# Designing a Recycling Network for the Circular Economy of Plastics with Different Multi-Criteria Optimization Approaches

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Designing Reverse Logistic Networks

#### 2.1.1. Lexicographic Optimization

#### 2.1.2. Goal Programming

## 3. Case Study: Plastic Recycling Network for Europe

#### 3.1. Mathematical Formulation

#### 3.1.1. Lexicographic Optimization

#### 3.1.2. Goal Programming

#### 3.2. Input Data

#### 3.2.1. Plastic Waste Volume

#### 3.2.2. Recycled Plastic Demand

#### 3.2.3. Recycling and Transportation Costs

#### 3.2.4. Environmental Burdens

#### 3.2.5. Distances

#### 3.3. Implementation

^{®}Core™ i5-8265U at 1.60 GHz; 8.0 GB RAM). The integration of the CPLEX solver into Python is accomplished via the docplex library. When solving the formulated programs, a termination criterion with a selected time limit of 600 s is set for each optimization run to achieve comparability.

## 4. Results

#### 4.1. Single Objective Optimization

#### 4.2. Lexicographic Optimization

#### 4.3. Goal Programming

## 5. Discussion

#### 5.1. Case Study

#### 5.2. Multi-Objective Decision-Making Approaches

## 6. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

- PlasticsEurope. Plastics—The Facts 2020: An Analysis of European Plastics Production, Demand and Waste Data. 2020. Available online: https://plasticseurope.org/knowledge-hub/plastics-the-facts-2020/ (accessed on 20 April 2022).
- IEA. The Future of Petrochemicals: Towards More Sustainable Plastics and Fertilisers. 2018. Available online: https://iea.blob.core.windows.net/assets/bee4ef3a-8876-4566-98cf-7a130c013805/The_Future_of_Petrochemicals.pdf (accessed on 25 April 2022).
- Cabernard, L.; Pfister, S.; Oberschelp, C.; Hellweg, S. Growing environmental footprint of plastics driven by coal combustion. Nat. Sustain.
**2021**, 5, 139–148. [Google Scholar] [CrossRef] - Ellen MacArthur Foundation. The New Plastics Economy: Rethinking the Future of Plastics. 2016. Available online: https://www.ellenmacarthurfoundation.org/assets/downloads/EllenMacArthurFoundation_TheNewPlasticsEconomy_Pages.pdf (accessed on 15 May 2019).
- European Commission. A European Strategy for Plastics in a Circular Economy. 2018. Available online: https://ec.europa.eu/environment/circular-economy/pdf/plastics-strategy-brochure.pdf (accessed on 13 April 2022).
- De Mello Soares, C.T.; Ek, M.; Östmark, E.; Gällstedt, M.; Karlsson, S. Recycling of multi-material multilayer plastic packaging: Current trends and future scenarios. Resour. Conserv. Recycl.
**2022**, 176, 105905. [Google Scholar] [CrossRef] - Alassali, A.; Picuno, C.; Chong, Z.K.; Guo, J.; Maletz, R.; Kuchta, K. Towards higher quality of recycled plastics: Limitations from the material’s perspective. Sustainability
**2021**, 13, 13266. [Google Scholar] [CrossRef] - Schwarz, A.E.; Ligthart, T.N.; Godoi Bizarro, D.; de Wild, P.; Vreugdenhil, B.; van Harmelen, T. Plastic recycling in a circular economy; determining environmental performance through an LCA matrix model approach. Waste Manag.
**2021**, 121, 331–342. [Google Scholar] [CrossRef] - Neo, E.R.K.; Soo, G.C.Y.; Tan, D.Z.L.; Cady, K.; Tong, K.T.; Low, J.S.C. Life cycle assessment of plastic waste end-of-life for India and Indonesia. Resour. Conserv. Recycl.
**2021**, 174, 105774. [Google Scholar] [CrossRef] - Faraca, G.; Martinez-Sanchez, V.; Astrup, T.F. Environmental life cycle cost assessment: Recycling of hard plastic waste collected at Danish recycling centres. Resour. Conserv. Recycl.
**2019**, 143, 299–309. [Google Scholar] [CrossRef] - Civancik-Uslu, D.; Nhu, T.T.; van Gorp, B.; Kresovic, U.; Larrain, M.; Billen, P.; Ragaert, K.; de Meester, S.; Dewulf, J.; Huysveld, S. Moving from linear to circular household plastic packaging in Belgium: Prospective life cycle assessment of mechanical and thermochemical recycling. Resour. Conserv. Recycl.
