# Optimizing a Reverse Supply Chain Network for Electronic Waste under Risk and Uncertain Factors

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Problem Description

## 3. A Developed Mathematical Model

- -
- The location of collection centers, the landfill site, and secondary and main markets are known in advance.
- -
- The transportation cost is calculated depending on the product/part types and the distance travelled.
- -
- The size of dismantling, repairing, and recycling centers is limited.
- -
- Pessimistic and optimistic values for all imprecise parameters are identified as 10% less and more of the most likely value adopted from Özceylan and Paksoy [29].

c | set of collection centers, c = 1,…, C; |

d | set of possible locations of dismantling centers, d = 1,…, D; |

e | set of possible locations of repairing centers, e = 1,…, E; |

r | set of possible locations of recycling centers, r = 1,…, R; |

s | set of secondary markets, s = 1,…, S; |

m | set of main markets, m = 1,…, M; |

l | set of landfill site, l = 1,…, L; |

p | set of used products, p = 1,…, P; |

u | set of reusable parts, u = 1,..., U; |

w | set of renewable parts, w = 1,…, W; |

i | set of recycling materials, i = 1,…, I; |

h | set of disposal parts, h = 1,…, H. |

${\tilde{Tp}}_{p}$ | unit transportation cost of used product p ϵ P; |

${\tilde{Tu}}_{u}$ | unit transportation cost of reused component u ϵ U; |

${\tilde{Tw}}_{w}$ | unit transportation cost of renewable component w ϵ W; |

${\tilde{Ti}}_{i}$ | unit transportation cost of recycling material i ϵ I; |

${\tilde{Th}}_{h}$ | unit transportation cost of disposal item h ϵ H; |

${\tilde{Od}}_{pd}$ | unit processing cost of used product p at dismantling center d; |

${\tilde{Oe}}_{we}$ | unit processing cost of renewable component w at repairing center e; |

${\tilde{Or}}_{ir}$ | unit processing cost of recycling material i at recycling center r; |

${\tilde{D}}_{h}$ | unit disposal cost of disposal item h; |

${\tilde{CL}}_{p}$ | Unit collection cost of used product p at collection area; |

${\tilde{Sd}}_{d}$ | set-up cost of dismantling center d; |

${\tilde{Se}}_{e}$ | set-up cost of repairing center e; |

$S{\tilde{r}}_{r}$ | set-up cost of recycling center r; |

${\tilde{Pu}}_{u}$ | selling price per unit of reusable component u; |

${\tilde{Pw}}_{w}$ | selling price per unit of renewable component w; |

${\tilde{Pi}}_{i}$ | selling price per unit of recycling material i; |

$B{1}_{cd}$ | distance c–d; |

$B{2}_{ds}$ | distance d–s; |

$B{3}_{de}$ | distance d–e; |

$B{4}_{dr}$ | distance d–r; |

$B{5}_{dl}$ | distance d–l; |

$B{6}_{es}$ | distance e–s; |

$B{7}_{rm}$ | distance r–m; |

$B{8}_{rl}$ | distance r–l; |

${\tilde{A}}_{pc}$ | the amount of used product p at collection center c; |

${\tilde{\epsilon 1}}_{up}$ | the average unit of reused item u obtained from the used product p; |

${\tilde{\epsilon 2}}_{wp}$ | the average unit of renewable item w obtained from the used product p; |

${\tilde{\epsilon 3}}_{ip}$ | the average unit of recycling material i obtained from the used product p; |

${\tilde{\epsilon 4}}_{hp}$ | the average unit of disposal item h obtained from the used product p; |

${\tilde{\beta}}_{h}$ | the average fraction of disposal item h obtained from recycling center; |

${\tilde{\beta}}_{i}$ | the average fraction of recycling material i obtained at recycling center; |

${\tilde{Nu}}_{us}$ | maximum demand for reused item u at secondary market s; |

${\tilde{Nw}}_{ws}$ | maximum demand for renewable component w at secondary market s; |

${\tilde{Ni}}_{im}$ | maximum demand for recycling material i at main market m; |

${\tilde{Kd}}_{pd}$ | maximum capacity of used product p at dismantling center d; |

${\tilde{Ke}}_{we}$ | maximum capacity of renewable item w at repairing center e; |

${\tilde{Kr}}_{ir}$ | maximum capacity of recycling material i at recycling center r; |

${\tilde{Kl}}_{hl}$ | maximum capacity of disposal item h at landfill site l; |

${\tilde{P1}}_{d}$ | the possibility of an unexpected event occurred at dismantling center d; |

${\tilde{P2}}_{e}$ | the possibility of an unexpected event occurred at repairing center e; |

${\tilde{P3}}_{r}$ | the possibility of an unexpected event occurred at recycling center r; |

${\tilde{P4}}_{cd}$ | the possibility of an unexpected event occurred on the way c–d; |

${\tilde{P5}}_{ds}$ | the possibility of an unexpected event occurred on the way d–s; |

${\tilde{P6}}_{de}$ | the possibility of an unexpected event occurred on the way d–e; |

${\tilde{P7}}_{dr}$ | the possibility of an unexpected event occurred on the way d–r; |

${\tilde{P8}}_{dl}$ | the possibility of an unexpected event occurred on the way d–l; |

${\tilde{P9}}_{es}$ | the possibility of an unexpected event occurred on the way e–s; |

${\tilde{P10}}_{rm}$ | the possibility of an unexpected event occurred on the way r–m; |

${\tilde{P11}}_{rl}$ | the possibility of an unexpected event occurred on the way r–l; |

${\tilde{I1}}_{d}$ | the impact of an unexpected event occurred at dismantling center d; |

${\tilde{I2}}_{e}$ | the impact of an unexpected event occurred at repairing center e; |

${\tilde{I3}}_{r}$ | the impact of an unexpected event occurred at recycling center r; |

${\tilde{I4}}_{cd}$ | the impact of an unexpected event occurred on the way c–d; |

${\tilde{I5}}_{ds}$ | the impact of an unexpected event occurred on the way d–s; |

${\tilde{I6}}_{de}$ | the impact of an unexpected event occurred on the way d–e; |

${\tilde{I7}}_{dr}$ | the impact of an unexpected event occurred on the way d–r; |

