis-
ibu ed on in e als o di e en wid h.
By u he examining he annui y o mula (1), one could no ice ha he
u u e alue o sa ings is linea ly dependen on he egula paymen s, linea ly
dependen on he in e es a e (bu he wo a e mul iplied ein o cing he
e ec o each o he , which is shown in Figu e13.1), bu exponen ially a ec ed
by he numbe o pe iods (Figu e13.2). Thus, he du a ion o sa ings is he
key o weal hy u u e, i only one can emain pe sis en o e he long e m.
By le ing he sa ings pe iod a y be ween 1 and 50yea s, he dis ibu ion
o u u e sa ings changes d ama ically. Sa ings a e now no only impac ed
by he exponen ial e ec o he numbe bu also ein o ced by he in e ac ion
be ween he mon hly sa ing amoun and he in e es a e (Figu e13.3).
Sa ing o 17yea s o less ba ely p oduces a hund ed housand eu os
e en unde he mos a ou able condi ions (high in e es a e and high €300
mon hly paymen ) – see ed scena ios. Only hose who can sus ain 50yea s
o mon hly sa ings can da e o d eam o becoming a millionai e – see he
long ail o he g een scena ios.
Figu e 13.2 Fu u e alue o €200 mon hly sa ings a 5% in e es a e as an expo-
nen o he numbe o yea s. (colou image is accessible ia he link)
336 Anna Sido enko e al.
Figu e 13.3 Fu u e sa ings alue unde unce ain in e es a e (0–10%), a iable du a ion (1–50yea s), and mon hly paymen
(€100, €200, o €300). The X-axis is unca ed; he maximum amoun o sa ings app oaches se en million eu os
when all ac o s a e a ou able. (colou image is accessible ia he link)
New le el o pe sonal decision-making 337
2.2 Coun y choice
On 24 Feb ua y 2022, he li es o millions we e sha e ed when Russia
in aded Uk aine and s a ed a ull-scale wa . Ai s ikes, explosions, ma ial
law, o al panic, and he b u ali y o wa a e – ha is how a amily om Kyi
ended up in Finland. Th ee sis e s, all unde 25, wi h he younges sibling
being 15, we e aken in by a close ela i e. Ayea has since passed - Finn-
ish language cou ses ha e been aken, and esidency documen s ha e been
iled. While he middle sibling mo ed back o Kyi , Da ia, he oldes , ound
he sel con empla ing he u u e. Does she wan o s ay in Finland, e u n
o Uk aine, mo e somewhe e else, and i so, o whe e? Da ia decided ha
i she we e o mo e somewhe e else, i had o be o an English-speaking
coun y – he USA o he UK – whe e he language ba ie would no be a
subs an i e conce n.
Wi h hese ou op ions in mind, Da ia was con on ed wi h ano he
dilemma: How could she make he choice, and wha ac o s should she
accoun o ? Since she had a younge sibling o ca e o , Da ia decided ha
he mos impo an c i e ion o he was o gua an ee he sis e ’s well-being.
Apa om ha , Da ia de eloped six c i e ia ha e lec ed he li e alues:
job a ailabili y, language ba ie , well-being, clima e, heal hca e, and qual-
i y o ood. The c i e ia we e weigh ed by hei pe cei ed impo ance. Each
c i e ion o each coun y was sco ed on a scale om 0 o 100, in a ange
ha e lec ed he subjec i e assessmen , om he mos nega i e o he mos
posi i e ou comes (Table13.2.)
Wide sco e anges e lec he le el o unp edic abili y and ola ili y o
a c i e ion pe cep ion. Gi en he clima e di e si y in he USA, he le el o
sa is ac ion a ies signi ican ly i an exac loca ion o po en ial esidence is
no speci ied. Howe e , na ow anges can s ill deno e unp edic abili y as in
he i s c i e ia sco e o Uk aine. In his ins ance, Da ia o e ed a sco e o
50 ou o 100, posi ioning hei assessmen igh in he middle o he ange.
