Ci a ion: Šomplák, R.; Smejkalo á, V.;
Rosecký, M.; Szászio á, L.; Ne lý, V.;
H abec, D.; Pa las, M.
Comp ehensi e Re iew on Was e
Gene a ion Modeling. Sus ainabili y
2023,15, 3278. h ps://doi.o g/
10.3390/su15043278
Academic Edi o s: An onis A. Zo pas
and Filomena A dolino
Recei ed: 9 No embe 2022
Re ised: 17 Janua y 2023
Accep ed: 7 Feb ua y 2023
Published: 10 Feb ua y 2023
Copy igh : © 2023 by he au ho s.
Licensee MDPI, Basel, Swi ze land.
This a icle is an open access a icle
dis ibu ed unde he e ms and
condi ions o he C ea i e Commons
A ibu ion (CC BY) license (h ps://
c ea i ecommons.o g/licenses/by/
4.0/).
sus ainabili y
Re iew
Comp ehensi e Re iew on Was e Gene a ion Modeling
Rado an Šomplák1, Ve onika Smejkalo á1,* , Ma in Rosecký2, Lenka Szászio á1, Vlas imí Ne lý1,
Dušan H abec 3and Ma in Pa las 1
1Ins i u e o P ocess Enginee ing, Facul y o Mechanical Enginee ing, B no Uni e si y o Technology,
Technická2, 616 69 B no, Czech Republic
2Czech Ma h, a.s., Šuma ská416/15, 602 00 B no, Czech Republic
3
Ins i u e o Ma hema ics, Facul y o Applied In o ma ics, Tomas Ba a Uni e si y in Zlín, Nad S ánˇemi 4511,
760 05 Zlín, Czech Republic
*Co espondence: e onika.smejkalo a1@ u b .cz
Abs ac :
S a egic plans o was e managemen equi e in o ma ion on he cu en and u u e
was e gene a ion as a p ima y da a sou ce. O e he yea s, a ious app oaches and me hods o
was e gene a ion modeling ha e been p esen ed and applied. This e iew p o ides a summa y o
he asks ha equi e in o ma ion on was e gene a ion ha a e mos equen ly handled in was e
managemen . I is hypo hesized ha he e is no cu en ly a modeling app oach uni e sally sui able
o o ecas ing any ac ion o was e. I is also hypo hesized ha mos models do no allow o
modeling di e en scena ios o u u e de elopmen . Almos 360 publica ions we e examined in
de ail, and all o he acked a ibu es a e included in he supplemen a y. A gene al s ep-by-s ep
guide o was e gene a ion o ecas ing, comp ising da a p epa a ion, p e-p ocessing, p ocessing, and
pos -p ocessing, was p oposed. The p oblems ha occu ed in he indi idual s eps we e speci ied,
and he au ho s’ ecommenda ions o hei solu ion we e p o ided. A o ecas ing app oach based
on a sho ime se ies is p esen ed, due o insu icien op ions o app oaches o his p oblem. An
app oach is p esen ed o c ea ing p ojec ions o was e gene a ion depending on he expec ed sys em
changes. Resea che s and s akeholde s can use his documen as a suppo ing ma e ial when deciding
on a sui able app oach o was e gene a ion modeling o was e managemen plans.
Keywo ds:
was e gene a ion modeling; was e p oduc ion; was e p edic ion and o ecas ing; p ojec-
ion; sho ime se ies
1. In oduc ion
In de eloping coun ies, he p e ailing goal is o dispose o was e, while in de eloped
coun ies (e.g., he ones in he EU), he e is an e o o p ocess he was e mo e sus ainably.
The p e e ed me hods o was e managemen (WM) and disposal in he EU ha e been
s ipula ed in he Was e Managemen Hie a chy [
1
] o make use o he was e po en ial. The
EU membe s a es ha e been implemen ing he necessa y legisla i e changes, and he nex
s ep is o adap he exis ing WM sys ems o mee he espec i e objec i es. S a egic plans
o he mode niza ion and cons uc ion o was e collec ion and p ocessing in as uc u e
equi e in o ma ion on he gene a ion and composi ion o was e, including hei expec ed
de elopmen , as a p ima y da a sou ce. The aim is o c ea e a WM sys em ha is sus ainable
om bo h he economic and en i onmen al poin s o iew. In esponse o his si ua ion,
he e is a g owing numbe o publica ions dealing wi h was e gene a ion modeling. This
e iew aims o summa ize he a ailable modeling app oaches and discuss hei sui abili y
o di e en applica ions in WM.
Sus ainabili y 2023,15, 3278. h ps://doi.o g/10.3390/su15043278 h ps://www.mdpi.com/jou nal/sus ainabili y
Sus ainabili y 2023,15, 3278 2 o 29
1.1. Applica ion-Based Ta ge ing
WM is a e y complex ield in which many asks and p oblems can be encoun e ed
in decision-making. The di ec ion o WM de elopmen is condi ioned by he app op ia e
s a egic planning o he a ious componen s o he WM sys em (was e collec ion, cons uc-
ion o new ea men acili ies, change in acili y capaci y). A whole se ies o in e en ions
in he sys em equi es se e al yea s o he p epa a ion and implemen a ion o he plan. I
is he e o e necessa y o s a om well-de eloped comp ehensi e s a egic plans, which,
among o he hings, ake in o accoun he expec ed de elopmen o he gene a ion o he
was e ac ions in ques ion.
Each ask is unique in na u e, bu all s ages o he p ocess equi e speci ic inpu da a,
di e ing mainly in hei ime o e i o ial de ail. The mos challenging pa ame e s a e
he gene a ion a es o di e en ypes o was e and was e composi ion (mos ly MMW o
sepa a ely collec ed was e, e.g., pape , plas ic). The e o e, he asks a e di ided in o h ee
logical blocks, whe e hei cha ac e is ics a e desc ibed o c ea e models associa ed wi h
he cu en o u u e was e quan i ies.
1.1.1. Was e Managemen Legisla ion and Policy
The p ope speci ica ion o he ecycling o was e p e en ion a ge s included in legis-
la ion equi es eliable long- e m knowledge o was e gene a ion and ea men . His o ical
da a can iden i y he links o a ious socio-economic and demog aphic ac o s o WM
de elopmen [
2
]. The connec ions iden i ied may e eal po en ial socie al changes and,
consequen ly, posi i ely a ec was e gene a ion ends and p ocessing me hods.
In he con ex o long- e m o ecas ing (5–20 yea s), he Ci cula economy package o
he EU is ele an because i se s ecycling a ge s o municipal solid was e (MSW) un il
2035 [
3
] and land ill es ic ions [
4
]. A he coun y le el, he da a a e usually agg ega ed
annually, and as such, a e sui able o o ecas ing. The disad an age o en is he a ailabili y
o only sho his o ical da a se ies, due o annual da a eco ds. The only easonable
al e na i e o o ecas ing is inding he end ha he da a ollow (Sec ion 4.3.2). Ghinea
e al. (2016) [
5
] conside ed mul iple unc ions o desc ibing ends, o which he S-cu e
p o ed o be he mos sui able o MSW. Ayele u e al. (2018) [
6
] used a linea dependence
o desc ibe he expec ed ci y-le el a e o he gene a ion o MSW. O he a ailable wo ks
deal wi h e y complex models ha a e no sui able o o ecas ing. A comple e o e iew
is gi en in he Supplemen a y Ma e ials (see Sec ion 2.1).
Modeling was e gene a ion makes i possible o compa e mos ly e y ambi ious
legisla i e goals wi h he o ecas ed alues. The mos signi ican sho coming o he
me hods o he longe - e m es ima ion o was e gene a ion is he ailu e o conside
po en ial in e en ions in he was e sys em i sel . I he o ecas is no in line wi h he
goals, hen he p ojec ions a e modeled. This can e eal he po en ial o changes in
indi idual e i o ial uni s. Wi hin he p ojec ions, he o ecas s a e modi ied o achie e he
se a ge [7].
1.1.2. S a egic Decision-Making on Was e Managemen In as uc u e
S a egic decision-making in WM conce ns he planning and implemen a ion o long-
e m p ojec s o acili y cons uc ion [
8
]. Compa ed o he p e ious pa , was e manage-
men legisla ion and policy, was e gene a ion o ecas ing usually ocuses on he egional
le el. Da a a he egional le el a e o en a ailable on an annual basis and es ima ing
ends om his o ical da a is possible. Howe e , he da a and ends also usually ea u e
signi ican ola ili y, which makes o ecas ing mo e complica ed and less accu a e. I is
good o keep in mind he condi ions in he su ounding egions ha may a ec he planned
p ojec [
9
]. A hie a chical e i o ial di ision can ensu e consis en o ecas s be ween e-
gions and he en i e coun y [
10
]. The de ini ion o possible scena ios o u u e was e
amoun s akes place in he s a egic planning. Such scena ios a ise om ex e nal in e -
en ions in o he WM sys em, and hey allow o e alua ing he impac on he planned
p ojec s’ sus ainabili y [11].
Sus ainabili y 2023,15, 3278 3 o 29
A signi ican ly sho e ime ho izon is su icien o collec ion s a egy planning due o
he ela i ely sho se ice li e o collec ion con aine s and equen legisla i e changes [
12
].