${\tilde{I8}}_{dl}$ | the impact of an unexpected event occurred on the way d–l; |

${\tilde{I9}}_{es}$ | the impact of an unexpected event occurred on the way e–s; |

${\tilde{I10}}_{rm}$ | the impact of an unexpected event occurred on the way r–m; |

${\tilde{I11}}_{rl}$ | the impact of an unexpected event occurred on the way r–l. |

Note that symbols with a tilde (~) denote uncertain parameters. |

## 4. Proposed Approach

#### 4.1. Converting the FMILP Model to the Auxiliary Crisp Model

#### 4.2. Interactive Fuzzy

## 5. An Illustrative Example

_{1}, d

_{2}), one repairing center (e

_{1}), and two recycling centers (r

_{1}, r

_{2}) should be constructed. Table 16 presents the flow of materials and components transported within the RSC network. For example, the second row in column 2 of Table 17 (Q1

_{111}= 34) indicates that there are 34 used products (p = 1) which are transferred from the collection center (c = 1) to the dismantling center (d = 1). Similarly, the last row of column 5 of Table 17 (Q4

_{225}= 170) shows that 170 units of recycling material (I = 5) are transported from the dismantling center (d = 2) to the recycling center (r = 2). The rest of the figures can be addressed in the same way.

## 6. Conclusions and Further Work

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Nomenclature

$Q{1}_{cdp}$ | the volume of used product p sent from c to d; |

$Q{2}_{dsu}$ | the volume of reused component u sent from d to s; |

$Q{3}_{dew}$ | the volume of renewable component w sent from d to e; |

$Q{4}_{dri}$ | the volume of recycling material i sent from d to r; |

$Q{5}_{dlh}$ | the volume of disposal substance h sent from d to l; |

$Q{6}_{esw}$ | the volume of renewable component w sent from e to s; |

$Q{7}_{rmi}$ | the volume of recycling material i sent from r to m; |

$Q{8}_{rlh}$ | the volume of disposal materials h sent from r to l; |

${X}_{d}$ | $\left\{0,1\right\}$ variable, ${X}_{d}$ = 1 if a dismantling center is built at location d, ${X}_{d}=0$otherwise; |

${X}_{e}$ | $\left\{0,1\right\}$ variable, ${X}_{e}$ = 1 if a repairing center is built at location e, ${X}_{e}$ = 0 otherwise; |

${X}_{r}$ | $\left\{0,1\right\}$ variable, ${X}_{r}$ = 1 if a recycling center is built at location r, ${X}_{r}$ = 0 otherwise. |

## Appendix A

Parameters | Quantity | Units of Measurement | References |
---|---|---|---|

Used product | 2–5 | units | [17,21] |

Components (reuse parts, recycling materials, etc.) | 1–10 | units | [17,63] |

Distance from site to site (i.e., collection center to dismantling center) | 6–200 | km | [13,17,21] |

Costs (transportation, recycling, processing costs per unit) | 0.1–10 | USD | [13,22,63] |

