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Hierarchical optimisation model for waste management forecasting in EU

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Abstract

The level of waste management varies significantly from one EU state to another and therefore they have different starting position regarding reaching defined EU targets. The forecast of waste production and treatment is essential information for the expected future EU targets fulfilment. If waste treatment does not meet the targets under the current conditions, it is necessary to change waste management strategies. This contribution presents a universal approach for forecasting waste production and treatment using optimisation models. The approach is based on the trend analysis with the subsequent data reconciliation (quadratic programming). The presented methodology also provides recommendations to include the quality of trend estimate and significance of territory in form of weights in objective function. The developed approach also allows to put into context different methods of waste handling and production. The variability of forecast is described by prediction and confidence intervals. Within the EU forecast, the expected demographic development is taken into account. The results show that most states will not meet EU targets with current trend of waste management in time. Presented methodology is developed at a general level and it is a suitable basis for strategic planning at the national and transnational level.

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Data availability

The demographic data and data about municipal solid waste used in the case study are available from the database of the Eurostat – European statistical office and Waste Management Information System of Czech Republic called ISOH (ISOH 2021).

Abbreviations

\(j,\overline{j} \in J\) :

All territories, i.e. individual states and the EU as a whole

\(h,\overline{h} \in H\) :

Waste handling /production, incineration, recycling, landfilling, treatment/

\(t \in T\) :

Time period of historical data and forecast

\(\beta \in B\) :

Bootstrap resampling

\(a,b,c\) :

Regression coefficients for trend estimate

\(A_{{j,\overline{j}}}\) :

Membership matrix for territory hierarchy

\(\tilde{k}_{ii}\) :

Diagonal element of regression matrix

\(l_{t,j,h}\) :

Binary parameter taking into account results from data pre-processing

\(m_{t,j,h}\) :

Forecasted result of waste production or handling after data reconciliation

\(\tilde{m}_{t,\beta }^{j,h}\) :

Forecasted result of bootstrap generated data

\(n\) :

Number of points in time series used for trend estimate

\(p_{t,j,h}\) :

Trend value for territorial unit \(j\) and waste handling \(h\)

\(q\) :

Number of parameters in regression used for trend estimates

\(\tilde{t}\) :

Order of predicting year

\(t_{{{\text{n}} - q}} \left( {1 - \alpha /2} \right)\) :

\(\left( {1 - \alpha /2} \right)\)-Quantile of Student's t-distribution with \(n - q\) degree of freedom

\(T_{j,h}\) :

Total number of available points in time series after data pre-processing

\(U_{{h,\overline{h}}}\) :

Membership matrix for waste production and handling hierarchy

\(v_{j,h}\) :

Weight characterising the size of the producent

\(w_{j,h}\) :

Weight characterising the quality of data fitting

\(x_{i,j,h}\) :

Historical data point in time series

\(\tilde{x}_{t,\beta }^{j,h}\) :

Generated data for confidence interval bootstrap construction

\(\in_{t}^{j,h}\) :

Data residuals from evaluated trend

\(\in_{t,\beta }^{j,h}\) :

Selected residual from the set of data residuals in bootstrap

\(\tilde{ \in }_{t}^{j,h}\) :

Scaled data residuals from evaluated trend

\(\sigma_{t}^{2}\) :

Variance estimate of prognosis based on bootstrap repetition

\(\tilde{\sigma }^{2}\) :

Variance estimate of residual component

\(\varepsilon_{t,j,h}\) :

Error included into trend to maintain links in the system

\(\varepsilon_{t,j,h}^{ + }\) :

Positive part of error

\(\varepsilon_{t,j,h}^{ - }\) :

Negative part of error

\(\delta_{t,j,h}\) :

Multiplier of trend in data reconciliation

BE:

Belgium

CEP:

Circular economy package

CZ:

Czechia

DK:

Denmark

ES:

Spain

EU:

European Union

FI:

Finland

IT:

Italy

LR:

Linear regression

LT:

Lithuania

LV:

Latvia

MSW:

Municipal solid waste

RO:

Romania

SE:

Sweden

TSA:

Time-series analysis

WM:

Waste management

References

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Acknowledgements

The authors gratefully acknowledge the financial support provided by ERDF within the research projects No. CZ.02.1.01/0.0/0.0/16_026/0008413 "Strategic Partnership for Environmental Technologies and Energy Production". This work was supported by Grant No. GA 22-11867S of the Czech Science Foundation. The support is gratefully acknowledged.