Models o collec ion planning usually ocus on he daily o weekly da a se s. This ype
o da a is common o ci ies and municipali ies, whe e moni o ing is conduc ed in g ea e
de ail and du ing longe ime ho izons.
To ensu e he inancial and echnical sus ainabili y o a p ojec , i is necessa y o
assume, du ing i s e alua ion, ha se e al pa ame e s a e unce ain, including he gene -
a ion a e and he was e composi ion [
13
]. The cu en s a e and ou look o he a ea o
in e es a e needed o app op ia ely si e a new acili y o collec ion in as uc u e wi h a
well-chosen capaci y.
1.1.3. Ope a ional Decision-Making in Was e Managemen
The las poin is ela ed o he planning o daily ope a ions. Con aine le el da a a e
needed in was e collec ion applica ions ha use ou ing models (a summa y o ou ing
p oblems and hei applica ion was p esen ed by [
14
], which may ea u e a ious a ge s. A
ypical ep esen a i e o his is dynamic collec ion planning, whe e he was e quan i ies a
he indi idual collec ion poin s a e es ima ed each day. On he o he hand, when c ea ing
a new collec ion plan, weekly o mon hly da a a e equi ed o p ope ly se he collec ion
equency. The equency i sel depends on bo h he was e p ope ies and he capaci ies o
he collec ion poin s. Collec ion planning is closely ela ed o he si ing o he collec ion
poin s, which was discussed in de ail in he p e ious sec ions.
1.2. Tasks Encoun e ed in Was e Gene a ion Modeling
When building was e gene a ion models, i is necessa y o dis inguish whe he an
es ima e o he cu en o he u u e gene a ion a e is made. The di e ences in he
e minology ega ding p edic ion, o ecas ing, and p ojec ion a e p o ided in he ollowing
sec ions.
1.2.1. P edic ion
The p edic ion o was e gene a ion is used o desc ibe he cu en o u u e si ua ion.
Es ima ing he cu en was e gene a ion a e is essen ial o de ine he links in he sys em
and o de elop he models o o he e i o ial uni s. These links can be used o model he
expec ed u u e was e gene a ion. A common applica ion is in he modeling o he was e
gene a ion a e, depending on a ious socio-economic, demog aphic, and o he ac o s. The
pi alls o such models we e desc ibed by [
15
] in mo e de ail. The main weakness is ha he
links in he sys em can change o e ime. P oblems may occu when he links a e modeled
using all o he his o ical da a, wi hou ega d o hei empo al a iance. Consequen ly,
his may impac he quali y o he u u e p edic ions o he espec i e models.
A common mis ake is also o build models using he absolu e da a, wi hou s anda d-
iza ion. Then, mul icollinea i y is o en obse ed, which nega i ely impac s he ob ained
esul s. In addi ion, he da a yielded by a WM model should always include in o ma ion
on he unce ain y, e.g., ia con idence in e als.
1.2.2. Fo ecas ing
Fo ecas ing, some imes e med p ognosis, exclusi ely conce ns he es ima ion o
u u e de elopmen . Mos o ecas s in WM in ol e was e gene a ion. O he o ecas ing
a ge s (was e composi ion, was e ea men ) a e a e. When making a o ecas , i is
necessa y o emembe ha in e ing he u u e de elopmen based on he cu en o
his o ical da a is always a di icul —and o en la gely unsol able— ask.
Fo ecas ing models assume ha he espec i e pa ame e s will e ol e in a simila way
o hei pas de elopmen . The p ima y ea u e o a o ecas is ha no change in he cu en
condi ions is expec ed. Da a om e en sho - e m o ecas s mus be e alua ed ca e ully.
Longe - e m o ecas s a e mo e indica i e in e ms o how he de elopmen o was e
gene a ion migh mani es i no hing changes (e.g., wi hou any changes being made o he
Sus ainabili y 2023,15, 3278 4 o 29
legisla ion). When i comes o was e gene a ion, he p oblem is u he compounded by he
ac ha o en only da a se s co e ing e y sho ime anges a e a ailable. I sociology-,
economics-, o demog aphy- ela ed da a om a “p edic ion” model a e o be used, i is
impe a i e ha such a p edic ion is o su icien quali y.
Fo ecas s should also conside he links be ween he was e s eams, which a e in e -
ela ed (highe gene a ion o sepa a ed was e leads o lowe amoun o mixed municipal
was e (MMW) e c.). A model should always alloca e a ce ain numbe o da a poin s a
he end o he ime se ies o e i ica ion pu poses. E en in o ecas ing, he esul s should
include in o ma ion on he unce ain y.
1.2.3. P ojec ion
P ojec ions also deal wi h he es ima ion o u u e de elopmen ; howe e , in con as
o o ecas ing, hey assume ha a change will happen in he bounda y condi ions (legisla-
i e, echnological p og ess). These condi ions, which a ec was e gene a ion, canno be
o ecas ed. The e o e, p ojec ions a e o en u u e scena ios gi en he speci ic bounda y
condi ions chosen by he au ho s. Scena ios can be c ea ed wi h espec o he objec i es o
he WM, bu de ia ions om he co esponding o ecas should be as sligh as possible.
Due o e i o ial hie a chy, i is app op ia e o conside he di ision o na ional a ge s (i.e.,
indi idual egions acco ding o hei po en ial o change). Mono ony in e ms o was e
gene a ion po en ial should be main ained. Possible links among was e ac ions should
also be aken in o accoun .
1.3. Resea ch Ques ions
The unde lying goal o his e iew is o ga he suppo ing ma e ial o he de elop-
men o a comp ehensi e was e gene a ion model, pa icula ly wi h ega d o i s applica ion
(see Sec ion 1.1). Be o e s udying he a ailable li e a u e, he esea ch ques ions ha a e
add essed in he ollowing ex a e o mula ed.
•
Wha a e he common sho comings o he a ailable da a, and how many da a poin s
in a ime se ies a e su icien ? Response: Sec ions 2.1 and 3.
•
Which app oaches and me hods a e sui able o ce ain applica ions? Response:
Sec ion 3.
•
Can gene al ecommenda ions be o mula ed o da a p ocessing? Response: Sec ion 4.
•
Can p edic ion models be used o es ima e u u e da a? Unde wha condi ions?
Response: Sec ion 5.
•
How o implemen changes and in e en ions in WM (legisla i e in e en ions, changes
in da a epo ing me hodology, in oduc ion o new was e ca alogue numbe s) wi hin
ma hema ical models? Response: Sec ion 5.
The ac ual e iew me hodology is desc ibed in Sec ion 2. A de ailed o e iew o he
s udied publica ions can be ound in Supplemen a y Ma e ials. An ex ensi e e iew was
ca ied ou in o de o c ea e an o e iew o he me hods and app oaches o da e. Based on
his, i is possible o choose a sui able app oach o o he asks. In he e en ha he exis ing
app oaches a e insu icien o some ypes o asks, i is app op ia e o conside he issue o
de eloping new app oaches. Sec ion 3p esen s he p ocess o choosing a modeling me hod.
Sec ion 4 hen summa izes he modeling p ocesses (p epa a ion, p e-p ocessing, p ocessing,
pos -p ocessing) in he o m o he p oblems and he au ho s’ ecommenda ions. A SWOT
analysis o he indi idual models is p o ided o each me hod in Appendix A. The main
bene i o his con ibu ion is he combined app oach o o ecas ing and p ojec ion based
on a sho ime se ies, see Sec ion 5. The p esen ed me hod is designed as a uni e sal
app oach o any was e ac ion. The lack o a mul ipu pose app oach was ound o be a
esea ch gap. A common and p oblema ic ea u e o he a ailable da a is a sho ime se ies.
Conside ing his ea u e, he app oach is based on a end analysis o he his o ical da a,
ollowed by da a econcilia ion. This choice ook place acco ding o he decision-making
p ocess in Sec ion 3. A b ie summa y is p o ided in Sec ion 6, including he sugges ions
ega ding u he esea ch di ec ions.
Sus ainabili y 2023,15, 3278 5 o 29
2. Li e a u e Re iew
Fi s , a en ion was paid o p e iously published e iew pape s on he discussed opic,
wi h he aim being o p e en epe i ion, he summa y is in Table 1.
Table 1. P e iously published e iew pape s.