Fixed facility costs | 100–2000 | USD | [22,64] |

Risk | 1–10 | [50] |

## References

- Richey, R.G.; Chen, H.; Genchev, S.E.; Daugherty, P.J. Developing effective reverse logistics programs. Ind. Mark. Manag.
**2005**, 34, 830–840. [Google Scholar] [CrossRef] - Ruan Barbosa de Aquino, Í.; Ferreira da Silva Junior, J.; Guarnieri, P.; Camara e Silva, L. The Proposition of a Mathematical Model for the Location of Electrical and Electronic Waste Collection Points. Sustainability
**2021**, 13, 224. [Google Scholar] [CrossRef] - Forti, V.; Baldé, C.P.; Kuehr, R.; Bel, G. The Global E-Waste Monitor 2020; United Nations University (UNU): Bonn, Germany; International Telecommunication Union (ITU): Geneva, Switzerland; International Solid Waste Association (ISWA): Rotterdam, The Netherlands, 2020. [Google Scholar]
- Yang, J.; Lu, B.; Xu, C. WEEE flow and mitigating measures in China. Waste Manag.
**2008**, 28, 1589–1597. [Google Scholar] [CrossRef] - Aboelmaged, M. E-waste recycling behaviour: An integration of recycling habits into the theory of planned behaviour. J. Clean. Prod.
**2021**, 278, 4182. [Google Scholar] [CrossRef] - Sthiannopkao, S.; Wong, M.H. Handling e-waste in developed and developing countries: Initiatives, practices, and consequences. Sci. Total Environ.
**2013**, 463, 1147–1153. [Google Scholar] [CrossRef] [PubMed] - Namias, J. The Future of Electronic Waste Recycling in the United States: Obstacles and Domestic Solutions; Columbia University: New York, NY, USA, 2013. [Google Scholar]
- Nagalingam, S.V.; Kuik, S.S.; Amer, Y. Performance measurement of product returns with recovery for sustainable manufacturing. Robot. Comput. Integr. Manuf.
**2013**, 29, 473–483. [Google Scholar] [CrossRef] - Rahman, S.; Subramanian, N. Factors for implementing end-of-life computer recycling operations in reverse supply chains. Int. J. Prod. Econ.
**2012**, 140, 239–248. [Google Scholar] [CrossRef] - Fleischmann, M.; Bloemhof-Ruwaard, J.M.; Dekker, R.; van der Laan, E.; van Nunen, J.A.E.E.; Van Wassenhove, L.N. Quantitative models for reverse logistics: A review. Eur. J. Oper. Res.
**1997**, 103, 1–17. [Google Scholar] [CrossRef] [Green Version] - Pishvaee, M.S.; Kianfar, K.; Karimi, B. Reverse logistics network design using simulated annealing. Int. J. Adv. Manuf. Technol.
**2010**, 47, 269–281. [Google Scholar] [CrossRef] - Lee, C.K.M.; Lam, J.S.L. Managing reverse logistics to enhance sustainability of industrial marketing. Ind. Mark. Manag.
**2012**, 41, 589–598. [Google Scholar] [CrossRef] - John, S.T.; Sridharan, R.; Ram Kumar, P.N.; Krishnamoorthy, M. Multi-period reverse logistics network design for used refrigerators. Appl. Math. Model.
**2018**, 54, 311–331. [Google Scholar] [CrossRef] - Amin, S.H.; Zhang, G.; Akhtar, P. Effects of uncertainty on a tire closed-loop supply chain network. Expert Syst. Appl.
**2017**, 73, 82–91. [Google Scholar] [CrossRef] [Green Version] - Zarbakhshnia, N.; Soleimani, H.; Ghaderi, H. Sustainable third-party reverse logistics provider evaluation and selection using fuzzy SWARA and developed fuzzy COPRAS in the presence of risk criteria. Appl. Soft Comput.
**2018**, 65, 307–319. [Google Scholar] [CrossRef] - Rogers, D.S.; Melamed, B.; Lembke, R.S. Modeling and analysis of reverse logistics. J. Bus. Logist.
**2012**, 33, 107–117. [Google Scholar] [CrossRef] - Dat, L.Q.; Truc Linh, D.T.; Chou, S.Y.; Yu, V.F. Optimizing reverse logistic costs for recycling end-of-life electrical and electronic products. Expert Syst. Appl.
**2012**, 39, 6380–6387. [Google Scholar] [CrossRef] - Gomes, M.I.; Barbosa-Povoa, A.P.; Novais, A.Q. Modelling a recovery network for WEEE: A case study in Portugal. Waste Manag.
**2011**, 31, 1645–1660. [Google Scholar] [CrossRef] [PubMed] - Mahmoudi, H.; Fazlollahtabar, H. An integer linear programming for a comprehensive reverse supply chain. Cogent Eng.
**2014**, 1, 939440. [Google Scholar] [CrossRef] - Kilic, H.S.; Cebeci, U.; Ayhan, M.B. Reverse logistics system design for the waste of electrical and electronic equipment (WEEE) in Turkey. Resour. Conserv. Recycl.
**2015**, 95, 120–132. [Google Scholar] [CrossRef] - John, S.T.; Sridharan, R.; Kumar, P.R. Multi-period reverse logistics network design with emission cost. Int. J. Logist. Manag.
**2017**, 28, 127–149. [Google Scholar] [CrossRef] - John, S.T.; Sridharan, R. Modelling and analysis of network design for a reverse supply chain. J. Manuf. Technol. Manag.
**2015**, 26, 853–867. [Google Scholar] [CrossRef] - Phuc, P.N.K.; Yu, V.F.; Tsao, Y.C. Optimizing fuzzy reverse supply chain for end-of-life vehicles. Comput. Ind. Eng.
**2016**, 113, 757–765. [Google Scholar] [CrossRef] - Demirel, E.; Demirel, N.; Gökçen, H. A mixed integer linear programming model to optimize reverse logistics activities of end-of-life vehicles in Turkey. J. Clean. Prod.
**2016**, 112, 2101–2113. [Google Scholar] [CrossRef] - Galvez, D.; Rakotondranaivo, A.; Morel, L.; Camargo, M.; Fick, M. Reverse logistics network design for a biogas plant: An approach based on MILP optimization and Analytical Hierarchical Process (AHP). J. Manuf. Syst.
**2015**, 37, 616–623. [Google Scholar] [CrossRef] - Alshamsi, A.; Diabat, A. A reverse logistics network design. J. Manuf. Syst.
**2015**, 37, 589–598. [Google Scholar] [CrossRef] - Grunow, M.; Gobbi, C. Designing the reverse network for WEEE in Denmark. CIRP Ann. Manuf. Technol.
**2009**, 58, 391–394. [Google Scholar] [CrossRef] - Hazen, B.T.; Overstreet, R.E.; Hall, D.J.; Huscroft, J.R.; Hanna, J.B. Antecedents to and outcomes of reverse logistics metrics. Ind. Mark. Manag.
**2015**, 46, 160–170. [Google Scholar] [CrossRef] - Özceylan, E.; Paksoy, T. Fuzzy multi-objective linear programming approach for optimising a closed-loop supply chain network. Int. J. Prod. Res.
**2013**, 51, 2443–2461. [Google Scholar] [CrossRef] - Jindal, A.; Sangwan, K.S. Closed loop supply chain network design and optimisation using fuzzy mixed integer linear programming model. Int. J. Prod. Res.
**2014**, 52, 4156–4173. [Google Scholar] [CrossRef] - Pishvaee, M.S.; Razmi, J. Environmental supply chain network design using multi-objective fuzzy mathematical programming. Appl. Math. Model.
**2012**, 36, 3433–3446. [Google Scholar] [CrossRef] - Cheng, Y.H.; Lee, F. Outsourcing reverse logistics of high-tech manufacturing firms by using a systematic decision-making approach: TFT-LCD sector in Taiwan. Ind. Mark. Manag.