Author information

Authors and Affiliations

  1. Institute of Process Engineering, Faculty of Mechanical Engineering, Brno University of Technology, Brno, Czech Republic

    V. Smejkalová, R. Šomplák & J. Pluskal

  2. Department of Geography, Faculty of Science, Jan Evangelista Purkyně University, Ústí nad Labem, Czech Republic

    K. Rybová

Authors
  1. V. Smejkalová
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  2. R. Šomplák
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  3. J. Pluskal
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  4. K. Rybová
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Contributions

All authors contributed to the presented study. Conceptualisation was provided by RŠ. The data collection and formal analysis was performed by VS and KR. Development of methodology and creation of models were performed by VS and RŠ. Validation of results was performed by VS, RŠ and JP. The figures and overall visualisation were performed by VS and JP. The first draft of the manuscript was written by VS, RŠ and JP. All authors read and approved the final manuscript.

Corresponding author

Correspondence to J. Pluskal.

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Appendices

Appendix 1: The summarized forecasts within selected waste management plans

Czech Republic (Ministry of the Environment of Czech Republic 2014).

  • MSW definition: Group 20 from all producers and 15 01 from citizens based on Waste catalogue (ANION CS, 2021)

  • Treatment: yes

  • Territory level: state

  • Data detail: year

  • Number of data: 4

  • Forecast length: 12

  • Method: Design of 3 models: 1. linear regression, 2. exponential trend, 3. multidimensional linear model.

Austria (Federal Ministry for Climate Protection, Environment, Energy, Mobility, Innovation and Technology 2017).

  • MSW definition: Municipal waste is waste from private households and other types of waste which, on account of its nature or composition, is similar to domestic waste. This includes fractions such as mixed municipal waste (residual waste), bulky waste or biogenic waste collected separately.

    There is no reference to the waste catalogue in the document.

  • Treatment: no

  • Territory level: state

  • Data detail: end state

  • Number of data: no information

  • Forecast length: 6

  • Method: No information

Germany (LAGA 2021).

There is no national waste management planning in Germany. Instead, each Federal State develops a waste management plan for its area.

  1. (a)

    Berlin (Senate Department for Environment, traffic and climate protection 2011)

    • MSW definition: MSW is waste that, based on its origin, can be allocated to private households and is collected as part of public waste collection. MSW also includes waste from commercial industry and wastewater treatment plants

    • Treatment: no

    • Territory level: Federal state

    • Data detail: 2 milestones (2015, 2020)

    • Number of data: 1

    • Forecast length: 9

    • Method: Setting progressive targets to be met and will have an impact on waste production. Inclusion of demographic projection.

  2. (b)

    Nordrhein-Westfalen (Ministry for Climate Protection, Environment, Agriculture, Nature and Consumer Protection of the State of North Rhine-Westphalia 2015)

    • MSW definition: Household waste is waste and packaging that is usually produced predominantly in private households and collected as part of public waste collection or from Take-back systems according to the Packaging Ordinance or Packaging Act, the so-called dual system. This typical household waste includes household and bulky waste, organic and green waste, separately collected valuable waste or packaging (including paper, light packaging, glass) as well as waste that is collected as part of municipal pollutant collections.

    • Treatment: no

    • Territory level: District, administrative districts and municipalities

    • Data detail: year

    • Data detail: End state

    • Number of data: 1

    • Forecast length: 14

    • Method: Population projection combined with assumption about per capita waste production.