Table 13.2 Inpu s o mul i- c i e ia decision-making p oblem: choosing a coun y
based on se en c i e ia
C i e ion Impo ance Finland Uk aine UK USA
Min Max Min Max Min Max Min Max
Peace o mind 100 % 80 100 50 50 20 60 060
abou sis e
Job a ailabili y 100 % 020 50 70 050 050
Language com o 90 % 40 50 90 100 50 60 70 80
Wellbeing 100 % 80 100 050 10 60 0100
Clima e 80 % 10 70 50 100 060 0100
Medicine 80 % 70 75 70 80 0100 40 50
Food 80 % 020 100 100 020 050

338 Anna Sido enko e al.
Consis en wi h i s lack o a iabili y, i po en ially con eys a sen imen o
high unce ain y ela ed o he sa e y o he younge sis e . The esul ing
ambigui y deno es ha i is bene icial o examine he assessmen logic and i s
con ex , ins ead o ocusing solely on he sco ing esul s.
Agg ega ions comp ised o many c i e ia in which he e alua ion is
sp ead h oughou se e al choice op ions a e no s aigh o wa d o com-
p ehend. Thus, decision suppo sys ems ac as a g ea assis ance in he
decision-making p ocess. Aquick in ui i e guess, gi en igh a e he in e -
iew was conduc ed and p io o esul s isualiza ion, sugges ed a ou ing
Finland o e o he op ions.
Fo each c i e ion, a uni o mly dis ibu ed andom numbe is d awn
be ween i s speci ied minimum and maximum. A simple weigh ed sum
agg ega ion is used o compu e he o e all sco e (T ian aphyllou & Sánchez,
1997), which also accoun s o whe he each c i e ion is posi i e o nega-
i e. In each simula ion i e a ion, a ca ego ical a iable deno ing he coun-
y de ines alues o which coun y a e used o compu e he sco e. Thus,
a single simula ion un c ea es a holis ic da ase ha ep esen s he en i e
decision si ua ion. The decomposi ion o esul s by coun y is p esen ed in
Figu e13.4.3
The isualiza ion shows ha he o e all p e e ence winne is Uk aine, con-
a y o wha he ini ial in e iew indica ed. Finland – he coun y o cu en
esidence – ollowed in second place wi h a high p obabili y o being “ma -
ginally a e age”, wi hou any o e whelmingly nega i e o posi i e ou comes.
On he o he hand, he UK and he USA demons a ed he highes deg ees o
a iabili y o achie ing sa is ac ion on he designa ed c i e ia. Figu e13.4
exempli ies ha mul i-c i e ia decision-making can be unin en ionally d i en
by alse pa e n assessmen s and a dis ega d o he complexi ies wi hin he
in e play o he c i e ia.
Del ing in o speci ics, he p ospec s o in eg a ion a e acili a ed by he
scale o in e ac ion in he local language. Since Uk ainian is Da ia’s na i e
language, he le el o com o associa ed wi h i is high. Despi e sco ing sec-
ond o e all, Finland is he coun y wi h he lowes deg ee o pe cei ed com-
munica ion con idence. Despi e being luen in English, he UK and he USA
p oduce di e en ou comes since he local accen a ia ions led o conside -
able a iabili y in he sco ing (Figu e13.5).
Bo h isualiza ions o coun y sco ing esul ed in a highe deg ee o unde -
s anding o he op ions a s ake. The agg ega ed assessmen in Figu e13.4
allowed us o gain a mo e comp ehensi e pic u e o coun y p e e abili y and
he di e en deg ees o a ia ion in he es ima es. Decomposi ion on he lan-
guage c i e ion in Figu e13.5 p o ided u he insigh s, he eby p e en ing
ushed and/o simpli ied decision-making by Da ia, while igge ing a enues
o u he esea ch.
New le el o pe sonal decision-making 339
2.3 Mo gage
Ma iia d eams o owning a house igh on he lake sho e, wi h he e asse
so close o he wa e one could hea gen le ipples o wa e while enjoying
mo ning co ee. Conside a ion o buying a new house, howe e , had been
da kened by he ab up ly ising in e es a es and high unce ain y associa ed
wi h he cou se o hei u u e di ec ion. The ques ion o whe he o assume
a new mo gage s ood in he way o he d eam.