Ci a ion Time Range Numbe o
Publica ions C i e ia
(Beigl e al., 2008 [16]); Un il 2005 45
egional scale, MSW was e s eams, independen
a iables, modeling me hods
(Che ian and Jacob, 2012 [17]) Un il 2011 9
egional scale, MSW was e s eams, independen
a iables, modeling me hods, socio-economic
ac o s
(Koleka e al., 2016 [18]) 2006–2014 20
modeling me hods, e i o ial di ision, amoun
and equency o ime-dependen da a,
independen a iables, was e s eam
(Goel e al., 2017 [19]) 1972–2016 106
classi ica ion in o ypical (mul iple linea
eg ession—MLR, ime se ies analysis—TSA,
ac o analysis) and uncon en ional ( uzzy
me hods, a i icial neu al ne wo ks—ANN)
app oaches
(Alzamo a e al., 2022 [20]) 2008–2021 120 MSW s eam, geog aphic scale, da a ype,
modeling echnique, independen a iables
(Abdallah e al., 2020 [21]) 2004–2019 85
a i icial in elligence in WM, iden i ied six
applica ions; desc ibed mul iple models incl.
hyb id ones
(Guo e al., 2021 [22]) 2003–2020 40
machine lea ning me hods in o ganic solid was e
ea men
(Xu e al., 2021 [23]) 2010–2020 177
ANN models, ca ego ies o e iew scales:
mac oscale (mainly ocused on was e
gene a ion), mesoscale (was e p ope ies and
p ocess pa ame e s), meso-mic oscale (was e
p ocess e iciencies), mic oscale ( eac ion
mechanisms o mic os uc u es)
Olde e iews clea ly speci y he as-o -ye un esol ed esea ch gap, while he mo e
ecen wo ks—e.g., [
21
–
23
]—deal exclusi ely wi h a i icial in elligence and do no conside
o he me hods. As he wo ks by [
17
,
18
] desc ibed he a ge pe iods wi h only a modes
numbe o published models, a new e iew o ha pe iod has been conduc ed in he
p esen pape . The con ibu ion [
19
] p esen ed a ela i ely ex ensi e e iew, bu u he
applica ions equi e mo e elabo a ion in he con ex o was e ac ions. The con ibu ion [
20
]
aims o in es iga e he ela ionship be ween was e gene a ion and socioeconomic ac o s.
Thus, a e iew o app oaches ha do no use in luen ial ac o s o models (e.g., TSA) is
no p o ided. The e o e, he e iew will be ca ied ou again in his con ibu ion, wi h
a b oade scope o he me hods used. The e iew [
16
] is aken as he s a ing poin , he
publica ion is ca. 15 yea s old and, he e o e, an upda e is due. The e iew [
16
] summa izes
he me hods used un il 2005, bu he e a e no desc ibed new app oaches ha ha e no been
add essed un il hen. I is he e o e no necessa y o s udy he con ibu ions be o e 2006, as
his pe iod has al eady been well co e ed in pape [16].
The e iew is he e o e conduc ed o a icles published in 2006 and la e . The main
da abases que ied we e ScienceDi ec and Scopus wi h he keywo ds being: “msw p edic-
ion“, “msw o ecas “, “was e p edic ion“, “was e o ecas “, “was e gene a ion“, “was e
p oduc ion“, “was e o ecas ing“, “municipal was e p edic ion“ o “municipal was e o e-
cas “. The a icles we e so on “ ele ance”.

Sus ainabili y 2023,15, 3278 6 o 29
Fo he a icles ha ma ched he lis ed keywo ds, hei ele ance o his e iew was
assessed agains he i le o abs ac . The c i e ion is ha he chosen a icle p esen s a model
o ei he he cu en o u u e was e gene a ion. When so ing by ele ance, he a icles
sui able o e iew a e i s displayed. Then, mo e occu ed, which we e excluded om
he e iew. When he e we e mo e han 20 non- ele an a icles in a ow when so ing by
ele ance, he sea ch was e mina ed. A o al o 359 a icles we e iden i ied o he de ailed
examina ion wi hin he e iew.
The ollowing ex is pa icula ly bene icial because i con ains de ailed modeling
ecommenda ions o speci ic WM applica ions. The c i e ia u ilized in [
16
] ha e been kep
and se e al new pa ame e s ( he amoun o da a, was e ypes, e c.) ha e been added.
2.1. Summa y o he Resul s
This s udy e alua ed he 359 selec ed publica ions om se e al poin s o iew. A
de ailed o e iew o all he moni o ed c i e ia is a ailable in Supplemen a y Ma e ials;
he main ex con ains e e ences only o he undamen al publica ions ha he au ho s
ha e chosen o he ci a ion in indi idual pa s o he ex . Supplemen a y Ma e ials is
s uc u ed as ollows:
•
Publica ion de ails (columns B–H): i le, au ho s, jou nal, yea , na ionali y acco ding
o he a ilia ion o he main au ho , numbe o ci a ions, keywo ds.
•O igin o da a (columns I–K): s a e, con inen , he sou ce o WM da a.
•
Da a de ails (columns L–R): numbe o dependen a iables, ime in e al, numbe o
ime in e als, e i o ial di ision, numbe o e i o ies.
•Fo ecas ing (columns S, T): o ecas ing (yes/no), o ecas ing pe iod leng h.
•Was e s eams (columns U–AK): MSW, MMW, bio-was e, pape , plas ics, glass, e c.
•
In luencing ac o s (columns AL–AT): in luencing ac o s (yes/no), popula ion size,
educa ion, age, income, g oss domes ic p oduc (GDP), e c.
•U ilized me hods (columns AU–BF): LR, gene al eg ession (GR), TSA, ANN, e c.
•
P ocessing (columns BG–BH): p e-p ocessing (yes/no), e i ica ion o assump ions o
LR.
•
Model quali y (columns BI–BM): coe icien o de e mina ion (R
2
), mean absolu e e o
(MAE), mean absolu e pe cen age e o (MAPE), e c.
2.1.1. Da a P e-P ocessing
P e-p ocessing is included in 26% o he pape s, bu i is o en in oduced e y b ie ly
wi hou a de ailed desc ip ion o he ac ual p ocedu es used. Only 60 pape s ou o
359 in ol ed p e-p ocessing and simul aneously e alua ed he quali y o he de eloped
model. App oxima ely 32% o hese 60 a icles wi h p e-p ocessing used weekly o daily
da a [
24
] and abou 47% o he a icles wi h p e-p ocessing used annual da a. Howe e ,
he models wi h annual da a a e usually c ea ed on many e i o ial uni s, whe e, again,
i was possible o use common me hods such as z-sco e [
25
], G ubb’s es , o Dixon’s
es [
26
]. Ou lie s occu ing in a sho ime se ies we e o en deal wi h expe ly. The
au ho s’ ecommenda ions ega ding he p e-p ocessing o sho ime se ies a e p o ided
in Sec ion 4.2. I should be men ioned ha p e-p ocessing did no add ess changepoin
de ec ion in he s udied pape s, al hough i can ha e a majo impac on he model.
2.1.2. The De ail o a Da ase
The selec ed publica ions ocused on di e en was e ypes, as shown in Figu e 1.
The mos equen ly modeled componen was MSW, a 54%. This was ollowed by he
sepa a ely collec ed was e wi h high po en ial o ma e ial eco e y (pape , plas ics, glass,
bio-was e), wi h a equency o abou 15%. Sepa a ed was e (SEP) was also modeled as
one s eam, i.e., he sepa a ely collec ed bu no indi idually dis inguished componen s o
MSW. I is wo h no ing ha a ela i ely small pe cen age o he publica ions (6%) ocused
on MMW gene a ion ( e minology is no uni o m, in some publica ions also called esidual
Sus ainabili y 2023,15, 3278 7 o 29
was e). The eason o his migh ha e been ha his s eam is qui e di icul o model due
o he ela ionship be ween MMW and he so ed componen s.
Sus ainabili y 2023, 15, x FOR PEER REVIEW 7 o 30
s eam, i.e., he sepa a ely collec ed bu no indi idually dis inguished componen s o
MSW. I is wo h no ing ha a ela i ely small pe cen age o he publica ions (6%) ocused
on MMW gene a ion ( e minology is no uni o m, in some publica ions also called esid-
ual was e). The eason o his migh ha e been ha his s eam is qui e di icul o model
due o he ela ionship be ween MMW and he so ed componen s.
Figu e 1. Was e ypes s udied in he e alua ed publica ions. Legend: MSW—municipal solid was e;
PAP—pape ; PLA—plas ics; GLA—glass; BIO—bio was e; C and D—cons uc ion and demoli ion
was e; MMW—mixed municipal was e; SEP—sepa a ed was e.
The ollowing e i o ial di isions we e moni o ed: s a e, egion, municipali y,
household, building, hospi al and “o he s” (which included all he emaining le els due
o hei in equen occu ence). Some e i o ial di isions we e di ec ly ela ed o speci ic
was e ypes, e.g., building (cons uc ion and demoli ion was e), hospi al, ho el, o ai c a .
Figu e 2 shows he ela ionship o he e i o ial de ail wi h he ime di ision and he inpu
da a acquisi ion me hod. The household da a we e mos o en a ailable on a daily basis
(mo e han 55%). This was because hey came om su eys in which he p oduced was e
was commonly collec ed om a sample o households and weighed e e y day. The na-
ional-le el da a, on he o he hand, we e a ailable yea ly in 87% o cases.
Rega ding he household-le el da a (was e gene a ion and socio-economic in o -
ma ion), hey we e usually ob ained ia su eys o in e iews. Exis ing da abases abou
epo s we e mos ly used as he sou ce o collec ing he da a o hie a chically highe
le els (municipali y, egion, s a e).
Figu e 1.
Was e ypes s udied in he e alua ed publica ions. Legend: MSW—municipal solid was e;
PAP—pape ; PLA—plas ics; GLA—glass; BIO—bio was e; C and D—cons uc ion and demoli ion
was e; MMW—mixed municipal was e; SEP—sepa a ed was e.
The ollowing e i o ial di isions we e moni o ed: s a e, egion, municipali y, house-
hold, building, hospi al and “o he s” (which included all he emaining le els due o
hei in equen occu ence). Some e i o ial di isions we e di ec ly ela ed o speci ic
was e ypes, e.g., building (cons uc ion and demoli ion was e), hospi al, ho el, o ai c a .
