The results of the case study are presented in this section. First, the optimal objective values for single objective optimization are presented. They are the basis for determining relative deviations between multi-criteria optimization solutions and individual optimality for each objective. Furthermore, they are needed to normalize the
variable in the CGP approach. Second, the results of the lexicographic optimization are provided. We calculated two approaches: one without deviation from the optimal solution and one where a small deviation of
is allowed. Third, the results of the introduced CGP approach are presented. A comparison and discussion of the results follow in
Section 5.
4.2. Lexicographic Optimization
The lexicographic optimization approach in this study considers the objective function in the following sequence: costs, GWP, TA, ET, and HTc. The lexicographic approach finds a solution that reaches the optimal value for total costs as the costs are the prioritized objective (see
Table 6). Minimizing the GWP within the remaining solution space results in a deviation of 33% from the optimal solution obtained in the single objective optimization. As expected, the deviation further increases for the following two objectives to 64% (TA) and 257% (ET). For the HTc impact, there is only a deviation of 11% from its optimal value from the single objective optimization, as there is no strong conflict with the cost objective.
Figure 3 provides an overview of the opening of MRFs and material transportation throughout Europe within the lexicographic approach. Here, central MRFs with a capacity of up to 200,000 Mg input per year are placed throughout Southern Europe. In Western Europe, there are also decentral MRFs with a capacity of up to 50,000 Mg input per year. Specifically, in The Netherlands, there are multiple MRFs placed. In Northern and Eastern Europe, fewer MRFs are placed, and plastic waste is transported long distances. When comparing the results with the model’s input data, economies of scale lead to a cost advantage of central MRFs over smaller decentral MRFs.
A slight deviation (
= 1%) from the lexicographic objective function values is introduced to soften the lexicographic constraint and enable more flexibility in the solution approach. The results for this approach are presented in
Table 7 and show a reduction in the deviation from the single objective optimal value of the GWP, TA, and ET compared to the strict lexicographic approach above. The cost optimization uses
, leading to a reduction in the deviation for GWP, TA, ET, and HTc by 7, 13, 124, and 3 percentage points, respectively. Relaxing the optimality for the single objectives can lead to a more balanced result.
Figure 4 displays the recycling network for the lexicographic solution with
. Here, and compared to the strict lexicographic solution, fewer decentral MRFs with smaller capacities are opened while the number of central MRFs only increases by four. They are placed in Western Europe, replacing decentral MRFs in The Netherlands. The layout also decreases the transport distance.
A sensitivity analysis (
Figure 5) is performed to identify the effects of parameter variations on the objective values of the different indicators. In this case, all cost and environmental impact parameters of the recycling process, opening facilities, and transportation are varied separately within their corresponding parameter groups (recycling, opening, and transport).
The analysis reveals the following dependencies between total cost and the individual parameter groups: a 10% reduction of all recycling costs results in a 5% decrease in total costs, a 10% reduction of all opening costs causes a 4% decrease in total costs, while a 10% reduction of transportation costs has no influence on the total costs. These results and their linear relationship show that recycling costs significantly impact the cost target.
In contrast, the results of the environmental impact categories do not demonstrate a linear correlation as the objectives are developed based on the previous cost optimization. The sequential procedure leads to contingent shifts in the solution space for the environmental indicators that can allow for more flexibility and aid in aligning the results with each optimum. Despite these non-linear dependencies, certain trends regarding the impacts of parameter variations on GWP, TA, ET, and HTc can be identified.
Concerning GWP, the recycling process is found to have the most significant impact, causing a 7% decrease in total GWP when burdens are reduced by 10%. In contrast, varying the GWP impact for facility openings does not influence the total GWP at all and reducing the value associated with transportation by 10% causes only a 3% decrease in total GWP.
Transportation does, however, considerably influence the TA and ET impact categories. A 10% decrease in the parameters is found to cause a 4% (TA) and 5% (ET) reduction of total impact, while a 10% increase results in a 6% (TA) and 8% (ET) increase. In contrast, the final environmental indicator, HTc, is shown to be mostly influenced by the recycling process, with transportation having no impact.
The analysis results indicate competing objectives where cost and environmental impacts of GWP, TA, and ET are concerned. The softened lexicographic approach is, however, inherently incapable of calculating a more balanced solution, which considers both environmental and economic indicators. For this reason, an alternative method, namely the CGP approach, is implemented and presented in the next chapter.
4.3. Goal Programming
Solving the introduced optimization problem with the CGP approach leads to objective values presented in
Table 8 and a recycling network displayed in
Figure 5. Here, many decentral MRFs are opened to avoid heavy transport activity. Transportation is limited to short distances between neighboring regions. Central MRFs with higher capacity are placed in regions with very high waste volumes when a decentral MRF’s capacity is insufficient for handling all the plastic packaging waste in that region.
Table 8 and
Figure 6 show different results for both lexicographic approaches. Less central MRFs are placed throughout Europe. Instead, multiple decentral MRFs reduce the transport activities. The difference in results can also be seen in deviations of the objectives from their optimal single objective value. Within the CGP approach, the costs deviate from their optimal value by 23%, and the HTc impact deviates by 23% from its optimal value. However, compared to the lexicographic approaches, the impacts of GWP (13% vs. 26%), TA (5% vs. 51%), and ET (23% vs. 133%) deviate less from their optimal values. Overall, the CGP approach reduces the maximum deviation from 133% in the adapted lexicographic approach to 23%. The CGP approach reaches a balance between the objectives, satisfying them with the objective value
.
A sensitivity analysis is performed to vary the recycling, opening, and transport group parameters (
Figure 7), illustrating their effects on the total cost and environmental impacts of the recycling network. In contrast to the previously applied lexicographic approach, utilizing the CGP method allows for linear relationships between all parameters and indicators.
The results indicate that the total costs of the recycling network are mainly influenced by the recycling costs themselves. A 10% reduction in recycling costs leads to a 6% overall decrease, while the same reduction in opening or transportation costs causes only a 3% and 1% in total cost decrease, respectively.
These numbers remain consistent for all indicators as the parameters are sorted into their respective groups, and both cost and environmental impacts are varied simultaneously within said groups. It can, therefore, be concluded that the recycling process has the most significant impact overall. In addition, the opening of a facility plays a more consequential role in the examined indicators than the transport of materials.
Overall, the results from both the CGP approach and lexicographic optimization show that a trade-off occurs between the cost and environmental indicators and all individual environmental indicators in the design of plastic recycling networks within a European circular economy.