Colou Coun y Coun y sco e
Min Mean Max
Finland 43 52 61
Uk aine 58 67 76
UK 16 35 54
US 19 43 67
Figu e 13.4 Accumula ed assessmen o coun y p e e abili y. (colou image is
accessible ia he link)
340 Anna Sido enko e al.
Colou Coun y Language
com o Coun y sco e
Min Mean Max
Finland Poo 43 52 61
Medium - - -
High - - -
Uk aine Poo - - -
Medium - - -
High 58 67 76
UK Poo 16 35 52
Medium 17 35 54
High - - -
US Poo - - -
Medium 19 42 67
High 21 43 65
Figu e 13.5 Language com o speci ic assessmen o coun y p e e abili y. (colou
image is accessible ia he link)
New le el o pe sonal decision-making 341
Table 13.3 De ails o he conside ed mo gage
I em Value
House p ice €289,000
Ini ial capi al €150,000
Loan €139,000
Ini ially assumed du a ion 20yea s
Base a e 3.88%
Vola ili y 40.00%
Ma gin 0.88%
Cap le el 5.00%
Cap ee 0.25%
The house cos s sligh ly unde 300,000 eu os Hal o his amoun is eadily
accessible, while he o he hal would need o be bo owed (see Table13 3)
The e e ence in e es a e, EURIBOR, is modelled as a s ochas ic p ocess,
whe e he a e each yea equals he alue om he p e ious yea (s a ing
om 3 88% cu en ly) co ec ed acco ding o a andomly changing ola ili y
ha assumes alues in he ange ±40% (see equa ion1)
EURIBORE
=+URIBOR−1
()
1 , (1)
whe e is he ola ili y, is he ime pe iod (yea ), and is a uni o mly
dis ibu ed andom a iable in he ange be ween −1 and 1 Vola ili y is se
a bi a ily a 40% le el, which gi es a dis ibu ion o in e es a es a he
wen ie h yea in acco dance wi h pe cei ed unce ain y
The loan in e es a e is calcula ed as EURIBOR plus a ma gin o 0 88%
The ma gin is no mally a subjec o nego ia ion wi h he bank and may
depend on he pe sonal his o y wi h he bank, o he o e s, e c The in e es
a e upda es on an annual basis In addi ion, he possibili y o an in e es a e
cap is modelled wi h he cap applied o he annual in e es a e i i is abo e
5% As a paymen o he cap, a cap ee o 0 25% is added o he ma gin
Figu e13 6 illus a es one o he s ochas ic ealiza ions o he in e es a e
pa h wi h a cap
Apa om he s ochas ic in e es a e, ano he dynamic a iable is
bina y – he ac ual swi che o he on/o cap – so in he simula ion one
would be able o ace i s e ec All o he inpu s a e assumed ixed
Based on he gi en inpu s, a simple Excel model4 compu es he annual
mo gage expenses and he du a ion o he loan using he basic annu-
i y o mula The simula ion decomposed by he s ochas ic in e es a e
and he on/o in e es cap is shown in Figu e13 7 He e we can see ha
bo h ou pu s, al hough exp essed in di e en uni s, ha e he same dis ibu-
ion and a e a ec ed by he inpu s in he same way (same decomposi ion)
348 Anna Sido enko e al.
Colou Ca Sco e
Min Mean Max
Own bioe hanol 0.10 0.14 0.18
Second-hand elec ic 0.06 0.09 0.12
New elec ic 0.07 0.10 0.13
Second-hand hyb id 0.15 0.18 0.21
Figu e 13.10 Ca eplacemen op ion assessmen . (colou image is accessible ia
he link)
conce ns ela ed o emissions gene a ed, cos was de e mined o be he mos
in luen ial decision-making ac o .
The analy ical esul s indica e ha he op imal solu ion is o acqui e a
second-hand hyb id ehicle. The isualiza ion in Figu e13.10 indica es ha
bo h elec ic ca op ions a e ac ually he leas a ou able when all c i e ia
a e conside ed, despi e hem p oducing he lowes nega i e en i onmen al
con ibu ions. In compa ison o he elec ic ca op ions, Yannick’s exis ing
ca is also p e e able.

New le el o pe sonal decision-making 349
Colou Ca Cos s Sco e
Min Mean Max Sha e
Own bioe hanol Cheap 0.12 0.15 0.18 15%
Medium 0.10 0.12 0.15 10%
Expensi e 0.10 0.11 0.13 1%
Second-hand elec ic Cheap 0.09 0.11 0.12 5%
Medium 0.07 0.09 0.12 13%
Expensi e 0.06 0.08 0.10 6%
New elec ic Cheap
Medium
Expensi e 0.07 0.10 0.13 25%
Second-hand hyb id Cheap 0.17 0.19 0.21 13%
Medium 0.15 0.17 0.19 10%
Expensi e 0.15 0.16 0.17 1%
Figu e 13.11 Ca eplacemen op ion decomposed by he cos s. (colou image is
accessible ia he link)
Since i was indica ed ha cos s we e he mos in luencing ac o , a subse-
quen decomposi ion was pe o med ocused solely on he associa ed expenses
(see Figu e 13.11). The i s gla ing insigh sugges s ha a second-hand
elec ic ca is no ha much mo e expensi e when all cos s a e conside ed.