Figu e 2shows he ela ionship o he e i o ial de ail wi h he ime di ision and he
inpu da a acquisi ion me hod. The household da a we e mos o en a ailable on a daily
basis (mo e han 55%). This was because hey came om su eys in which he p oduced
was e was commonly collec ed om a sample o households and weighed e e y day. The
na ional-le el da a, on he o he hand, we e a ailable yea ly in 87% o cases.
Rega ding he household-le el da a (was e gene a ion and socio-economic in o ma-
ion), hey we e usually ob ained ia su eys o in e iews. Exis ing da abases abou
epo s we e mos ly used as he sou ce o collec ing he da a o hie a chically highe
le els (municipali y, egion, s a e).
Sus ainabili y 2023,15, 3278 8 o 29
Sus ainabili y 2023, 15, x FOR PEER REVIEW 8 o 30
Figu e 2. The ela ionship be ween da a o igin and e i o ial di ision (le column in each pai ),
and ime and e i o ial di ision ( igh column).
2.1.3. App oaches Applied
The alues in Figu e 3 indica e he sha es o pape s u ilizing each me hod (please
no e ha some a icles employed mul iple me hods). The mos common me hod — ap-
pea ing in 31% o he s udies—was MLR. In his case, he was e gene a ion was es ima ed
based on he a ailable sociological, economic, demog aphic, and o he da a. ANN, which
belongs o a i icial in elligence me hods and has become inc easingly popula in ecen
yea s, was he second mos used (26% app oach), ollowed by he simple desc ip i e ap-
p oach and gene al eg ession—GR (e.g., gene alized linea model—GLM, analysis o
a iance—ANOVA, o nonlinea eg ession). Some publica ions also ea u ed o he me h-
ods han hose lis ed explici ly in Figu e 3 (g ouped unde “O he s”). These included, o
ins ance, mass balance, he heo y o planned beha io , o models based on geog aphical
in o ma ion sys ems (GIS). The colo s in he espec i e composi e ba cha indica e
whe he he models desc ibed in he e alua ed pape s we e p edic i e o included o e-
cas ing as well.
Figu e 2.
The ela ionship be ween da a o igin and e i o ial di ision (le column in each pai ), and
ime and e i o ial di ision ( igh column).
2.1.3. App oaches Applied
The alues in Figu e 3indica e he sha es o pape s u ilizing each me hod (please no e
ha some a icles employed mul iple me hods). The mos common me hod—appea ing in
31% o he s udies—was MLR. In his case, he was e gene a ion was es ima ed based on
he a ailable sociological, economic, demog aphic, and o he da a. ANN, which belongs o
a i icial in elligence me hods and has become inc easingly popula in ecen yea s, was he
second mos used (26% app oach), ollowed by he simple desc ip i e app oach and gene al
eg ession—GR (e.g., gene alized linea model—GLM, analysis o a iance—ANOVA, o
nonlinea eg ession). Some publica ions also ea u ed o he me hods han hose lis ed
explici ly in Figu e 3(g ouped unde “O he s”). These included, o ins ance, mass balance,
he heo y o planned beha io , o models based on geog aphical in o ma ion sys ems (GIS).
The colo s in he espec i e composi e ba cha indica e whe he he models desc ibed in
he e alua ed pape s we e p edic i e o included o ecas ing as well.
Sus ainabili y 2023,15, 3278 9 o 29
Sus ainabili y 2023, 15, x FOR PEER REVIEW 9 o 30
Figu e 3. Dis ibu ion o me hods used in he e alua ed s udies. Legend: MLR—mul iple linea e-
g ession; ANN—a i icial neu al ne wo k; GR—gene al eg ession; CA—co ela ion analysis;
TSA— ime se ies analysis; SVM—suppo ec o machine; GM—g ay models; DT—decision ees
and o es s; SD—sys em dynamics; FL— uzzy logic.
Se e al models we e es ed in pape [27], o which he mos accu a e esul s we e
ob ained o he u ilized da a se using gamma eg ession (GLM). Ka pušenkai ė e al.
(2016) [28] es ed di e en models o a speci ic was e ac ion (namely, medical was e),
and di e en ime se ies leng hs. The esul was ha no uni e sally applicable model ex-
is s, bu he GLM models p o ided he bes esul s o he egional-le el da a. Kannanga a
e al. (2018) [29] compa ed DT and ANN and ound ha ANN achie ed highe accu acy,
while he esul s om DT could be in e p e ed mo e clea ly. Acco ding o [23], 45% o
WM pape s using ANN wo ked wi h a mos 100 da a poin s, bu ANN ha e s ill become
popula in WM. Pe idis e al. (2016) [30] compa ed di e en models o ime se ies, and
au o eg essi e mo ing a e age (ARMA) p o ided he mos accu a e esul s, bu he Box-
Jenkinson me hodology (ARMA, au o eg essi e in eg a ed mo ing a e age—ARIMA,
and hei modi ica ions) achie es good esul s on long ime se ies. Ghinea e al. (2016) [5]
p esen ed S-cu e models as he mos sui able op ion o end analyses depending on he
da a a ailable.
A di e en ou e is ollowed by hyb id models, which combine he ad an ages o he
indi idual me hods used. Xu e al. (2013) [31] showed ha he combina ion o he seasonal
ARIMA (SARIMA) and g ey sys em was obus enough o i he seasonal and annual
dynamic beha io o was e gene a ion. Howe e , he men ioned models a e ocused on
he speci ic was e ac ion, and gene al applicabili y canno be deduced. This is a ea u e
o mos o he models in he e iew. The me hodology p oposed in [32] combined he S-
cu e end and ANN, whe e o he u u e cons uc ion p ojec s, he S-cu e end was
linked o he p ojec cha ac e is ics ia he ANN o ecas ing o was e gene a ion. T end
Figu e 3.
Dis ibu ion o me hods used in he e alua ed s udies. Legend: MLR—mul iple linea
eg ession; ANN—a i icial neu al ne wo k; GR—gene al eg ession; CA—co ela ion analysis; TSA—
ime se ies analysis; SVM—suppo ec o machine; GM—g ay models; DT—decision ees and
o es s; SD—sys em dynamics; FL— uzzy logic.
Se e al models we e es ed in pape [
27
], o which he mos accu a e esul s we e
ob ained o he u ilized da a se using gamma eg ession (GLM). Ka pušenkai
˙
e e al.
(2016) [
28
] es ed di e en models o a speci ic was e ac ion (namely, medical was e), and
di e en ime se ies leng hs. The esul was ha no uni e sally applicable model exis s,
bu he GLM models p o ided he bes esul s o he egional-le el da a. Kannanga a
e al. (2018) [
29
] compa ed DT and ANN and ound ha ANN achie ed highe accu acy,
while he esul s om DT could be in e p e ed mo e clea ly. Acco ding o [
23
], 45% o
WM pape s using ANN wo ked wi h a mos 100 da a poin s, bu ANN ha e s ill become
popula in WM. Pe idis e al. (2016) [
30
] compa ed di e en models o ime se ies, and
au o eg essi e mo ing a e age (ARMA) p o ided he mos accu a e esul s, bu he Box-
Jenkinson me hodology (ARMA, au o eg essi e in eg a ed mo ing a e age—ARIMA, and
hei modi ica ions) achie es good esul s on long ime se ies. Ghinea e al. (2016) [
5
]
p esen ed S-cu e models as he mos sui able op ion o end analyses depending on he
da a a ailable.
A di e en ou e is ollowed by hyb id models, which combine he ad an ages o he
indi idual me hods used. Xu e al. (2013) [
31
] showed ha he combina ion o he seasonal
ARIMA (SARIMA) and g ey sys em was obus enough o i he seasonal and annual
dynamic beha io o was e gene a ion. Howe e , he men ioned models a e ocused on he
speci ic was e ac ion, and gene al applicabili y canno be deduced. This is a ea u e o
mos o he models in he e iew. The me hodology p oposed in [
32
] combined he S-cu e
end and ANN, whe e o he u u e cons uc ion p ojec s, he S-cu e end was linked
o he p ojec cha ac e is ics ia he ANN o ecas ing o was e gene a ion. T end analysis,
Sus ainabili y 2023,15, 3278 16 o 29
Expe judgmen is he only way o assess he esul s and e alua e he p e-p ocessing
quali y.
4.3. Da a P ocessing
4.3.1. Fo ecas ing o Inpu Pa ame e s
P1: Finding models ha desc ibe he was e gene a ion based on he inpu pa ame e s
wi h su icien accu acy is no gua an eed.
R1: Clus e ing can be applied o e i o ies, and hen he model can be buil a he
clus e le el [
61
]. By compiling a model o each clus e sepa a ely, highe accu acy can be
achie ed due o local condi ions. The di e en links can be desc ibed in speci ic clus e s o
e i o ies and inc ease he model accu acy.
P2: Fo ecas ing models equi e he o ecas s o all hei inpu pa ame e s o he
desi ed le el o e i o ial di ision [
62
], bu o some in luencing ac o s, hese a e no
a ailable. Al e na i ely, only sho - e m o ecas s o he in luencing ac o s a e a ailable,
bu hey do no co e he en i e was e gene a ion o ecas ing ho izon [
34
]. Eno mous
unce ain y would en e was e modeling igh a he beginning (no o men ion he ac
ha i is no desi able o p oceed wi h lawed inpu da a).