**2021**, 171, 105633. [Google Scholar] [CrossRef] - Volk, R.; Stallkamp, C.; Steins, J.J.; Yogish, S.P.; Müller, R.C.; Stapf, D.; Schultmann, F. Techno–economic assessment and comparison of different plastic recycling pathways: A German case study. J. Ind. Ecol.
**2021**, 25, 1318–1337. [Google Scholar] [CrossRef] - Jeswani, H.; Krüger, C.; Russ, M.; Horlacher, M.; Antony, F.; Hann, S.; Azapagic, A. Life cycle environmental impacts of chemical recycling via pyrolysis of mixed plastic waste in comparison with mechanical recycling and energy recovery. Sci. Total Environ.
**2021**, 769, 144483. [Google Scholar] [CrossRef] - Tonini, D.; Schrijvers, D.; Nessi, S.; Garcia-Gutierrez, P.; Giuntoli, J. Carbon footprint of plastic from biomass and recycled feedstock: Methodological insights. Int. J. Life Cycle Assess.
**2021**, 26, 221–237. [Google Scholar] [CrossRef] - Keller, F.; Voss, R.L.; Lee, R.P.; Meyer, B. Life cycle assessment of global warming potential of feedstock recycling technologies: Case study of waste gasification and pyrolysis in an integrated inventory model for waste treatment and chemical production in Germany. Resour. Conserv. Recycl.
**2022**, 179, 106106. [Google Scholar] [CrossRef] - Voss, R.; Lee, R.P.; Fröhling, M. Chemical Recycling of Plastic Waste: Comparative Evaluation of Environmental and Economic Performances of Gasification- and Incineration-based Treatment for Lightweight Packaging Waste. Circ. Econ. Sustain.
**2022**. [Google Scholar] [CrossRef] - Egri, P.; Dávid, B.; Kis, T.; Krész, M. Robust facility location in reverse logistics. Ann. Oper. Res.
**2021**. [Google Scholar] [CrossRef] - Walther, G. Nachhaltige Wertschöpfungsnetzwerke: Überbetriebliche Planung und Steuerung von Stoffströmen Entlang des Produktlebenszyklus; Springer: Berlin/Heidelberg, Germany, 2010. [Google Scholar]
- Nickel, S.; Stein, O.; Waldmann, K.H. Operations Research, 2nd ed.; Springer-Lehrbuch; Springer Gabler: Berlin/Heidelberg, Germany, 2014. [Google Scholar]
- Mohammadi, M.; Jämsä-Jounela, S.L.; Harjunkoski, I. Optimal planning of municipal solid waste management systems in an integrated supply chain network. Comput. Chem. Eng.
**2019**, 123, 155–169. [Google Scholar] [CrossRef] - Couto, M.C.L.; Lange, L.C.; Rosa, R.d.A.; Couto, P.R.L. Planning the location of facilities to implement a reverse logistic system of post-consumer packaging using a location mathematical model. Waste Manag. Res.
**2017**, 35, 1254–1265. [Google Scholar] [CrossRef] - Achillas, C.; Vlachokostas, C.; Aidonis, D.; Moussiopoulos, T.; Iakovou, E.; Banias, G. Optimising reverse logistics network to support policy-making in the case of Electrical and Electronic Equipment. Waste Manag.
**2010**, 30, 2592–2600. [Google Scholar] [CrossRef] - Pluskal, J.; Šomplák, R.; Nevrlý, V.; Smejkalová, V.; Pavlas, M. Strategic decisions leading to sustainable waste management: Separation, sorting and recycling possibilities. J. Clean. Prod.
**2021**, 278, 123359. [Google Scholar] [CrossRef] - Santibañez-Aguilar, J.E.; Flores-Tlacuahuac, A.; Rivera-Toledo, M.; Ponce-Ortega, J.M. Dynamic optimization for the planning of a waste management system involving multiple cities. J. Clean. Prod.
**2017**, 165, 190–203. [Google Scholar] [CrossRef] - Dekker, R.; Fleischmann, M.; Inderfurth, K.; van Wassenhove, L.N. (Eds.) Reverse Logistics: Quantitative Models for Closed-Loop Supply Chains; Springer: Berlin/Heidelberg, Germany; New York, NY, USA, 2004. [Google Scholar]
- Oberschmidt, J. Multikriterielle Bewertung von Technologien zur Bereitstellung von Strom und Wärme. Ph.D. Thesis, Universität Göttingen, Göttingen, Germany, 2010. [Google Scholar]