350 Anna Sido enko e al.
Howe e , e en wi h acquisi ion cos s aken in o conside a ion, he se en-yea
main enance and uel cos p ojec ions s ill esul ed in he second-hand hyb id
op ion being he mos p e e able. Wi h ei he an al eady-owned bioe hanol
o a po en ially pu chased second-hand hyb id ca , any posi ioning in he
expensi e ange o he cos ’s scena io model is highly imp obable.
All ac o s conside ed, he second-hand hyb id op ion gene a es he high-
es sco e ange, so i is ecommended ha Yannick should ac ually eplace his
exis ing ca wi h a second-hand hyb id ehicle.
2.6 Fa pe cen age
Alexand a g ee s he mo nings on he iny balcony wi h a cup o co ee in
he hand. He i ual includes 15 minu es app ecia ing he iews o a Cali o -
nia e eille – including he empowe ing sigh o ou doo wo kou s, unne s,
and ska e s wea ing h ough he communal hus le and bus le. Be o e mo -
ing he e, Alexand a had ne e been su ounded by so many people ocused
on well-being. As he social ci cle expanded o include na i e Cali o nians,
he “wellness” cul u e began pe mea ing Alexand a’s own li e – she now
s udies sel -ca e li e a u e and lis ens o i ness podcas s. A some poin , she
shi ed ocus o he own nu ien in ake. In he mids o he pola izing deba e
on “body accep ance”, he Cali o nia a mosphe e is s ill o e whelmed wi h
messaging ha e e yone should wo k owa d achie ing “ hei pe ec body”.
Inspi ed by hese ibes o ex eme heal h and li es yle moni o ing, Alexand a
decided o e alua e he c edibili y o a once-hea d s a emen “go build some
muscle o educe you a pe cen age” and o assess whe he she needed o
li weigh s o mo e in o he “lean body” club.
The amewo k o a simple model7 ha sums up he weigh o lean issue,
a issue, and bone mine al con en and calcula es he body a pe cen age
as a sha e o a issue o he whole weigh was quickly ske ched ou . The
nume ic assump ions a e p esen ed in Table13.5.
As one o he heal h KPIs o many Cali o nians, a pe cen age became he
a ge o ou analysis. Figu e13.12 showcases how he body weigh and he
a pe cen age a e a ec ed by he mass o a and lean issue.
Table 13.5 Nume ic inpu s o he body a pe cen age calcula ion
Inpu a iable Measu ed alue Assumed a ia ion o
simula ion
Min Max
Fa issue, kg 13.7 10 16
Lean issue, kg 39.5 39.5 46
Bone mine al con en , kg 2.3 2.3 2.3
New le el o pe sonal decision-making 351
Na u ally, hese wo ou pu s om a simple addi i e model ha e di e en
dependency s uc u es. While bo h a and lean issue play a ole in he o e -
all body weigh , o he a pe cen age, only a issue makes a signi ican di -
e ence wi h lean issue playing an inconsequen ial ole. In essence, g owing
muscle does no help o educe a pe cen age! The lean body a ge is ha d
o each unless i is ollowed up by die ing o dec ease he a issue olume.
Al hough his SimDec exe cise was insigh ul in e ealing he ac ual le e s
behind he KPIs, i s execu ion di ec ed Alexand a o econside he o e all
p oblem o mula ion and o abandon he a ge al oge he .