**2010**, 39, 1111–1119. [Google Scholar] [CrossRef] - Sadjadi, S.J.; Soltani, R.; Eskandarpour, A. Location based treatment activities for end of life products network design under uncertainty by a robust multi-objective memetic-based heuristic approach. Appl. Soft Comput.
**2014**, 23, 215–226. [Google Scholar] [CrossRef] - Ayvaz, B.; Bolat, B.; Aydın, N. Stochastic reverse logistics network design for waste of electrical and electronic equipment. Resour. Conserv. Recycl.
**2015**, 104, 391–404. [Google Scholar] [CrossRef] - Lee, D.H.; Dong, M. Dynamic network design for reverse logistics operations under uncertainty. Transp. Res. Part E Logist. Transp. Rev.
**2009**, 45, 61–71. [Google Scholar] [CrossRef] - Listeş, O.; Dekker, R. A stochastic approach to a case study for product recovery network design. Eur. J. Oper. Res.
**2005**, 160, 268–287. [Google Scholar] [CrossRef] - Kara, S.S.; Onut, S. A stochastic optimization approach for paper recycling reverse logistics network design under uncertainty. Int. J. Environ. Sci. Technol.
**2010**, 7, 717–730. [Google Scholar] [CrossRef] [Green Version] - Pishvaee, M.S.; Torabi, S.A. A possibilistic programming approach for closed-loop supply chain network design under uncertainty. Fuzzy Sets Syst.
**2010**, 161, 2668–2683. [Google Scholar] [CrossRef] - Dubois, D.; Fargier, H.; Fortemps, P. Fuzzy scheduling: Modelling flexible constraints vs. coping with incomplete knowledge. Eur. J. Oper. Res.
**2003**, 147, 231–252. [Google Scholar] [CrossRef] - Pishvaee, M.S.; Razmi, J.; Torabi, S.A. Robust possibilistic programming for socially responsible supply chain network design: A new approach. Fuzzy Sets Syst.
**2012**, 206, 1–20. [Google Scholar] [CrossRef] - Bilgen, B. Application of fuzzy mathematical programming approach to the production allocation and distribution supply chain network problem. Expert Syst. Appl.
**2010**, 37, 4488–4495. [Google Scholar] [CrossRef] - Liang, T.F. Distribution planning decisions using interactive fuzzy multi-objective linear programming. Fuzzy Sets Syst.
**2006**, 157, 1303–1316. [Google Scholar] [CrossRef] - Liang, T.F. Fuzzy multi-objective production/distribution planning decisions with multi-product and multi-time period in a supply chain. Comput. Ind. Eng.
**2008**, 55, 676–694. [Google Scholar] [CrossRef] - Liang, T.F.; Cheng, H.W. Application of fuzzy sets to manufacturing/distribution planning decisions with multi-product and multi-time period in supply chains. Expert Syst. Appl.
**2009**, 36, 3367–3377. [Google Scholar] [CrossRef] - Ramezani, M.; Kimiagari, A.M.; Karimi, B.; Hejazi, T.H. Closed-loop supply chain network design under a fuzzy environment. Knowl. Based Syst.
**2014**, 59, 108–120. [Google Scholar] [CrossRef] - Doan, L.T.T.; Amer, Y.; Lee, S.H.; Phuc, P.N.K.; Dat, L.Q. E-Waste Reverse Supply Chain: A Review and Future Perspectives. Appl. Sci.
**2019**, 9, 5195. [Google Scholar] [CrossRef] [Green Version] - Hudnurkar, M.; Deshpande, S.; Rathod, U.; Jakhar, S. Supply Chain Risk Classification Schemes: A Literature Review. Oper. Supply Chain Manag. Int. J.
**2017**, 10, 182–199. [Google Scholar] [CrossRef] [Green Version] - Kumar, S.K.; Tiwari, M.; Babiceanu, R.F. Minimisation of supply chain cost with embedded risk using computational intelligence approaches. Int. J. Prod. Res.
**2010**, 48, 3717–3739. [Google Scholar] [CrossRef] - Zsidisin, G.A.; Ellram, L.M.; Carter, J.R.; Cavinato, J.L. An analysis of supply risk assessment techniques. Int. J. Phys. Distrib. Logist. Manag.
**2004**, 34, 397–413. [Google Scholar] [CrossRef] - El Dabee, F.; Marian, R.; Amer, Y. A novel optimization model for simultaneous cost-risk reduction in multi-suppliers just-in-time systems. J. Comput. Sci.
**2013**, 9, 1778–1792. [Google Scholar] [CrossRef] [Green Version] - Thun, J.H.; Hoenig, D. An empirical analysis of supply chain risk management in the German automotive industry. Int. J. Prod. Econ.
**2011**, 131, 242–249. [Google Scholar] [CrossRef] - Nooraie, S.V.; Mellat Parast, M. A multi-objective approach to supply chain risk management: Integrating visibility with supply and demand risk. Int. J. Prod. Econ.
**2015**, 161, 192–200. [Google Scholar] [CrossRef] - Li, G.; Fan, H.; Lee, P.K.C.; Cheng, T.C.E. Joint supply chain risk management: An agency and collaboration perspective. Int. J. Prod. Econ.
**2015**, 164, 83–94. [Google Scholar] [CrossRef] - Sheu, J.B. A coordinated reverse logistics system for regional management of multi-source hazardous wastes. Comput. Oper. Res.
**2007**, 34, 1442–1462. [Google Scholar] [CrossRef] - Sharma, A.; Revankar, A.M.; Sathvik, R.S. Risk management in reverse supply chain. In Proceedings of the International Conference on Challenges and Opportunities in Mechanical Engineering, Industrial Engineering and Management Studies, Bangalore, Indian, 11–13 July 2012. [Google Scholar]
- Kazancoglu, Y.; Ozkan-Ozen, Y.D.; Mangla, S.K.; Ram, M. Risk assessment for sustainability in e-waste recycling in circular economy. Clean Technol. Environ. Policy
**2020**, 1–13. [Google Scholar] [CrossRef] - Parajuly, K.; Habib, K.; Liu, G. Waste electrical and electronic equipment (WEEE) in Denmark: Flows, quantities and management. Resour. Conserv. Recycl.
**2017**, 123, 85–92. [Google Scholar] [CrossRef] - Yuksel, H. An analytical hierarchy process decision model for e-waste collection center location selection. In Proceedings of the CIE 2009 International Conference on Computers & Industrial Engineering, Troyes, France, 6–9 July 2009; pp. 1684–1689. [Google Scholar]
- Sohani, N.; Chaurasia, M.K. Analysis of Risk Management for Reverse Supply Chain Network. Imp. J. Interdiscip. Res.
**2016**, 2. [Google Scholar] [CrossRef] [Green Version] - Jiménez, M.; Arenas, M.; Bilbao, A.; Rodriguez, M.V. Linear programming with fuzzy parameters: An interactive method resolution. Eur. J. Oper. Res.
**2007**, 177, 1599–1609. [Google Scholar] [CrossRef] - Heilpern, S. The expected value of a fuzzy number. Fuzzy Sets Syst.
**1992**, 47, 81–86. [Google Scholar] [CrossRef] - Parra, A.M.; Terol, B.A.; Gladish, P.B.; Uría, R.M.V. Solving a multiobjective possibilistic problem through compromise programming. Eur. J. Oper. Res.
**2005**, 164, 748–759. [Google Scholar] [CrossRef] - Doan, L.T.T.; Amer, Y.; Lee, S.H.; Phuc, P.N.K. Optimizing the Total Cost of an E-waste Reverse Supply Chain Considering Transportation Risk. Oper. Supply Chain Manag. Int. J.
**2018**, 11, 151–160. [Google Scholar] [CrossRef] - Soleimani, H.; Govindan, K. Reverse logistics network design and planning utilizing conditional value at risk. Eur. J. Oper. Res.
**2014**, 237, 487–497. [Google Scholar] [CrossRef]