- Geldermann, J.; Lerche, N. Leitfaden zur Anwendung von Methoden der Multikriteriellen Entscheidungsunterstützung: PROMETHEE. 2014. Available online: https://www.uni-goettingen.de/de/document/download/285813337d59201d34806cfc48dae518-en.pdf/MCDA-Leitfaden-PROMETHEE.pdf (accessed on 27 April 2022).
- Farahani, R.Z.; Steadieseifi, M.; Asgari, N. Multiple criteria facility location problems: A survey. Appl. Math. Model.
**2010**, 34, 1689–1709. [Google Scholar] [CrossRef] - Ulungu, E.L.; Teghem, J. Multi-objective combinatorial optimization problems: A survey. J.-Multi-Criteria Decis. Anal.
**1994**, 3, 83–104. [Google Scholar] [CrossRef] - Marler, R.T.; Arora, J.S. Survey of multi-objective optimization methods for engineering. Struct. Multidiscip. Optim.
**2004**, 26, 369–395. [Google Scholar] [CrossRef] - Colapinto, C.; Jayaraman, R.; Marsiglio, S. Multi-criteria decision analysis with goal programming in engineering, management and social sciences: A state-of-the art review. Ann. Oper. Res.
**2017**, 251, 7–40. [Google Scholar] [CrossRef] - Jones, D.; Tamiz, M. Practical Goal Programming; International Series in Operations Research & Management Science; Springer US: Boston, MA, USA, 2010; Volume 141. [Google Scholar] [CrossRef]
- Flavell, R.B. A new goal programming formulation. Omega
**1976**, 4, 731–732. [Google Scholar] [CrossRef] - Eurostat. Packaging Waste Statistics. 2022. Available online: https://ec.europa.eu/eurostat/statistics-explained/index.php?title=Packaging_waste_statistics (accessed on 6 April 2022).
- Schiessl, A.; Müller, R.; Volk, R.; Zimmer, K.; Breun, P.; Schultmann, F. Integrating site-specific environmental impact assessment in supplier selection: Exemplary application to steel procurement. J. Bus. Econ.
**2020**, 90, 1409–1457. [Google Scholar] [CrossRef] - Müller, R.C.; Schiessl, A.; Volk, R.; Schultmann, F. Assessment of site-specific greenhouse gas emissions of chemical producers: Case studies of propylene and toluene diisocyanate. J. Clean. Prod.
**2021**, 317, 128086. [Google Scholar] [CrossRef] - Eurostat. Population and NUTS 2 Region. 2022. Available online: https://appsso.eurostat.ec.europa.eu/nui/show.do?dataset=demo_r_d2jan&lang=en (accessed on 14 April 2022).
- Cimpan, C.; Maul, A.; Wenzel, H.; Pretz, T. Techno-economic assessment of central sorting at material recovery facilities—The case of lightweight packaging waste. J. Clean. Prod.
**2016**, 112, 4387–4397. [Google Scholar] [CrossRef] - Eurostat. Labour Cost Levels. 2022. Available online: https://ec.europa.eu/eurostat/databrowser/view/LC_LCI_LEV__custom_3096795/default/table?lang=en (accessed on 20 April 2022).
- Doka, G. Municipal Waste Collection Service by 21 Metric Ton Lorry, RoW, Allocation Cut-Off. Retrieved from Ecoinvent Database Version 3.8. 2021. Available online: https://v38.ecoquery.ecoinvent.org/Details/LCIA/7370042e-e19a-4f51-a57b-94b3d90d60b8/290c1f85-4cc4-4fa1-b0c8-2cb7f4276dce (accessed on 30 March 2022).
- Kägi, T. Waste Preparation Facility Construction, RoW, Allocation Cut-Off. Retrieved from Ecoinvent Database Version 3.8. 2021. Available online: https://v38.ecoquery.ecoinvent.org/Details/LCIA/7e221508-848b-4a2e-845c-8c4debc80501/290c1f85-4cc4-4fa1-b0c8-2cb7f4276dce (accessed on 30 March 2022).
- European Commission. Environmental Footprint (EF). 2022. Available online: https://eplca.jrc.ec.europa.eu/LCDN/developerEF.xhtml (accessed on 21 April 2022).
- Delivand, M. Assessing the Feasibility of Process Chains for Energy Production from Rice Straw in Thailand. Ph.D. Thesis, Joint Graduate School of Energy and Environment, Krung Thep Maha Nakhon, Thailand, 2011. [Google Scholar]
- Diehlmann, F.; Zimmer, T.; Glöser-Chahoud, S.; Wiens, M.; Schultmann, F. Techno-economic assessment of utilization pathways for rice straw: A simulation-optimization approach. J. Clean. Prod.
**2019**, 230, 1329–1343. [Google Scholar] [CrossRef]