R2: The inclusion o he in luencing ac o s in he was e gene a ion o ecas is no
sui able i he o ecas o he in luencing ac o s does no co e he whole o ecas ing
ho izon o he e is signi ican unce ain y. Then, i is ecommended o use he p inciples o
TSA. Fo ecas s o demog aphic in luencing ac o s di e om o he socio-economic cha ac-
e is ics, and i is ecommended o include demog aphic de elopmen in WM o ecas s [
34
].
Long- e m demog aphic p ojec ions a e usually o su icien accu acy, bu un o una ely,
hey may no be a ailable o smalle egions. I mus be no ed ha demog aphic models
a e, in ac , p ojec ions because hey a e c ea ed in he o m o scena ios [63].
4.3.2. Applica ion o he Selec ed Me hod
P1: A speci ic me hod o TSA mus be chosen conce ning he da a equency de ail
and he leng h o he ime se ies.
R1: I daily, weekly, o a mos mon hly da a a e a ailable, hen i is possible o moni o
he cyclic and seasonal componen s, and sho - e m o ecas ing usually is possible [
49
].
O he wise, when only yea ly da a a e a ailable o agg ega ed e i o ies ( egion, s a e, i.e.,
mos da a se s commonly p o ided by s a es o go e nmen s a egic planning agencies),
solely he end can be examined by he eg ession unc ion [
5
]. In some cases, i can be
ad an ageous o use Poisson eg ession. In he compa ison wi h he end in he o m
o a nonlinea unc ion, he Poisson eg ession has less accu a e esul s. Howe e , he
ad an age is lowe compu a ional ime.
P2: The choice o he eg ession unc ion o desc ibing he end in he da a is no
clea (se e al di e en unc ions can gi e simila esul s).
R2: I is ad isable o look o a comp omise be ween he quali y o he i ing acco ding
o he chosen c i e ia (e.g., R
2
, MAPE) and he p ope ies o he selec ed unc ions. The
au ho s e alua ed he ollowing p ope ies as subs an ial:
•
Mono ony— he end o e he o ecas ing ho izon should no change om ising
o declining and ice e sa, so he end is assumed o be mono onous. Oscilla ions
a ound he end caused by he seasonal o cyclical componen a e no possible o
desc ibe in sho ime se ies. Requi ing mono ony will also educe he isk o model
o e i ing. I is ecommended o use he powe unc ion o end modeling. The
ad an age is i s wide applica ion o bo h ising and declining ends [34].
•
Limi ed g ow h—some ime se ies ha e a e y signi ican g ow h in his o ical da a
( esp. decline), which may be exponen ial. Such a end is usual a e he sys em
change, e.g., by collec ing a new was e ac ion. I canno be expec ed o con inue his
end o e he en i e o ecas ho izon. The mo e likely de elopmen is ha he was e
gene a ion will slow down he g ow h. In such cases, i is app op ia e o model he
end using an S-shaped cu e [34].

Sus ainabili y 2023,15, 3278 17 o 29
I is ecommended o model he end wi h a simple model and a cons an alue in he
ollowing cases, see [34]:
•
By excluding da a a e p e-p ocessing, he ime se ies emains oo sho o end
es ima ion. The minimum numbe o da a can be adjus ed o he speci ic leng h o he
ime se ies.
•
The end model in he da a using he unc ions desc ibed abo e is o poo quali y. As
a c i e ion ecommends using R2, he c i ical limi R2 can be cus omized.
•
A simple model wi h a cons an alue leads o esul s ha a e compa able o a mo e
complex model.
•
As a special case, ime se ies con aining ze o gene a ion o was e in ecen yea s should
be ex apola ed as a ze o alue–i is no expec ed o s a gene a ing his was e again.
P3: A en ion should be paid o possible special cases o he was e s eams. Fo
example, he legisla ion may change, which may hen cause a changepoin , e c. Comple ely
new was e s eams may also be in oduced a e he legisla i e in e en ion. His o ical
da a hen canno be used o o ecas ing in he usual manne .
R3: The men ioned special cases should be de ec ed in p e-p ocessing i he change has
al eady been e lec ed in he his o ical da a. I is possible o conside he end o ecas ing
e en i no all egions ha e al eady esponded o he change. In o he wo ds, mo e
ad anced egions may ou line he u u e di ec ions o he less de eloped ones (Smejkalo á
e al., 2020 [
64
]). An analogous idea can be applied a he s a e le el conside ing coun ies
wi h di e en ly ad anced WM. O he no able special cases ep esen was e ac ions whose
quan i ies a e di ec ly in luenced by he de elopmen s o speci ic ex e nal ac o s. A ypical
example is me al was e, which is linked o he pu chase p ice o aw ma e ials. The
pu chase p ice is di icul o o ecas due o i s cyclic beha io , leading o complica ed
o ecas ing o he me al was e ac ion.
4.3.3. Da a Reconcilia ion
P1: His o ical was e gene a ion da a can con ain in e nal consis ency links, which
o m a hie a chical s uc u e: he s a e comp ises he egions, he egions comp ise he
municipali ies. These links a e no always main ained a e applying he selec ed me hod
(Sec ion 4.3.2).
R1: The au ho s ecommend co ec ing was e gene a ion models o es o e he sys em
links using, o example, a da a econcilia ion model [
33
]. I is assumed ha he amoun
o was e gene a ed a a highe e i o ial uni is equal o he sum o he amoun s in he
e i o ies ha belong o i (e.g., municipali ies loca ed in a pa icula egion). The second
ype o in e nal balance assumes links be ween he was e ac ions. An example is he e ec
o sepa a ed was e gene a ion on he amoun o MMW [10].
P2: The da a econcilia ion model is signi ican ly a ec ed by he model weigh se ings,
o example, di e en impo ance o he esul s ha a e balanced.
R2: I is necessa y o pay a en ion o app op ia ely chosen weigh s when balancing;
weigh s should be conside ed bo h in e ms o o al was e gene a ion (p e e ably in he
squa e oo ) and in e ms o he quali y o he es ima e. In he case o he balance, pe cen age
changes mus also be aken in o accoun [34].
P3: An inc ease in he gene a ion o one ac ion does no mean a dec ease in he
p oduc ion o ano he ac ion by exac ly his amoun ; ha is, he o e low o was e
amoun s is no consis en .
R3: The in e dependence o was e ac ions mus be cap u ed in a o m ha co e-
sponds o eali y; he alues o he ansi ion be ween he ac ions do no ha e o be equal;
indi idual was e s eams a e c ea ed and disappea [60].
P4: The possibili ies o he chosen sol e can signi ican ly a ec he success o he
calcula ion when he model is s a ed as a ma hema ical p og amming p oblem.
R4: The da a econcilia ion model can be o mula ed in addi i e o mul iplica i e
o m [
34
]. The mul iplica i e o m has a signi ican ad an age o was es wi h high
a iabili y be ween indi idual ac ions. P oduce s wi h signi ican ly di e en was e
Sus ainabili y 2023,15, 3278 18 o 29
gene a ions can occu a di e en le els o he e i o y. The addi i e o mula ion causes
nume ical and ounding e o s. The se ing o he model weigh s also depends on he
o mula ion. In addi ion, he mul iplica i e o m wo ks wi h he pe cen age change, which
is a p oblem in he case o ze o alues [34].
P5: The sol e is no able o ind he op imal solu ion due o he ask size o compu a-
ional complexi y p oblems.
R5: Usually, a leas a elaxed solu ion is a ailable, i.e., he balances a e no me exac ly.
This may no be a p oblem o some o ecas s. In o he cases, i is ecommended o educe
he op imiza ion ask so ha smalle se s o was e s eams will be balanced, e.g., only o
indi idual ca alogue numbe s.
4.3.4. Exp ession o Unce ain y
P1: Each o ecas should p o ide con idence in e als [
65
], ideally also p edic ion
in e als. I da a econcilia ion has been ca ied ou (p e ious s ep, Sec ion 4.3.3), i is no
possible o use common in e al cons uc s wi h a no mal p obabili y dis ibu ion a ound
he model mean alue.
R1: The au ho s sugges simula ing he con idence and p edic ion in e als wi h he
boo s ap me hod. I is possible o use his o ical da a as one o he possible ealiza ions,
and hen i s a iance o gene a e new da a se s. A o ecas is made o hese gene a ed da a,
which c ea es di e en ealiza ions o he o ecas . Based on he p ope ies o o ecas s o
indi idual ealiza ions, con idence and p edic ion in e als a e compiled [
34
]. In he case
o a limi ed numbe o possible gene a ions wi hin he boo s ap, he a iance o o ecas s
o he cons uc ion in e al is es ima ed. In his case, app oxima ely 30 boo s aps a e
conside ed su icien [34].
4.4. Da a Pos -P ocessing
4.4.1. Modeling o Scena ios
P1: A o ecas does no include possible changes o he sys em, as desc ibed in
Sec ion 1.2. P ojec ions de ia e om a basic o ecas because hey mus obey he model
cons ain s and p ede ined bounda y condi ions. I is essen ial o ensu e he easibili y and
consis ency o a p ojec ion.