3 Discussion and conclusions
This chap e has explo ed six pe sonal s o ies which ea u ed he in e-
g a ion o SimDec in o he decision p ocess. To ou p o agonis s, he six
decision-making cases we e qui e complex and con ained a high deg ee o
obscu i y. F equen ly, he goal o quan i ica ion is o desc ibe a eal-li e phe-
nomenon o sys em ia an abs ac simpli ica ion. As a esul , he scope
o he compu a ional model complexi y is cong uen wi h he scope o he
complexi y o he eal-wo ld p oblem. Fo he models conside ed, SimDec
Figu e 13.12 Decomposi ion o body weigh and a pe cen age by mass o a and
lean issue. (colou image is accessible ia he link)
352 Anna Sido enko e al.
se ed as a suppo sys em in he p oblem analysis. The p o agonis s we e
p o ided insigh s in o wha , om a pu ely ma hema ical pe spec i e, could
be ep esen ed by a simple unc ion. Howe e , i was demons a ed ha
SimDec pe mi ed a clea and comp ehensi e e alua ion o a ious insigh s
and ac o in e connec edness wi hin he p oblems wi hou sac i icing hei
complexi y.
When he e a e se e al ac o s o accoun o , i was es ablished ha he
answe o a ques ion is ne e qui e as in ui i e as i migh ha e ini ially seemed.
A e he p oblem has been decomposed, isualized, and i s esul s analyzed,
a mo e comple e unde s anding o he deep-sea ed ole hese unde lying ac-
o s play becomes much mo e appa en . One consequence was ha he oun-
da ional ques ion pa adigm o MCDM has o be shi ed. Ins ead o ecei ing
an answe s a ing which al e na i e is “ he bes ”, he p ocess needs o allow
decision-make s o explo e wha d i es “pe sonal choice” and how “can
one’s op ions be made be e ”. In he cases o Yannick and Da ia, he explo-
a ion unco e ed inhe en con lic be ween wha each belie ed should be he
bes op ion and wha is ac ually he bes op ion based on he mul i-c i e ia
assessmen . All o he cases in ol ed goal-o ien ed app oaches. Whe he i
was success ul language acquisi ion o ideal body a pe cen age, SimDec was
used o in es iga e scena ios o how he indi idual a ge could be achie ed
and whe he i would be achie able unde he ixed se o condi ions.
In e e y ins ance, he decomposi ion analysis igge ed u he in es-
iga ion o he p oblem and led o e-e alua ions o wha was pe sonally
impo an . These e lec ions posed new ques ions: Do we need o adjus ou
belie s o he ou come, o mus we make a new assessmen o he in luenc-
ing ac o s? Ins ead o s a ing and ending wi h a s a ic decision-making
model, decomposi ion analysis p o okes i e a i e explo a ion pa hways. The
esul ing p oblem design con e sions igge ed ac i e e o mula ions o he
decision-making pa ame e s. SimDec applicabili y is e sa ile and, al hough
a compu a ional ool, he supplied isualiza ions empowe ed he seemingly
quali a i e p oblems. Whe he i is a p edominan ly p esc ip i e o desc ip-
i e issue, whe he he da a inpu consis s o ca e ully sou ced measu es o
subjec i e p e e ence a ios, i was clea ly demons a ed ha SimDec p o-
duced aluable insigh s in e e y ins ance.
Acknowledgemen s
The wo k is suppo ed by g an 220178 om he Finnish Founda ion o
Economic Educa ion and by g an OGP0155871 om he Na u al Sciences
and Enginee ing Resea ch Council o Canada. The au ho s exp ess g a i ude
o all p o agonis s o he cases desc ibed in his chap e .
New le el o pe sonal decision-making 353
No es
1 h ps://gi hub.com/Simula ion-Decomposi ion/da a-models/ ee/main/Chap e 14.
Sido enko.
2 h ps://gi hub.com/Simula ion-Decomposi ion/da a-models/blob/main/
Chap e 14.Sido enko/1.Sa ings.xlsm.
3 h ps://gi hub.com/Simula ion-Decomposi ion/da a-models/blob/main/
Chap e 14.Sido enko/2.Coun y_choice.xlsm.
4 h ps://gi hub.com/Simula ion-Decomposi ion/da a-models/blob/main/
Chap e 14.Sido enko/3.Mo gage.xlsm.
5 h ps://gi hub.com/Simula ion-Decomposi ion/da a-models/blob/main/Chap e 14.
Sido enko/4.Lea ning.xlsm.
6 h ps://gi hub.com/Simula ion-Decomposi ion/da a-models/blob/main/Chap e 14.
Sido enko/5.Ca .xlsm.
7 h ps://gi hub.com/Simula ion-Decomposi ion/da a-models/blob/main/Chap e 14.
Sido enko/6.Body_ a .xlsm.
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