**Figure 3.**Results of the lexicographic optimization approach. Locations of decentral (blue triangles) and central MRFs (black circles) as well as transportation routes (black lines) are displayed. The size of the MRFs represents the allocated amount of plastic waste that is handled there.

**Figure 4.**Results of the softened lexicographic optimization approach. Locations of decentral (blue triangles) and central MRFs (black circles) as well as transportation routes (black lines) are displayed. The size of the MRFs represents the allocated amount of plastic waste that is handled there.

**Figure 6.**Results of the CGP approach. Locations of decentral (blue triangles) and central MRFs (black circles) as well as transportation routes are displayed. The size of the MRFs represents the allocated amount of plastic waste that is handled there.

Sets | |
---|---|

S | Set of regions with recyclable plastic waste ($s\in S$) |

R | Set of regions with potential locations for MRFs ($r\in R$) |

D | Set of regions with demand for recycled plastic material ($d\in D$) |

I | Set of input capacity classes of MRFs ($i\in I$) |

Parameters | |

${c}^{transport}$ | Transportation costs for 1 Mg waste per material and kilometer |

${c}_{i,r}^{recycling}$ | Recycling costs for 1 Mg plastic waste in an MRF of capacity class i in region r |

${c}_{i}^{opening}$ | Opening costs for an MRF of capacity class i |

$gw{p}^{transport}$ | GWP impact of transportation of 1 Mg waste per material per kilometer |

$gw{p}_{i}^{recycling}$ | GWP impact of recycling 1 Mg plastic waste in an MRF of capacity class i |

$gw{p}_{i}^{opening}$ | GWP impact of opening an MRF of capacity class i |

$t{a}^{transport}$ | TA impact of transportation of 1 Mg waste per material per kilometer |

$t{a}_{i}^{recycling}$ | TA impact of recycling 1 Mg plastic waste in an MRF of capacity class i |

$t{a}_{i}^{opening}$ | TA impact of opening an MRF of capacity class i |

$e{t}^{transport}$ | ET impact of transportation of 1 Mg waste per material per kilometer |

$e{t}_{i}^{recycling}$ | ET impact of recycling 1 Mg plastic waste in an MRF of capacity class i |