α Values | Different Linguistic Levels of DM |
---|---|

α = 0 | Solution is not accepted |

α = 0.1 | Solution is not practically accepted |

α = 0.2 | Solution is almost not accepted |

α= 0.3 | Solution is very not accepted |

α = 0.4 | Solution is quite not accepted |

α = 0.5 | Solution is not accepted |

α = 0.6 | Solution is quite accepted |

α = 0.7 | Solution is very accepted |

α = 0.8 | Solution is almost accepted |

α = 0.9 | Solution is practically accepted |

α = 1 | Solution is completely accepted |

1st Used Product (Unit) | 2nd Used Product (Unit) | |
---|---|---|

Reuse components | 1 | 1 |

Renewable components | 1 | 1 |

Recycling materials | 3 | 2 |

Disposal items | 4 | 3 |

C | D | E | R | S | M | L | P | U | W | I | H |
---|---|---|---|---|---|---|---|---|---|---|---|

2 | 2 | 2 | 2 | 2 | 2 | 1 | 2 | 2 | 2 | 5 | 7 |

**Table 4.**The average percentage of recycling materials and disposal items generated from recycling centers.

${\tilde{\mathit{\beta}}}_{\mathit{i}}$ | ${\tilde{\mathit{\beta}}}_{\mathit{h}}$ |
---|---|

(0.78,0.8,0.82) | (0.18,0.2,0.22) |

${\tilde{\mathit{A}}}_{1\mathit{c}}$ | ${\tilde{\mathit{A}}}_{2\mathit{c}}$ | |
---|---|---|

c = 1 | (288,320,352) | (252,280,308) |

c = 2 | (333,370,407) | (297,330,363) |

Dist. | C_{1} | C_{2} | E_{1} | E_{2} | R_{1} | R_{2} | L_{1} | S_{1} | S_{2} | Dist. | S_{1} | S_{2} | Dist. | M_{1} | M_{2} | L_{1} |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

D_{1} | 18 | 20 | 34 | 36 | 39 | 37 | 23 | 22 | 24 | E_{1} | 23 | 26 | R_{1} | 23 | 27 | 24 |

D_{2} | 22 | 26 | 25 | 26 | 40 | 42 | 29 | 23 | 25 | E_{2} | 24 | 24 | R_{2} | 25 | 28 | 26 |

Products | Reusable Items | Renewable Items | |||
---|---|---|---|---|---|

${\tilde{Tp}}_{1}$ | ${\tilde{Tp}}_{2}$ | ${\tilde{Tu}}_{1}$ | ${\tilde{Tu}}_{2}$ | ${\tilde{Tw}}_{1}$ | ${\tilde{Tw}}_{2}$ |

(1.08,1.2,1.32) | (0.9,1,1.1) | (0.63,0.7,0.77) | (0.72,0.8,0.88) | (0.45,0.5,0.55) | (0.36,0.4,0.44) |

Recycling materials | |||||

${\tilde{Ti}}_{1}$ | ${\tilde{Ti}}_{2}$ | ${\tilde{Ti}}_{3}$ | ${\tilde{Ti}}_{4}$ | ${\tilde{Ti}}_{5}$ | |

(0.27,0.3,0.33) | (0.27,0.3,0.33) | (0.18,0.2,0.22) | (0.18,0.2,0.22) | (0.24,0.3,0.33) | |

Disposal items | |||||

${\tilde{Th}}_{1}$ | ${\tilde{Th}}_{2}$ | ${\tilde{Th}}_{3}$ | ${\tilde{Th}}_{4}$ | ${\tilde{Th}}_{5}$ | ${\tilde{Th}}_{6}$ |

(0.36,0.4,0.44) | (0.36,0.4,0.44) | (0.27,0.3,0.33) | (0.45,0.5,0.55) | (0.18,0.2,0.22) | (0.36,0.4,0.44) |

${\tilde{Th}}_{7}$ | |||||

(0.18,0.2,0.22) |

Collection Cost | ||||

${\tilde{CL}}_{1}$ | ${\tilde{CL}}_{2}$ | |||

(1.8,2,2.2) | (0.9,1,1.1) | |||

Disposal Cost | ||||

${\tilde{D}}_{1}$ | ${\tilde{D}}_{2}$ | ${\tilde{D}}_{3}$ | ${\tilde{D}}_{4}$ | ${\tilde{D}}_{5}$ |

(1.26,1.4,1.54) | (1.08,1.2,1.32) | (1.8,2,2.2) | (0.9,1,1.1) | (1.26,1.4,1.54) |

${\tilde{D}}_{6}$ | ${\tilde{D}}_{7}$ | |||

(1.08,1.2,1.32) | (1.17,1.3,1.43) |

Used Products | Reusable Items | ||||
---|---|---|---|---|---|

${\tilde{Od}}_{1d}$ | ${\tilde{Od}}_{2d}$ | ${\tilde{Oe}}_{1e}$ | ${\tilde{Oe}}_{2e}$ | ||

d = 1 | (4.5,5,5.5) | (4.5,5,5.5) | e = 1 | (1.8,2,2.2) | (2.7,3,3.3) |

d = 2 | (3.6,4,4.4) | (2.7,3,3.3) | e = 2 | (3.6,4,4.4) | (2.7,3,3.3) |

Recycling Materials | |||||

${\tilde{Or}}_{1r}$ | ${\tilde{Or}}_{2r}$ | ${\tilde{Or}}_{3r}$ | ${\tilde{Or}}_{4r}$ | ${\tilde{Or}}_{5r}$ | |

r = 1 | (2.7,3,3.3) | (1.8,2,2.2) | (1.8,2,2.2) | (0.9,1,1.1) | (1.8,2,2.2) |

r = 2 | (1.8,2,2.2) | (1.8,2,2.2) | (2.7,3,3.3) | (1.8,2,2.2) | (2.7,3,3.3) |

No | ${\tilde{\mathit{S}\mathit{d}}}_{\mathit{d}}$ | ${\tilde{\mathit{S}\mathit{e}}}_{\mathit{e}}$ | ${\tilde{\mathit{S}\mathit{r}}}_{\mathit{r}}$ |
---|---|---|---|

