A bi-level optimization model for PET bottle recycling within a circular economy supply chain

Carlos Corpus; Ali Zahedi; Eva Selene Hernández-Gress; José-Fernando Camacho-Vallejo; Carlos Corpus; Ali Zahedi; Eva Selene Hernández-Gress; José-Fernando Camacho-Vallejo

doi:10.3934/environsci.2025010

AIMS Environmental Science

2025, Volume 12, Issue 2: 223-251. doi: 10.3934/environsci.2025010

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A bi-level optimization model for PET bottle recycling within a circular economy supply chain

1.
Centro de Investigación en Ciencias Físico-Matemáticas (CICFIM), Universidad Autónoma de Nuevo León
2.
Tecnologico de Monterrey, Escuela de Ingeniería y Ciencias, Monterrey, México

Received: 19 July 2024 Revised: 17 January 2025 Accepted: 14 February 2025 Published: 27 February 2025

The consumption and usage of polyethylene terephthalate (PET) bottles have significantly increased in recent years, necessitating action to mitigate their environmental impact. Recycling programs offer a viable solution to address this impact within the PET industry. Therefore, adopting a circular economy approach is appropriate for incorporating recycling initiatives. Nevertheless, it is crucial not to overlook the financial aspects of the supply chain. This paper proposed a bi-level model to address both the financial and environmental concerns of a circular economy supply chain. At the upper level, a recycling company (the leader) aimd to establish PET bottle collection facilities, set prices for each kilogram of PET received, and manage the transportation of collected PET to the treatment plant. At the lower level of the bi-level problem, persons (the followers) decided whether to recycle or not. They received economic incentives based on the amount deposited at the collection facilities, but this came with associated travel costs. The leader's objective was to maximize the profit of the recycling program, assuming the sale of recycled PET. Meanwhile, followers aimed to recycle if it was economically viable for them. To solve this problem, a matheuristic algorithm was proposed, which hybridized a greedy random adaptive search procedure with an exact routing process. The matheuristic managed solutions at the leader level, while followers' responses were derived by exploiting the problem's structure. A case study derived from Mexico City was solved, and practical managerial insights were provided. Sensitivity analysis revealed crucial aspects that should not be overlooked when implementing such a recycling program.
- circular economy,
- PET bottle recycling,
- bi-level optimization,
- matheuristic algorithms
Citation: Carlos Corpus, Ali Zahedi, Eva Selene Hernández-Gress, José-Fernando Camacho-Vallejo. A bi-level optimization model for PET bottle recycling within a circular economy supply chain[J]. AIMS Environmental Science, 2025, 12(2): 223-251. doi: 10.3934/environsci.2025010

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Abstract

The consumption and usage of polyethylene terephthalate (PET) bottles have significantly increased in recent years, necessitating action to mitigate their environmental impact. Recycling programs offer a viable solution to address this impact within the PET industry. Therefore, adopting a circular economy approach is appropriate for incorporating recycling initiatives. Nevertheless, it is crucial not to overlook the financial aspects of the supply chain. This paper proposed a bi-level model to address both the financial and environmental concerns of a circular economy supply chain. At the upper level, a recycling company (the leader) aimd to establish PET bottle collection facilities, set prices for each kilogram of PET received, and manage the transportation of collected PET to the treatment plant. At the lower level of the bi-level problem, persons (the followers) decided whether to recycle or not. They received economic incentives based on the amount deposited at the collection facilities, but this came with associated travel costs. The leader's objective was to maximize the profit of the recycling program, assuming the sale of recycled PET. Meanwhile, followers aimed to recycle if it was economically viable for them. To solve this problem, a matheuristic algorithm was proposed, which hybridized a greedy random adaptive search procedure with an exact routing process. The matheuristic managed solutions at the leader level, while followers' responses were derived by exploiting the problem's structure. A case study derived from Mexico City was solved, and practical managerial insights were provided. Sensitivity analysis revealed crucial aspects that should not be overlooked when implementing such a recycling program.

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