  3. (c)

    Baden-Württemberg (Ministry of Environment Climate and Energy 2015)

    • MSW definition: The document does not directly contain a definition of MSW, but the federal states have usually the same definition of MSW, see Nordrhein-Westfalen.

    • Treatment: no

    • Territory level: Federal state

    • Data detail: year

    • Number of data: 19

    • Forecast length: 10

    • Method: Determination of two scenarios for each type of waste. Scenarios are based on the expansion of the involved part of the population, the use of more efficient methods of collection, greater promotion, etc. Involvement of the demographic projection, the percentage decrease in the number of inhabitants is considered.

  4. (d)

    Hesse (Hessian Ministry for the Environment, Climate Protection, Agriculture and Consumer Protection 2015)

    • MSW definition: See Nordrhein-Westfalen.

    • Treatment: no

    • Territory level: Federal state

    • Data detail: 5 years

    • Number of data: 3

    • Forecast length: 12

    • Method: Population forecast and assumption of economic growth and fulfillment of goals in waste management.

Poland (Ministry Climate and Environment of Poland 2021).

  • MSW definition: Municipal waste is waste generated in households and waste generated in retail trade, enterprises, office buildings and educational institutions as well as health care and public administration institutions, and the nature and composition of this waste is similar to that of waste generated in households.

    There is no reference to the waste catalogue in the document.

  • Treatment: no

  • Territory level: Region, state

  • Data detail: 2 milestones (2025, 2030)

  • Number of data: 1

  • Forecast length: 16

  • Method: Based on population forecast and two waste generation indexes—it is still assumed the same year-on-year growth in production (0.6% or 1.0%) and a decrease in population.

Slovakia (Ministry of the Environment of Slovakia 2015).

Waste management plan does not include any forecast.

  • MSW definition: Code 20 in Waste catalogue

    Finland (Launonen 2019).

  • MSW definition: Municipal waste means waste generated in permanent dwellings, holiday homes, residential homes and other forms of dwelling, including sludge in cess pools and septic tanks, as well as waste comparable in its nature to household waste generated by administrative, service, business and industrial activities.

  • Treatment: yes

  • Territory level: state

  • Data detail: End state

  • Number of data: 1

  • Forecast length: 8

  • Method: The first scenario makes use of the waste volumes in 2015 as indicated in the waste statistics. The scenario presumes that the generation of waste has been successfully halted at the level of 2015. The second scenario makes use of the moderate waste quantity growth forecast to 2023 of the Forecasting waste volumes -project, in which future municipal waste quantities were modelled.

Switzerland–Canton Zürich (Kanton Zürich 2021).

  • MSW definition: waste from households, commercial and service companies with less than 250 full time employees.

  • Treatment: no

  • Territory level: Canton

  • Data detail: year

  • Number of data: 6

  • Forecast length: 18

  • Method: No information

Appendix 2: The waste management development for EU and its members

See Figs.

Fig. 5
figure 5

Waste management development for EU

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5,

Fig. 6
figure 6

Waste management development for Austria, Belgium, Bulgaria, Croatia, Cyprus and Czechia

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6,

Fig. 7
figure 7

Waste management development for Denmark, Estonia, Finland, France, Germany and Greece

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7,

Fig. 8
figure 8

Waste management development for Hungary, Ireland, Italy, Latvia, Lithuania and Luxembourg

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8,

Fig. 9
figure 9

Waste management development for Malta, Netherlands, Poland, Portugal and Romania

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9, and

Fig. 10
figure 10

Waste management development for Slovakia, Slovenia, Spain, Sweden and United Kingdom

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10.

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Smejkalová, V., Šomplák, R., Pluskal, J. et al. Hierarchical optimisation model for waste management forecasting in EU. Optim Eng 23, 2143–2175 (2022). https://doi.org/10.1007/s11081-022-09735-2

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  • DOI: https://doi.org/10.1007/s11081-022-09735-2

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