$e{t}_{i}^{opening}$ | ET impact of opening an MRF of capacity class i |

$ht{c}^{transport}$ | HTc impact of transportation of 1 Mg waste per material per kilometer |

$ht{c}_{i}^{recycling}$ | HTc impact of recycling 1 Mg plastic waste in an MRF of capacity class i |

$ht{c}_{i}^{opening}$ | HTc impact of opening an MRF of capacity class i |

${q}_{s}^{supply}$ | Recyclable waste generated in region s |

${q}_{d}^{demand}$ | Demand of recycled material in region d |

${K}_{i}$ | Maximum capacity of an MRF of capacity class i |

Variables | |

${x}_{sr,i}$ | Amount of transported plastic waste from s to r to MRF of capacity class i |

${x}_{rd,i}$ | Amount of transported recycled plastic from r to d out of MRF of capacity class i |

${y}_{r,i}$ | $\left\{\begin{array}{c}0,\phantom{\rule{4.pt}{0ex}}\mathrm{if}\phantom{\rule{4.pt}{0ex}}\mathrm{no}\phantom{\rule{4.pt}{0ex}}\mathrm{MRF}\phantom{\rule{4.pt}{0ex}}\mathrm{of}\phantom{\rule{4.pt}{0ex}}\mathrm{capacity}\phantom{\rule{4.pt}{0ex}}\mathrm{class}\phantom{\rule{4.pt}{0ex}}\mathrm{i}\phantom{\rule{4.pt}{0ex}}\mathrm{is}\phantom{\rule{4.pt}{0ex}}\mathrm{opened}\phantom{\rule{4.pt}{0ex}}\mathrm{in}\phantom{\rule{4.pt}{0ex}}\mathrm{region}\phantom{\rule{4.pt}{0ex}}\mathrm{r}\hfill \\ 1,\phantom{\rule{4.pt}{0ex}}\mathrm{if}\phantom{\rule{4.pt}{0ex}}\mathrm{an}\phantom{\rule{4.pt}{0ex}}\mathrm{MRF}\phantom{\rule{4.pt}{0ex}}\mathrm{of}\phantom{\rule{4.pt}{0ex}}\mathrm{capity}\phantom{\rule{4.pt}{0ex}}\mathrm{class}\phantom{\rule{4.pt}{0ex}}\mathrm{i}\phantom{\rule{4.pt}{0ex}}\mathrm{is}\phantom{\rule{4.pt}{0ex}}\mathrm{opened}\phantom{\rule{4.pt}{0ex}}\mathrm{in}\phantom{\rule{4.pt}{0ex}}\mathrm{region}\phantom{\rule{4.pt}{0ex}}\mathrm{r}\hfill \end{array}\right.$ |

Variables—Extension CGP approach | |

$dist$ | Maximum deviation from each normalized single objective optimum |

**Table 2.**Countries with missing plastic packaging waste data and chosen reference country for adoption of waste generation per capita.

Countries Missing Data | Reference Country | Waste per Capita (kg) |
---|---|---|

Switzerland | Austria | 33.31 |

Northern Ireland | United Kingdom | 35.52 |

Montenegro | Hungary | 35.01 |

Macedonia | Hungary | 35.01 |

Albania | Hungary | 35.01 |

Serbia | Hungary | 35.01 |

**Table 3.**Countries with missing plastic demand data and chosen reference country for adoption of demand per capita.

Countries Missing Data | Reference Country | Demand per Capita (kg) |
---|---|---|

Lichtenstein | Switzerland | 80.44 |

Luxembourg | Germany | 137.80 |

Montenegro | Hungary | 201.13 |

Macedonia | Hungary | 201.13 |

Albania | Hungary | 201.13 |

Serbia | Hungary | 201.13 |

**Table 4.**Costs and environmental burdens for opening MRFs, recycling, and transportation. Recycling costs are regionalized with the factor x; x: level of labor costs normalized to the level of Denmark.