1 | (1260,1400,1540) | (1215,1350,1485) | (1170,1300,1430) |

2 | (378,1300,462) | (1242,1380,1518) | (1206,1340,1474) |

${\tilde{Pu}}_{1}$ | ${\tilde{Pu}}_{2}$ | ${\tilde{Pw}}_{1}$ | ${\tilde{Pw}}_{2}$ | |

(2.7,3,3.3) | (3.6,4,4.4) | (1.8,2,2.2) | (2.7,3,3.3) | |

${\tilde{Pi}}_{1}$ | ${\tilde{Pi}}_{2}$ | ${\tilde{Pi}}_{3}$ | ${\tilde{Pi}}_{4}$ | ${\tilde{Pi}}_{5}$ |

(2.7,3,3.3) | (3.6,4,4.4) | (1.8,2,2.2) | (1.8, 2, 2.2) | (2.7,3,3.3) |

${\tilde{\mathit{K}\mathit{d}}}_{1\mathit{d}}$ | ${\tilde{\mathit{K}\mathit{d}}}_{2\mathit{d}}$ | ${\tilde{\mathit{K}\mathit{e}}}_{1\mathit{e}}$ | ${\tilde{\mathit{K}\mathit{e}}}_{2\mathit{e}}$ | ||

d = 1 | (450,500,550) | (540,600,660) | e = 1 | (810,900,990) | (990,1100,1210) |

d = 2 | (360,400,440) | (450,500,550) | e = 2 | (1080,1200,1320) | (900,1000,1100) |

${\tilde{\mathit{K}\mathit{r}}}_{1\mathit{r}}$ | ${\tilde{\mathit{K}\mathit{r}}}_{2\mathit{r}}$ | ${\tilde{\mathit{K}\mathit{r}}}_{3\mathit{r}}$ | ${\tilde{\mathit{K}\mathit{r}}}_{4\mathit{r}}$ | ${\tilde{\mathit{K}\mathit{r}}}_{5\mathit{r}}$ | |

r = 1 | (360,400,440) | (540,600,660) | (450,500,550) | (540,600,660) | (630,700,770) |

r = 2 | (360,400,440) | (270,300,330) | (450,500,550) | (360,400,440) | (450,500,550) |

${\tilde{\mathit{K}\mathit{l}}}_{1\mathit{l}}$ | ${\tilde{\mathit{K}\mathit{l}}}_{2\mathit{l}}$ | ${\tilde{\mathit{K}\mathit{l}}}_{3\mathit{l}}$ | ${\tilde{\mathit{K}\mathit{l}}}_{4\mathit{l}}$ | ${\tilde{\mathit{K}\mathit{l}}}_{5\mathit{l}}$ | |

l = 1 | (900,1000,1100) | (990,1100,1210) | (720,800,880) | (810,900,990) | (1080,1200,1320) |

${\tilde{\mathit{K}\mathit{l}}}_{6\mathit{l}}$ | ${\tilde{\mathit{K}\mathit{l}}}_{7\mathit{l}}$ | ||||

l = 1 | (1260,1400,1540) | (1080,1200,1320) |

${\tilde{\mathit{N}\mathit{u}}}_{1\mathit{s}}$ | ${\tilde{\mathit{N}\mathit{u}}}_{2\mathit{s}}$ | ${\tilde{\mathit{N}\mathit{w}}}_{1\mathit{s}}$ | ${\tilde{\mathit{N}\mathit{w}}}_{2\mathit{s}}$ | ||

s = 1 | (630,700,770) | (810, 900,990) | (1080,1200,1320) | (1350,1500,1650) | |

s = 2 | (900,1000,1100) | (297,330,363) | (1170,1300,1430) | (900,1000,1100) | |

${\tilde{\mathit{N}\mathit{i}}}_{1\mathit{m}}$ | ${\tilde{\mathit{N}\mathit{i}}}_{2\mathit{m}}$ | ${\tilde{\mathit{N}\mathit{i}}}_{3\mathit{m}}$ | ${\tilde{\mathit{N}\mathit{i}}}_{4\mathit{m}}$ | ${\tilde{\mathit{N}\mathit{i}}}_{5\mathit{m}}$ | |

m = 1 | (1260,1400,1540) | (1350,1500,1650) | (1170,1300,1430) | (720,800,880) | (900,1000,1100) |

m = 2 | (1080,1200,1320) | (990,1100,1210) | (1260,1400,1540) | (1350,1500,1650) | (1080,1200,1320) |

**Table 14.**Probability of accident occurrence and the impact at dismantling, repairing, and recycling centers.

Probability | |||||
---|---|---|---|---|---|

Dismantling Centers | Repairing Centers | ||||

${\tilde{P1}}_{1d}$ | ${\tilde{P2}}_{2d}$ | ${\tilde{P1}}_{1e}$ | ${\tilde{P2}}_{2e}$ | ||

d = 1 | (2.7,3,3.3) | (3.6,4,4.4) | e = 1 | (3.6,4,4.4) | (3.6,4,4.4) |

d = 2 | (1.8,2,2.2) | (1.8,2,2.2) | e = 2 | (1.8,2,2.2) | (1.8,2,2.2) |

Recycling centers | |||||

${\tilde{P3}}_{1r}$ | ${\tilde{P3}}_{2r}$ | ${\tilde{P3}}_{3r}$ | ${\tilde{P3}}_{4r}$ | ${\tilde{P3}}_{5r}$ | |

r = 1 | (2.7,3,3.3) | (3.6,4,4.4) | (3.6,4,4.4) | (4.5,5,5.5) | (3.6,4,4.4) |

r = 2 | (1.8,2,2.2) | (2.7,3,3.3) | (1.8,2,2.2) | (1.8,2,2.2) | (1.8,2,2.2) |

Impact | |||||

Dismantling centers | Repairing centers | ||||

${\tilde{I1}}_{1d}$ | ${\tilde{I1}}_{2d}$ | ${\tilde{I2}}_{1e}$ | ${\tilde{I2}}_{2e}$ | ||