R1: Legisla i e in e en ions ake place a he s a e le el o he le els o o he sel -
go e ning uni s. The dis ibu ion o he p ojec ion changes o he mic o- egion is essen ial
o de e mining he po en ial o u u e de elopmen . Fo analyses associa ed wi h he
po en ial o inc ease he sepa a ion o MSW, i is necessa y o ha e a ailable (o a leas
es ima e) he MMW composi ion, which allows es ima ing he po en ial o change. When
using p ojec ions, i is ecommended o conside he links be ween was e s eams [
60
]. Fo
he p ojec ions, i is necessa y o de e mine he po en ial o change. The ollowing applies
o scena io solu ions:
•
The scena io does no exceed he po en ial o change which was se o a speci ic
e i o ial uni .
•
All e i o ial uni s show a shi owa ds mee ing he scena io i he po en ial allows i .
•
The indi idual e i o ies do no o e ake in e ms o he ul illmen o po en ial and
a e mono onous.
4.4.2. Sel -Lea ning Mechanisms
P1: The esul s mus be upda ed when he inpu da a se changes. The change may
occu due o he da a edi ing in he o iginal da abase o he addi ion o new da a on was e
gene a ion om he nex pe iod.
R1: Du ing model e-e alua ion, one mus ca y ou all he o ecas ing s eps speci ied
in Figu e 6. When he da a a e dynamic in na u e, i is necessa y o eac quickly and
de elop an adequa e me hodology [
66
]. As an example, one migh men ion o ecas ing
u ilizing sma echnologies such as weigh o ill le el senso -equipped con aine s.
Sus ainabili y 2023,15, 3278 19 o 29
4.4.3. Model Diagnos ics and P esen a ion o Resul s
P1: The quali y o he models mus be e i ied.
R1: The quali y o a o ecas should be es ed using a p e-alloca ed es da a se . In
o he wo ds, he o ecas should be made using a smalle da a se , and he esul s should
hen be compa ed wi h he emaining alues ha we e no used as he model inpu da a.
Model e i ica ion can also be conduc ed ia con idence in e als.
R2: Fo ecas s p o ided by he models mus be p esen ed clea ly so ha hei end-use s
( he decision-make s) can easily in e p e hem. Me hods o ep esen ing esul s isual-
iza ion can be ound in he pape [
45
]. Ano he p omising app oach o communica ing
he esul s and inco po a ing hem in o he simula ion calcula ions is he gami ica ion
app oach [
67
]. Tools based on gami ica ion o s a egic planning in was e managemen
p o ide in e ac i e eedback wi h espec o he se c i e ia [68].
5. Modeling Fu u e Was e Gene a ion and T ea men Based on Sho Time Se ies
Au ho s o his con ibu ion ecommend applying a combina ion o ecas model and
a subsequen p ojec ion model, see Figu e 7. Compa ed o Figu e 6, Figu e 7shows he
essen ial s eps o he p ojec ion in g ea e de ail. In he i s s ep, a o ecas should be
c ea ed based on his o ical da a, which conside s main aining he cu en o m o WM in o
he u u e, see Sec ion 5.1. This pa co esponds o da a p epa a ion, p e-p ocessing and
p ocessing in Figu e 6. This is basic in o ma ion, bu was e gene a ion will be a ec ed by
sys ema ic changes (legisla i e, echnological e c.) and global ends (sociology, economy
e c.) in he eal wo ld. Using p edic i e models, he in luence o hese ac o s on was e
gene a ion can be es ima ed, bu hei de elopmen canno be well o ecas ed. The expec ed
de elopmen o he in luencing ac o s is a ma e o expe assessmen . Was e gene a ion
p ojec ion should be a combina ion o he o ecas esul s wi h a p edic i e model, and he
impac o he ex e nal in e en ions can be modelled as di e en scena ios. In he o m o
scena ios, an es ima e o u u e was e gene a ion can be achie ed, which will co espond
as bes as possible o he eal condi ions.
Sus ainabili y 2023, 15, x FOR PEER REVIEW 20 o 30
Figu e 7. Schema ic ep esen a ion o he in eg a ion o o ecas ing and p ojec ion. P edic i e
model [15].
5.1. Was e Gene a ion and T ea men Fo ecas
I is ecommended o apply a me hod based on end analysis wi h subsequen da a
econcilia ion in o de o main ain hie a chical links in he da a [34]. The end in he his-
o ical da a can be modelled by he sui able cu e. The model o he was e gene a ion
end  is signi ican ly a ec ed by he ype o he cu e  (1), whe e is he index o
ime including bo h he his o ical da a and a o ecas .
=

. (1)
Designa ion  indica es he cu e ha is ecommended in he o m o powe unc-
ion (2) o logis ic unc ion (3) based on he da a cha ac e :
=+, (2)
=1
1+󰇛󰇜. (3)
whe e , ,  a e he eg ession coe icien s. A model ha i s he his o ical da a well is
ex apola ed o co e he en i e o ecas ing ho izon.
The end es ima es do no gene ally main ain he hie a chical links, i.e., he sum o
he egional ends does no co espond o he na ional end and simila ly o o he links.
The e o e, i is ecommended o apply da a econcilia ion o ensu e hese links. This is
achie ed by a se o cons ain s. Fo he e i o ial hie a chy, his is cons ain (4), whe e
, de ines he ela ions be ween e i o ies ( is a supe io e i o ial uni and  is a
lowe e i o y). =

,.
∈ ∀

∈. (4)
Cons ain s in he case o links be ween was e ac ions can also be o mula ed simi-
la ly. Equa ion (5) connec s he was e gene a ion inpu da a  in pa icula ime wi h he
model a iable  and he was e gene a ion da a e o  in he o m o addi i e no a ion.
Figu e 7.
Schema ic ep esen a ion o he in eg a ion o o ecas ing and p ojec ion. P edic i e
model [15].
Sus ainabili y 2023,15, 3278 20 o 29
5.1. Was e Gene a ion and T ea men Fo ecas
I is ecommended o apply a me hod based on end analysis wi h subsequen da a
econcilia ion in o de o main ain hie a chical links in he da a [
34
]. The end in he
his o ical da a can be modelled by he sui able cu e. The model o he was e gene a ion
end
p
is signi ican ly a ec ed by he ype o he cu e
(1), whe e is he index o ime
including bo h he his o ical da a and a o ecas .
p = . (1)
Designa ion
indica es he cu e ha is ecommended in he o m o powe unc ion
(2) o logis ic unc ion (3) based on he da a cha ac e :
p =a+b c, (2)
p =1
1+e−(a+b ). (3)
whe e
a
,
b
,
c
a e he eg ession coe icien s. A model ha i s he his o ical da a well is
ex apola ed o co e he en i e o ecas ing ho izon.
The end es ima es do no gene ally main ain he hie a chical links, i.e., he sum o
he egional ends does no co espond o he na ional end and simila ly o o he links.
The e o e, i is ecommended o apply da a econcilia ion o ensu e hese links. This is
achie ed by a se o cons ain s. Fo he e i o ial hie a chy, his is cons ain (4), whe e
Aj,jde ines he ela ions be ween e i o ies (jis a supe io e i o ial uni and jis a lowe
e i o y).
kj=∑
j∈J
Aj,jkj.∀j∈J. (4)
Cons ain s in he case o links be ween was e ac ions can also be o mula ed simila ly.
Equa ion (5) connec s he was e gene a ion inpu da a
pj
in pa icula ime wi h he model
a iable
kj
and he was e gene a ion da a e o
εj
in he o m o addi i e no a ion. In some
cases, o easons o sol abili y, he mul iplica i e o m o no a ion is mo e ad an ageous.
kj=pj+εj.∀j∈J, (5)
Equa ion (6) ep esen s he objec i e unc ion o he a ian wi h weigh s
j
o ake
in o accoun he size o he p oduce and weigh s wjacco ding o quali y o i ing.
∑
j∈J jwj2ε+
j2+ε−
j2. (6)
The esul o he pe o med da a econcilia ion is a o ecas based on his o ical da a;
his is a basic scena io, u he ma ked BAU (business-as-usual scena io).
5.2. Was e Gene a ion and T ea men P ojec ion
P ojec ions o was e gene a ion a e usually o med o mee some a ge s ha a e se o
agg ega ed e i o y (na ional le el). The de aul in o ma ion is o ecas (BAU, Sec ion 5.1),
which is modi ied o achie e he condi ions o mula ed in he scena io. I is assumed
ha in e en ions can in luence was e sepa a ion and was e gene a ion p e en ion. The
inc ease in he was e sepa a ion wi hin he scena io is caused by he highe sepa a ion o
he modelled ac ion
(e.g., pape , plas ics, glass) om unsepa a ed was e u (e.g., MMW,
bulky was e). Thus, he expe assessmen includes se ing he ollowing pa ame e s:
•
pe cen age was e p e en ion (
p e SC,N1
:
SC
—ma king he scena io,
N
1— e i o ial
le el NUTS1),
•
sepa a ion a e o indi idual assessed was e ac ions (
SRSC,N1
u,
:
u
—unsepa a ed was e
ac ion, —modelled was e ac ion).