Decentral MRF | Central MRF | ||||
---|---|---|---|---|---|

Opening | Recycling (per Mg) | Opening | Recycling (per Mg) | Transportation (per Mg and km) | |

Costs [EUR] | 13,523,962 | 146 + $269\times x$ | 41,203,354 | 93 + $174\times x$ | 0.174 |

GWP [kg CO2-Eq] | 1,222,989 | 409 | 3,726,071 | 262 | 1.28 |

TA [mol H+-Eq] | 14,762 | 0.54 | 44,974 | 0.35 | 0.01 |

ET [mol N-Eq] | 26,494 | 1.36 | 80,720 | 0.87 | 0.04 |

HTc [CTUh] | 1.23 | 0.09 | 3.74 | 0.05 | $7.7\times {10}^{-8}$ |

Objective | Optimal Value | Unit | Recycling Effort | Opening MRFs | Transportation |
---|---|---|---|---|---|

Costs | 6,069,319,346 | (EUR) | 52% | 44% | 4% |

GWP | 4,191,261,971 | (kg CO2-Eq) | 77% | 18% | 5% |

TA | 11,405,202 | (mol H+-Eq) | 50% | 44% | 8% |

ET | 25,485,141 | (mol N-Eq) | 54% | 41% | 5% |

HTc | 675,943 | (CTUh) | >99% | <1% | <1% |

Objective | Single Objective Optimal Value | Lexicographic Optimization | Unit | Deviation |
---|---|---|---|---|

Costs | 6,069,319,346 | 6,069,319,346 | (EUR) | 0% |

GWP | 4,191,261,971 | 5,569,965,276 | (kg CO2-Eq) | 33% |

TA | 11,405,202 | 18,645,709 | (mol H+-Eq) | 64% |

ET | 25,485,141 | 65,367,610 | (mol N-Eq) | 257% |

HTc | 675,943 | 748,970 | (CTUh) | 11% |

**Table 7.**Results of the multi-objective lexicographic optimization allowing a 1% deviation from the preceding optimal objective function values.

Objective | Single Objective Optimal Value | Lexicographic Optimization ($\mathit{\u03f5}=0.01$) | Unit | Deviation |
---|---|---|---|---|

Costs | 6,069,319,346 | 6,130,012,540 | (EUR) | 1% |

GWP | 4,191,261,971 | 5,259,633,202 | (kg CO2-Eq) | 26% |

TA | 11,405,202 | 17,210,674 | (mol H+-Eq) | 51% |

ET | 25,485,141 | 59,317,974 | (mol N-Eq) | 133% |

HTc | 675,943 | 727,387 | (CTUh) | 8% |

Objective | Single Objective Optimal Value | Goal Programming | Unit | Deviation |
---|---|---|---|---|

Costs | 6,069,319,346 | 7,471,799,556 | (EUR) | 23% |

GWP | 4,191,261,971 | 4,720,630,372 | (kg CO2-Eq) | 13% |

TA | 11,405,202 | 11,995,494 | (mol H+-Eq) | 5% |

ET | 25,485,141 | 31,374,173 | (mol N-Eq) | 23% |

HTc | 675,943 | 832,138 | (CTUh) | 23% |

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. |

© 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Stallkamp, C.; Steins, J.; Ruck, M.; Volk, R.; Schultmann, F.
Designing a Recycling Network for the Circular Economy of Plastics with Different Multi-Criteria Optimization Approaches. *Sustainability* **2022**, *14*, 10913.
https://doi.org/10.3390/su141710913

**AMA Style**

Stallkamp C, Steins J, Ruck M, Volk R, Schultmann F.
Designing a Recycling Network for the Circular Economy of Plastics with Different Multi-Criteria Optimization Approaches. *Sustainability*. 2022; 14(17):10913.
https://doi.org/10.3390/su141710913

**Chicago/Turabian Style**

Stallkamp, Christoph, Justus Steins, Manuel Ruck, Rebekka Volk, and Frank Schultmann.
2022. "Designing a Recycling Network for the Circular Economy of Plastics with Different Multi-Criteria Optimization Approaches" *Sustainability* 14, no. 17: 10913.
https://doi.org/10.3390/su141710913