d = 1 | (2.7,3,3.3) | (3.6,4,4.4) | e = 1 | (3.6,4,4.4) | (3.6,4,4.4) |

d = 2 | (4.5,5,5.5) | (4.5,5,5.5) | e = 2 | (2.7,3,3.3) | (1.8,2,2.2) |

Recycling facilities | |||||

${\tilde{I3}}_{1r}$ | ${\tilde{I3}}_{2r}$ | ${\tilde{I3}}_{3r}$ | ${\tilde{I3}}_{4r}$ | ${\tilde{I3}}_{5r}$ | |

r = 1 | (5.4,6,6.6) | (5.4,6,6.6) | (6.3,7,7.7) | (4.5,5,5.5) | (5.4,6,6.6) |

r = 2 | (2.7,3,3.3) | (3.6,4,4.4) | (4.5,5,5.5) | (2.7,3,3.3) | (3.6,4,4.4) |

Probability | Impact | |||
---|---|---|---|---|

route c-d | ${\tilde{P4}}_{1d}$ | ${\tilde{P4}}_{2d}$ | ${\tilde{I4}}_{1d}$ | ${\tilde{I4}}_{2d}$ |

d = 1 | (2.7,3,3.3) | (1.8,2,2.2) | (1.8,2,2.2) | (2.7,3,3.3) |

d = 2 | (2.7,3,3.3) | (2.7,3,3.3) | (1.8,2,2.2) | (2.7,3,3.3) |

route d-s | ${\tilde{P5}}_{1s}$ | ${\tilde{P5}}_{2s}$ | ${\tilde{I5}}_{1s}$ | ${\tilde{I5}}_{2s}$ |

s = 1 | (2.7,3,3.3) | (2.7,3,3.3) | (2.7,3,3.3) | (2.7,3,3.3) |

s = 2 | (1.8,2,2.2) | (2.7,3,3.3) | (3.6,4,4.4) | (3.6,4,4.4) |

route d-e | ${\tilde{P6}}_{1e}$ | ${\tilde{P6}}_{2e}$ | ${\tilde{I6}}_{1e}$ | ${\tilde{I6}}_{2e}$ |

e = 1 | (3.6,4,4.4) | (3.6,4,4.4) | (3.6,4,4.4) | (1.8,2,2.2) |

e = 2 | (2.7,3,3.3) | (2.7,3,3.3) | (2.7,3,3.3) | (1.8,2,2.2) |

route d-r | ${\tilde{P7}}_{1r}$ | ${\tilde{P7}}_{2r}$ | ${\tilde{I7}}_{1r}$ | ${\tilde{I7}}_{2r}$ |

r = 1 | (3.6,4,4.4) | (3.6,4,4.4) | (3.6,4,4.4) | (3.6,4,4.4) |

r = 2 | (2.7,3,3.3) | (2.7,3,3.3) | (3.6,4,4.4) | (2.7,3,3.3) |

route d-l | ${\tilde{P8}}_{1l}$ | ${\tilde{P8}}_{2l}$ | ${\tilde{I8}}_{1l}$ | ${\tilde{I8}}_{2l}$ |

l = 1 | (5.4,6,6.6) | (6.3,7,7.7) | (6.3,7,7.7) | (5.4,6,6.6) |

route e-s | ${\tilde{P9}}_{1s}$ | ${\tilde{P9}}_{2s}$ | ${\tilde{I9}}_{1s}$ | ${\tilde{I9}}_{2s}$ |

s = 1 | (3.6,4,4.4) | (2.7,3,3.3) | (3.6,4,4.4) | (2.7,3,3.3) |

s = 2 | (2.7,3,3.3) | (1.8,2,2.2) | (1.8,2,2.2) | (1.8,2,2.2) |

route r-m | ${\tilde{P10}}_{1m}$ | ${\tilde{P10}}_{2m}$ | ${\tilde{I10}}_{1m}$ | ${\tilde{I10}}_{2m}$ |

m = 1 | (1.8,2,2.2) | (2.7,3,3.3) | (1.8,2,2.2) | (1.8,2,2.2) |

m = 2 | (1.8,2,2.2) | (1.8,2,2.2) | (1.8,2,2.2) | (1.8,2,2.2) |

route d-g | ${\tilde{P11}}_{1l}$ | ${\tilde{P11}}_{2l}$ | ${\tilde{I11}}_{1l}$ | ${\tilde{I11}}_{2l}$ |

l = 1 | (4.5,5,5.5) | (2.7,3,3.3) | (5.4,6,6.6) | (3.6,4,4.4) |

Feasibility Degree | Possibility Distributions of Objective Value | Compatibility Index of Each Solution | Degree of Balance of Each Solution |
---|---|---|---|

0.4 | (167,544; 182,128; 204,809) | 0.720 | 0.4 |

0.5 | (169,254; 183,972; 207888) | 0.684 | 0.5 |

0.6 | (169,864; 185,644; 208,663) | 0.652 | 0.6 |

0.7 | (170,505; 187,369; 210,821) | 0.619 | 0.619 |

0.8 | (173,029; 189,103; 211,795) | 0.586 | 0.586 |

0.9 | (175,816; 191,104; 214,036) | 0.547 | 0.547 |

1 | (176,262; 192,636; 219,605) | 0.518 | 0.518 |

No | $\mathit{Q}{1}_{\mathit{c}\mathit{d}\mathit{p}}$ | $\mathit{Q}{2}_{\mathit{d}\mathit{s}\mathit{u}}$ | $\mathit{Q}{3}_{\mathit{d}\mathit{e}\mathit{w}}$ | $\mathit{Q}{4}_{\mathit{d}\mathit{r}\mathit{i}}$ | $\mathit{Q}{5}_{\mathit{d}\mathit{l}\mathit{h}}$ | $\mathit{Q}{6}_{\mathit{e}\mathit{s}\mathit{w}}$ | $\mathit{Q}{7}_{\mathit{r}\mathit{m}\mathit{i}}$ | $\mathit{Q}{8}_{\mathit{r}\mathit{l}\mathit{h}}$ |
---|---|---|---|---|---|---|---|---|