Sus ainabili y 2023,15, 3278 21 o 29
The main esul s o scena io SC on agg ega ed e i o y N1 a e:
•Sepa a ed was e kSC,N1
u, .
The gene a ion o sepa a ed was e
, which o igina es in he unsepa a ed ac ion
u
, is
de e mined acco ding o (7). The exp ession
kBAU,N1
u, +lBAU,N1
u,
means he o al gene a ion
o ac ion
acco ding o BAU, i.e., sepa a ed
kBAU,N1
u,
o igina es in u and es o in
unsepa a ed ac ion
lBAU,N1
u,
amoun . F om he o al gene a ion, he sepa a ed amoun is
de e mined using he sepa a ion a e
SRSC,N1
u,
, and he impac o p e en ion is also aken
in o accoun as 1−p e SC,N1.
•Was e in unsepa a ed was e u:lSC,N1
u, .
The esul o his poin is he e o e he composi ion o he unsepa a ed was e u, and
i is de e mined acco ding o Equa ion (8). The p inciple is simila o he p e ious poin
o sepa a ed was e
kSC,N1
u,
, only he supplemen o he sepa a ion a e is conside ed as
1−SRSC,N1
u, .
•To al unsepa a ed was e LSC,N1
u.
The gene a ion o he unsepa a ed was e u is gi en by (9). I comes om he gene a ion
o u in BAU
LBAU,N1
u
, which is educed by he p e en ion in he o m
1−p e SC,N1
.
The was e ha was sepa a ed acco ding o he scena io SC is deduc ed om his amoun .
The sepa a ion o was e in he scena io SC is de e mined as he di e ence be ween quan i y
in BAU gi en by
∑ ∈FlBAU,N1
u, 1−p e SC,N1
and he new quan i y in
SC
scena io gi en
by ∑ ∈FlSC,N1
u, .
kSC,N1
u, =1−p e SC,N1kBAU,N1
u, +lBAU,N1
u, SRSC,N1
u, ∀u∈U,∀ ∈F(7)
lSC,N1
u, =kBAU,N1
u, +lBAU,N1
u, 1−SRSC,N1
u, 1−p e SC,N1∀u∈U,∀ ∈F(8)
LSC,N1
u=LBAU,N1
u1−p e SC,N1− ∑
∈F
lBAU,N1
u, 1−p e SC,N1−∑
∈F
lSC,N1
u, !∀u∈U(9)
The esul o he SC scena io a he agg ega ed (na ional) le el, gi en by (7)–(9), should
be subsequen ly di ided in o lowe e i o ial uni s, down o he municipali ies, because
he na ional WM is he esul o he ac i i ies o he lowe uni s (municipali ies). I is
ecommended o di ide he scena io o he na ional le el (N1) o he le el o municipali ies
(L2) acco ding o he po en ial ha indi idual municipali ies ha e o was e sepa a ion
imp o emen . A sui able indica o o his po en ial may be he sepa a ion a e.
The goal o he p esen ed app oach is a sugges ion o a gene al app oach ha is
applicable o any was e ac ion based on sho ime se ies. A he same ime, i is a unique
app oach, combining he p inciples o o ecas ing wi h he conside a ion o in luen ial
ac o s h ough scena ios. Thanks o modelled scena ios, he expec ed a iabili y o was e
gene a ion is aken in o accoun , which will enable mo e e icien planning o WM.
6. Conclusions
O e he yea s, a ious me hods used o was e gene a ion modeling ha e been
p oposed. P edic ion, o ecas ing, and p ojec ion mus be dis inguished, while he use o
a ious app oaches depends on he speci ic applica ion in WM. A de iciency was ound in
ha a signi ican numbe o pas publica ions ha e been de o ed o designing a sui able
modeling me hod. Howe e , he au ho s ecommend paying a en ion o he quali y o he
inpu da a, which has been minimal in he e iewed pape s. I is impo an o emembe
ha inpu da a a e essen ial o e e y model. In addi ion, he end-use o a o ecas ,
p edic ion, o p ojec ion mus be p o ided wi h he model unce ain ies in he o m o

Sus ainabili y 2023,15, 3278 22 o 29
con idence in e als o se e al scena ios. This is ano he key pa o each model ha was
missing in he majo i y o he e alua ed pape s on WM modeling. Al hough many me hods
do no o e a di ec way o exp essing he model unce ain y, boo s apping can be used o
a leas es ima e i .
The da a se a ailable, i s e i o ial and empo al de ail, and he p edic ion ho izon
a e decisi e o he modeling me hod choice. As p edic ion models ha e al eady been
elabo a ed in g ea e de ail [
15
], mos o he ex is de o ed o o ecas s and p ojec ions.
The au ho s o mula ed he decisi e p ocess o he choice o modeling me hod, which
p o ides unique suppo o u he o ecas e s. In summa y, i he in luencing ac o s
and hei links o was e gene a ion a e used o modeling, he in luencing ac o s mus
be o ecas ed as well. The use o TSA is o en limi ed by i s equi emen s o ime se ies
leng h. In addi ion, he p esen ed me hods a e in ended o speci ic was e ac ions. Based
on he men ioned conclusions o he e iew, he au ho s p esen ed a gene al app oach o
o ecas ing. To use his me hod, i is necessa y o ha e a ime se ies o his o ical da a on
was e gene a ion. Compa ed o o he TSA-based me hods, a signi ican ly sho e ime
se ies is su icien . The calcula ion o he me hod is based on he op imiza ion ask o
nonlinea p og amming. The use mus he e o e ha e so wa e sui able o his calcula ion
wi h adequa e sol e s (CONOPT, KNITRO, e c.). The main ea u e o o ecas ing is ha
i models u u e de elopmen s while main aining his o ical condi ions. The impac o
changing he in luen ial ac o s on was e gene a ion can be implemen ed in he o ecas in
he o m o scena ios.
Supplemen a y Ma e ials:
The ollowing suppo ing in o ma ion can be downloaded a : h ps:
//www.mdpi.com/a icle/10.3390/su15043278/s1. O e iew: A ached MS Excel ile.
Au ho Con ibu ions:
Concep ualiza ion, R.Š. and M.P.; me hodology, M.R.; in es iga ion, V.S.,
L.S., V.N. and D.H.; da a cu a ion, V.S. and L.S.; w i ing—o iginal d a p epa a ion, M.R. and V.S.;
w i ing— e iew and edi ing, V.S. and R.Š.; isualiza ion, L.S. and V.N.; supe ision, R.Š.; p ojec
adminis a ion, R.Š. and M.P.; unding acquisi ion, M.P. All au ho s ha e ead and ag eed o he
published e sion o he manusc ip .
Funding:
The a icle was w i en as pa o he p ojec TIRSMZP719 (“P ognosis o Was e Gene a ion
and De e mina ion o he Composi ion o Municipal Was e”). The au ho s g a e ully acknowledge
he suppo p o ided by Technology Agency o he Czech Republic and Minis y o he En i onmen
o he Czech Republic. The au ho s also g a e ully acknowledge inancial suppo p o ided by g an
No. SS02030008 “Cen e o En i onmen al Resea ch: Was e managemen , ci cula economy and
en i onmen al secu i y”; G an No. GA 20-00091Y o he Czech Science Founda ion and p ojec FSR
FORD 5-6/2022-23/FLKˇ
R/001 Sus ainabili y in T anspo : Mode n T ends and hei Impac on he
En i onmen .
Ins i u ional Re iew Boa d S a emen : No applicable.
In o med Consen S a emen : No applicable.
Da a A ailabili y S a emen :
The da a a e he ou pu o he conduc ed esea ch, see Supplemen a y
Ma e ials.
Acknowledgmen s:
We acknowledge he inancial suppo ecei ed om Technology Agency o he
Czech Republic, G an agency o he Czech Republic and Tomas Ba a Uni e si y in Zlín.
Con lic s o In e es :
The au ho s decla e no con lic o in e es . The unde s had no ole in he design
o he s udy; in he collec ion, analyses, o in e p e a ion o da a; in he w i ing o he manusc ip , o
in he decision o publish he esul s.
Appendix A. SWOT Analysis
The SWOT analyses, e alua ing s eng hs, weaknesses, oppo uni ies and h ea s, we e
pe o med o se e al p esen ed me hods: mul iple linea eg ession—MLR
(Table A1), gene alized linea eg ession—GLM (Table A2), me hods using decision ees—
DT (Table A3), a i icial neu al ne wo k—ANN (Table A4), ime se ies models—TSA
Sus ainabili y 2023,15, 3278 23 o 29
(Table A5) and scena io app oaches (Table A6). SWOT analyses enable be e insigh
in o he p oblems o indi idual me hods and enable e y aluable compa ison o hei
ad an ages and disad an ages.
Table A1. Mul iple linea eg ession.
S eng hs
I allows o quan i y he in luence o indi idual p edic o s (including he signi icance) o hei in e ac ion on he dependen a iable.
I p o ides a gene al in o ma ion on he unc ioning o he modeled p ocess om bo h a quali a i e (dependency di ec ion) and a
quan i a i e (size) pe spec i e.
I is easy o ob ain he con idence in e als (CI) and he p edic ion in e als (PI).
I is simple, compu a ional e icien and easy in e p e able.
