(195c) Optimization Methods for Plastics Management Supply Chain Design

Plastics have been essential in aiding the rapid growth of economies and improving our quality of life over the past several decades¹. However, the same properties that make plastics attractive materials—durability, resistance to degradation, ability to change properties with different additives and manufacturing methods—make them difficult to properly dispose of without harming the environment^1–3. Improperly disposed plastic which enters the environment as plastic pollution has widespread consequences on environmental, economic, and socio-political levels⁴. In addition to large pieces of plastic pollution posing a hazard to wildlife, be it through ingestion, entanglement, or other means, smaller micro-plastic particles may have as-yet undetermined negative impacts on human health and can be carried to remote areas far from any point sources of plastic pollution.

As a waste stream, plastic remains hard to recycle properly. Thus, it is essential that we develop our plastic waste management technology and infrastructure to better handle the current and ever-increasing amount of future mixed plastic waste (MPW) generated by modern life. One of the reasons that recycling rates are so low is that current recycling methods (primarily mechanical recycling) cannot handle all types of plastic waste⁵. In designing a functional and cost-effective MPW management supply chain (SC), we consider how to handle heterogeneous waste streams which might not be compatible with existing technologies. While mechanical recycling requires extensive cleaning and sorting of MPW (and is generally only cost-effective for relatively pure plastic waste streams), other technologies like pyrolysis, gasification, and incineration with energy recovery are viable candidates for handling mixed plastic streams^4–6.

Our work introduces three mixed-integer programming models to address a network design problem for MPW SCs. These models assess what a cost-effective MPW management SC might look like if we account for the impact of different plastic waste compositions and waste separation technologies. Each model determines: (1) flows of waste streams, of different compositions, between each stage of the waste management process, (2) where to locate facilities, and (3) what technologies should be employed at these facilities, in order to minimize the per ton cost of processing collected waste. The final SC solutions must satisfy sets of mass balances for each stage of the SC—from collection to transfer station to material recovery facility (MRF) to end-of-life treatment (EOL). Transfer stations aggregate waste collected from multiple collection sites, MRFs sort and separate the waste, then send it to EOLs to be recycled or to landfills to be disposed of.

To account for the impact of waste composition on the SC, the models track key components individually, and preserve proportions of components in multicomponent streams. This primarily affects mass balances for transfer stations and MRFs. The waste components being sent to a single transfer station from different collection sites are associated with different compositions depending on the collection site. Therefore, all streams leaving transfer stations have the potential to be multicomponent streams, with different proportions of components that must be preserved even if they are split between multiple downstream MRFs.

We also capture the limitations of MRF capabilities by defining sets of components which can and cannot be separated into pure streams by a particular MRF technology. For MRF mass balances, components which can be separated are modeled by single-component streams leaving MRFs, which can split between multiple downstream EOL locations without requiring split fractions. All pure component streams must proceed to an EOL. Components which cannot be separated into pure streams leave the MRF in multicomponent streams. These multicomponent streams cannot be sent to mechanical recycling EOLs. They can also be sent directly to landfills instead of an EOL.

By tracking waste compositions throughout the SC, the models make better informed decisions on the most effective technologies needed to process MPW. Note that we need to use split fractions to achieve multicomponent stream splitting that preserves the proportions of stream components. This introduces nonlinearities; we therefore examine three models with different approaches to preserving composition information in the SC, to investigate how best to handle stream composition information in these design problems. Model 1 (M1) is a mixed-integer linear model (MILP) which does not allow splitting for multicomponent streams. M1 uses binaries to restrict multicomponent streams to only have one downstream destination. Model 2 (M2) is an MILP that uses predefined discrete split fractions (with associated binaries) to simulate splitting without introducing nonlinearities. Model 3 (M3) is a mixed-integer quadratic constraint model (MIQCP) which utilizes continuous split fraction variables to fully account for splitting. Due to the different ways in which these three models account for multicomponent stream splitting, each model finds different optimal SC solutions and has different solution times.

We also introduce additional constraints based on integer variables that count the number of facilities established⁷, as well as select flow-related variables, to improve solution time and tighten the problem. Using different combinations of these additional constraints, we can achieve improvements in solution time. Our study also includes an extension of the models to address larger-scale problems. By cleverly defining the sets and parameters of the problem, and assuming an average composition for collected MPW, we can reduce the size and complexity of the model to solve problems that might be intractable for the full models. This allows us to apply the model to large-scale instances while still capturing the impact of waste composition and waste sorting capabilities.

Considering waste stream composition as a variable dependent on aggregation and separation decisions made at different stages in the SC provides a baseline approach for examining emerging MPW recycling technologies that may be more sensitive to input composition, as well as determining the extent to which advanced sorting is useful. Applied to a case study of New York City, the three models find different optimal solutions, with M3 finding the best solution, highlighting the importance of explicitly considering composition and splitting when designing MPW SCs. The impact of considering composition may become more relevant as newer MPW recycling technologies emerge which are more sensitive to feedstock composition.

References

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