111 | 34 | 392 | 0 | 0 | 219 | 55 | ||

112 | 0 | 320 | 98 | 0 | 296 | 74 | ||

121 | 282 | 392 | 392 | |||||

122 | 276 | 320 | 294 | |||||

211 | 364 | 277 | 277 | 0 | 309 | 77 | ||

212 | 325 | 272 | 277 | 0 | 232 | 58 | ||

221 | 0 | 277 | 669 | |||||

222 | 0 | 272 | 592 | |||||

113 | 213 | 0 | 386 | 97 | ||||

114 | 316 | 0 | 463 | 116 | ||||

115 | 0 | 0 | 80 | 20 | ||||

116 | 392 | |||||||

117 | 320 | |||||||

123 | 179 | |||||||

124 | ||||||||

125 | 320 | |||||||

213 | 277 | 0 | 141 | 35 | ||||

214 | 272 | 0 | ||||||

215 | 102 | 0 | 386 | 97 | ||||

216 | 277 | |||||||

217 | 272 | |||||||

225 | 170 |

No | $\mathit{Q}{1}_{\mathit{c}\mathit{d}\mathit{p}}$ | $\mathit{Q}{2}_{\mathit{d}\mathit{s}\mathit{u}}$ | $\mathit{Q}{3}_{\mathit{d}\mathit{e}\mathit{w}}$ | $\mathit{Q}{4}_{\mathit{d}\mathit{r}\mathit{i}}$ | $\mathit{Q}{5}_{\mathit{d}\mathit{l}\mathit{h}}$ | $\mathit{Q}{6}_{\mathit{e}\mathit{s}\mathit{w}}$ | $\mathit{Q}{7}_{\mathit{r}\mathit{m}\mathit{i}}$ | $\mathit{Q}{8}_{\mathit{r}\mathit{l}\mathit{h}}$ |
---|---|---|---|---|---|---|---|---|

111 | 130 | 500 | 500 | 100 | 0 | 690 | 232 | 58 |

112 | 0 | 330 | 330 | 410 | 0 | 610 | 480 | 120 |

121 | 190 | 0 | 0 | 400 | 0 | |||

122 | 280 | 0 | 0 | 90 | 0 | |||

211 | 370 | 190 | 190 | 190 | 0 | 0 | 320 | 80 |

212 | 330 | 280 | 280 | 190 | 0 | 0 | 72 | 18 |

221 | 0 | 0 | 0 | 0 | 152 | |||

222 | 0 | 0 | 0 | 0 | ||||

113 | 310 | 0 | 400 | 100 | ||||

114 | 320 | 0 | 480 | 120 | ||||

115 | 0 | 0 | 224 | 56 | ||||

116 | 500 | |||||||

117 | 330 | |||||||

123 | 190 | |||||||

124 | 10 | |||||||

125 | 330 | |||||||

213 | 280 | 0 | 152 | 38 | ||||

214 | 280 | 0 | ||||||

215 | 264 | 66 | ||||||

216 | 190 | |||||||

217 | 280 | |||||||

225 |

No | $\mathit{Q}{1}_{\mathit{c}\mathit{d}\mathit{p}}$ | $\mathit{Q}{2}_{\mathit{d}\mathit{s}\mathit{u}}$ | $\mathit{Q}{3}_{\mathit{d}\mathit{e}\mathit{w}}$ | $\mathit{Q}{4}_{\mathit{d}\mathit{r}\mathit{i}}$ | $\mathit{Q}{5}_{\mathit{d}\mathit{l}\mathit{h}}$ | $\mathit{Q}{6}_{\mathit{e}\mathit{s}\mathit{w}}$ | $\mathit{Q}{7}_{\mathit{r}\mathit{m}\mathit{i}}$ | $\mathit{Q}{8}_{\mathit{r}\mathit{l}\mathit{h}}$ |
---|---|---|---|---|---|---|---|---|

111 | 30 | 400 | 0 | 0 | 0 | 232 | 58 | |

112 | 0 | 330 | 100 | 0 | 0 | 312 | 78 | |

121 | 290 | 0 | 400 | 400 | 0 | |||

122 | 280 | 0 | 330 | 300 | 0 | |||

211 | 370 | 0 | 290 | 290 | 0 | 0 | 320 | 80 |

212 | 330 | 0 | 280 | 290 | 0 | 690 | 240 | 60 |

221 | 0 | 290 | 0 | 0 | ||||

222 | 0 | 280 | 0 | 610 | ||||

113 | 210 | 0 | 400 | 100 | ||||

114 | 320 | 0 | 480 | 120 | ||||

115 | 0 | 0 | 88 | |||||

116 | 440 | |||||||

117 | 330 | |||||||

123 | 190 | |||||||

124 | ||||||||

125 | 330 | |||||||

213 | 290 | 0 | 152 | 38 | ||||

214 | 290 | 0 | ||||||

215 | 110 | 0 | 400 | 100 | ||||

216 | 290 | |||||||

217 | 280 | |||||||

225 | 170 |

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

© 2021 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 (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Doan, L.T.T.; Amer, Y.; Lee, S.-H.; Phuc, P.N.K.; Tran, T.T.
Optimizing a Reverse Supply Chain Network for Electronic Waste under Risk and Uncertain Factors. *Appl. Sci.* **2021**, *11*, 1946.
https://doi.org/10.3390/app11041946

**AMA Style**

Doan LTT, Amer Y, Lee S-H, Phuc PNK, Tran TT.
Optimizing a Reverse Supply Chain Network for Electronic Waste under Risk and Uncertain Factors. *Applied Sciences*. 2021; 11(4):1946.
https://doi.org/10.3390/app11041946

**Chicago/Turabian Style**

Doan, Linh Thi Truc, Yousef Amer, Sang-Heon Lee, Phan Nguyen Ky Phuc, and Tham Thi Tran.
2021. "Optimizing a Reverse Supply Chain Network for Electronic Waste under Risk and Uncertain Factors" *Applied Sciences* 11, no. 4: 1946.
https://doi.org/10.3390/app11041946