Weaknesses
Necessi y o s ong assump ions compliance (especially o he no mali y o esidues, homoscedas ici y o da a and linea
dependence wi h espec o he coe icien s), which is o en iola ed in p ac ice.
The dependence is es ic ed o app oxima ely linea /linea izable wi h espec o he eg ession coe icien s.
The isk o mul i-collinea i y o da a, especially in mo e complex (mul idimensional) p oblems.
Accu acy, especially o complex non-linea p oblems.
Oppo uni ies
The possibili y o iden i ica ion and co ec ion in case o unexpec ed beha io o he model, leading o be e con ol o he model
c ea ion.
Da a p e-p ocessing me hods such as p incipal componen analysis (PCA) can be use ul o educe he dimension and ensu e he
independence a iables [69].
I s main ask in WM is o e eal he ac o s ha ha e undamen al in luence [
16
]. Thus, MLR is use ul especially o policy planning
and in as uc u e decision making (Sec ion 1.1).
As g ouping municipali ies in o clus e s based on hei cha ac e is ics can lead o models ea u ing highe accu acy [70], sepa a e
models we e hen c ea ed o each clus e .
Implemen ed in all s anda d s a is ical SW ools, o en wi h au oma ic c ea ion o ou pu s (especially he g aphical ones), which
may wa n e en less expe ienced use s ha some p e equisi es a e no me .
Th ea s
“Necessi y” o manual selec ion o p edic o s o o he o de o in e ac ions means ha smalle numbe o po en ial p edic o s can
be used in p ac ice (co ela ion analysis can be used o educe hei numbe , bu i is also ecommended o check he esul s and i
also equi es close inspec ion o p edic o s and hei dependence).
The assump ions a e qui e s ic , and i usually is qui e di icul o mee hem wi h WM da a, especially a lowe e i o ial le els.
WM sys ems a e complex and nonlinea in na u e, and he analysis o esiduals should be used o e alua e he app op ia eness o
linea app oxima ion.
In case o non-homogeneous da a, he e a e p oblems wi h he o m o he dependence o wi h he applicabili y o c ea ed model on
he ype o da a, which was no su icien ly ep esen ed in he model c ea ion phase.
Table A2. Gene alized linea models.
S eng hs
I p o ides in o ma ion on he p opo ion o he explained a iabili y o he dependen a iable h ough he included p edic o s
(independen a iables).
I p o ides gene al in o ma ion on he unc ioning o he modeled p ocess om bo h a quali a i e (dependency di ec ion) and a
quan i a i e (size) pe spec i e.
Compu a ionally no demanding.
Weaknesses
Assump ions on he dis ibu ion o esidues, homoscedas ici y o da a and linea dependence wi h espec o coe icien s.
A isk o mul i-collinea i y o da a, especially in mo e complex (mul idimensional) p oblems.
The e is no analy ical way o es ima e he model pa ame e s. Knowledge in WM is essen ial o de e mining sui able ini ial
es ima es. I also is possible o use he esul s o MLR as he s a ing poin o ano he GLM.
CI and PI gene ally do no exis , bu he e a e a emp s o cons uc hem o some special cases (e.g., o gamma eg ession) [71].
Lowe accu acy, especially o complex non-linea p oblems.
Sus ainabili y 2023,15, 3278 24 o 29
Table A2. Con .
Oppo uni ies
The possibili y o iden i ica ion and co ec ion in case o unexpec ed beha io o he model, leading o be e con ol o he model
c ea ion.
Be e lexibili y (compa ed o MRL).
The possibili y o include expe knowledge o he p ocess by selec ion o dis ibu ion o dependen a iable o by including known
e ec s (o se ).
The possibili y o speci y he smoo hness o he mono onici y o dependency (sui able also o main aining he same s uc u e o he
model when using new da a).
Rela ion o o he models such as gene alized addi i e models (GAM), penalized eg ession (Ridge, Lasso, Elas ic Ne ) o mixed
models.
Implemen ed in all s anda d s a is ical SW ools, o en wi h au oma ic c ea ion o ou pu s (especially he g aphical ones), which
may wa n e en less expe ienced use s ha some p e equisi es a e no me .
Th ea s
“Necessi y” o manual selec ion o p edic o s o o he o de o in e ac ions means ha smalle numbe o po en ial p edic o s (o
o de o ens) can be used in p ac ice (co ela ion analysis can be used o educe hei numbe bu i is also ecommended o check
he esul s and i equi es close inspec ion o p edic o s and hei dependence).
In case o non-homogeneous da a, he e a e p oblems wi h he o m o he dependence o wi h he applicabili y o c ea ed model on
he ype o da a, which was no su icien ly ep esen ed in he model c ea ion phase.
In gene al, a global op imum, when sea ching o pa ame e alues, is no gua an eed (does no apply o some special cases).
Some GLM ypes can model nega i e alues. Fo was e gene a ion modeling i is ecommended o use GLM ypes o which he
acquisi ion o only posi i e alues can be gua an eed (e.g., gamma eg ession).
Table A3. Me hods using decision ees.
S eng hs
I allows o desc ibe e en complex non-linea dependencies, which o en appea in WM.
High accu acy, especially in compa ison wi h adi ional me hods [72].
Models a e obus and no as sensi i e o he choice o in luencing ac o s as MLR o GLM.
Robus ness o andom o es (RF) and G adien boos ed eg ession ee (GBRT) [73].
Weaknesses
Compu a ionally demanding, especially o complex models and la ge numbe o obse a ions.
In e p e a ion is challenging o RF and GBRT. DT loses high accu acy.
Oppo uni ies
Da a assump ions.
The selec ion o a speci ic DT model also depends on he size o he da a se (de ail o he e i o ial di ision, moni o ed was e
ac ions).
Au oma ed p ocess wi h p edic o s enabling o wo k wi h la ge numbe o independen a iables.
In o ma ion on he impo ance o each a iable is p o ided, his helps wi h hei selec ion.
Pa ame e uning is less demanding (compa ed o ANN).
The compu a ion o RF can easily be pa allelized.
Th ea s
Gene ally, he PI cons uc ion is mo e complica ed (compa ed o MLR). Quan ile eg ession o esampling me hods may be used.
Fo DT, he in e als cons uc ion me hod was no ound, bu he in e als o indi idual models in ee lea es could be heo e ically
used.
GBRT is compu a ionally in ensi e.
In case o RF and GBRT, he e is insu icien insigh in o in e nal unc ioning o he model. This means ha i is di icul o ind he
oo cause i he model beha es unexpec edly (excep o DT).
Th ea o he model o e - i ing.
Sus ainabili y 2023,15, 3278 25 o 29
Table A4. A i icial neu al ne wo ks.
S eng hs
They allow o desc ibe e en complex non-linea dependencies.
ANN models ha e ew assump ions abou he da a in he e ms o dis ibu ion. F om his poin o iew, one could u ilize mos da a
se s coming om WM.
I is possible o wo k wi h many independen a iables ha in luence he o m o WM.
High accu acy, in compa ison wi h adi ional me hods [74].
Weaknesses
Compu a ionally demanding, especially o complex models and la ge numbe o obse a ions [75].
Requi es model speci ic expe ience [75].
ANN a e no sui able o “on- he- ly” decision making.
Oppo uni ies
Low da a assump ions.
Inpu da a can be compiled in p e-p ocessing o achie e he highes possible model accu acy.
I he pa ame e s a e se co ec ly, he esul s a e mos accu a e o nonlinea dependencies. Howe e , choosing app op ia e
pa ame e alues is no i ial, and unde s anding o WM is equi ed.
Au oma ed p ocess wi h p edic o s enabling o wo k wi h la ge numbe o independen a iables (e en hund eds o a iables bu
conside ing he compu a ional complexi y).
Th ea s
The e is insu icien insigh in o in e nal unc ioning o he model.
In gene al, a global op imum o pa ame e s is no gua an eed.
CI and PI a e sol able, bu i is ad isable o keep cau ion (as wi h me hods using decision ees).
T aining an ANN is compu a ionally in ensi e.
Models a e ypically used on la ge da a se s (ideally housands o da a poin s). Applica ion o smalle da a se s, which a e common
in WM, is p oblema ic.
Th ea o he model o e - i ing.
In e p e a ion challenge (black box models).
Table A5. Time se ies analysis.
S eng hs
I allows o cap u e he dynamic o de elopmen o he obse ed p ocess.
Good heo e ical basis.
CI and PI c ea ion clea and s aigh o wa d ( his is simila o MLR).
Weaknesses
Disad an ageous a io o amoun o da a needed o modeling and he leng h o he p edic ion (high ens o be e hund eds o
obse ed alues a e needed o p edic ion o o de o uni s).
I is di icul o ake in o conside a ion ex e nal in luences (socio-economic, demog aphic, e c.).
Lack o da a in he WM a ea.
Oppo uni ies
Recommended when e ealing he links in he sys em is no impo an , bu only he ime de elopmen (e en in he u u e).
The possibili y o be e unde s and he beha io o he dependen a iable i sel (seasonali y, end, au oco ela ion unc ion, e c.),
bu only p o ided enough da a is a ailable (i.e., seasonal e ec s on annual da a canno be asce ained).
Th ea s
Disp opo iona e con idence in he model buil on insu icien da a (since i is a “whi e box” model).