Sustainability assessment of plastic circular economy: transitional probabilities with innovative separation

Figures & data

Table 1. Summary of plastic recycling and waste generation based on four scenarios

Scenario	Separation with Innovation	Separation without Innovation
PLASTIC RECYCLING
Waste Incineration and Discard ($\mathit{S}1$)	$p_{\mathit{yx}}=1-{\left\{\frac{\mathit{y}\left(\mathit{t}+1\right)-y_s\left(\mathit{t}+1\right)}{\mathit{y}\left(\mathit{t}\right)exp\left[-\left(1-\mathit{\gamma }\right)\mathit{wt}\right]}\right\}}^{\frac{1}{1-\mathit{\gamma }}}$	$p_{yx}^{\mathrm{n}\mathrm{o}\mathrm{n}\_\mathrm{i}}=1-\frac{\mathit{y}\left(\mathit{t}+1\right)-y_s\left(\mathit{t}+1\right)}{\mathit{y}\left(\mathit{t}\right)exp\left[-\mathit{w}\mathit{t}\right]}$
Only Waste Discard ($\mathit{S}2$)	$p_{\mathit{yx}}=1-{\left\{\frac{\mathit{y}\left(\mathit{t}+1\right)-y_s\left(\mathit{t}+1\right)}{\mathit{y}\left(\mathit{t}\right)exp\left[-\left(1-\mathit{\gamma }\right)w_d\mathit{t}\right]}\right\}}^{\frac{1}{1-\mathit{\gamma }}}$	$p_{yx}^{\mathrm{n}\mathrm{o}\mathrm{n}\_\mathrm{i}}=1-\frac{\mathit{y}\left(\mathit{t}+1\right)-y_s\left(\mathit{t}+1\right)}{\mathit{y}\left(\mathit{t}\right)exp\left[-w_d\mathit{t}\right]}$
Only Waste Incineration ($\mathit{S}3$)	$p_{\mathit{yx}}=1-{\left\{\frac{\mathit{y}\left(\mathit{t}+1\right)-y_s\left(\mathit{t}+1\right)}{\mathit{y}\left(\mathit{t}\right)exp\left[-\left(1-\mathit{\gamma }\right)w_i\mathit{t}\right]}\right\}}^{\frac{1}{1-\mathit{\gamma }}}$	$p_{yx}^{\mathrm{n}\mathrm{o}\mathrm{n}\_\mathrm{i}}=1-\frac{\mathit{y}\left(\mathit{t}+1\right)-y_s\left(\mathit{t}+1\right)}{\mathit{y}\left(\mathit{t}\right)exp\left[-w_i\mathit{t}\right]}$
Absence of Waste Incineration and Discard ($\mathit{S}4$)	$p_{\mathit{yx}}=1-{\left[\frac{\mathit{y}\left(\mathit{t}+1\right)-y_s\left(\mathit{t}+1\right)}{\mathit{y}\left(\mathit{t}\right)}\right]}^{\frac{1}{1-\mathit{\gamma }}}$	$p_{yx}^{\mathrm{n}\mathrm{o}\mathrm{n}\_\mathrm{i}}=1-\frac{\mathit{y}\left(\mathit{t}+1\right)-y_s\left(\mathit{t}+1\right)}{\mathit{y}\left(\mathit{t}\right)}$
WASTE GENERATION
$\mathit{S}1,\dots ,\mathit{S}4$	$p_{\mathit{xy}}=1-{\left[\frac{\mathit{x}\left(\mathit{t}+1\right)-x_s\left(\mathit{t}+1\right)}{\mathit{x}\left(\mathit{t}\right)}\right]}^{\frac{1}{1-\mathit{\gamma \beta }}}$	$p_{{\mathit{ }}_{\mathit{xy}}}^{\mathrm{non}\_\mathrm{i}}=\frac{\mathit{x}\left(\mathit{t}+1\right)-x_s\left(\mathit{t}+1\right)}{\mathit{x}\left(\mathit{t}\right)}$

Table

Parameter	Value	Source
$\mathit{\psi }$	0.14642	(Addor et al., 2022a, 2022b; Wiah et al., 2022)
$\mathit{\mu }$	0.81474	(Addor et al., 2022a, 2022b; Wiah et al., 2022)
$W_i$	0.20642	(Addor et al., 2022a, 2022b; Wiah et al., 2022)
$W_d$	0.64716	(Addor et al., 2022a, 2022b; Wiah et al., 2022)
$\mathit{W}$	0.85358	(Addor et al., 2022a, 2022b; Wiah et al., 2022)
$\mathit{\beta }$	0.9	(Addor et al., 2022a; Wiah et al., 2022)
$\mathit{\gamma }$	0.81	Set based on the value of $\mathit{\beta }$

Figure 1. Plastic recycling transitional probabilities with innovation-driven separation.

Figure 2. Plastic recycling transitional probability with non-innovation-driven separation.

Figure 3. Innovative versus non-innovative separation-based recycling.

Figure 4. Plastic waste generation transitional probabilities with the integrated roles of separation with and without innovation.

Figure 5. Sensitivity of plastic waste recycling to variations in innovation.

Figure 6. Sensitivity of the plastic waste generation probability subject to variation in innovation.

Addor, J. A., Wiah, E. N., & Alao, F. I. (2022a). An improved two-states cyclical dynamic model for plastic waste management. Asian Research Journal of Mathematics, 18(5), 52–13. https://doi.org/10.9734/arjom/2022/v18i530378

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Addor, J. A., Wiah, E. N., & Alao, F. I. (2022b). Mathematical model for the cyclical dynamics of plastic waste management: A two-state closed model. Journal of Materials Science Research and Reviews, 9(2), 15–36. https://journaljmsrr.com/index.php/JMSRR/article/view/30234

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Wiah, E. N., Addor, J. A., & Alao, F. I. (2022). Transitional probability for plastic waste management and implication on sustainability. Sustainable Environment, 8(1), 2118654. https://doi.org/10.1080/27658511.2022.2118654

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Data availability statement

Data will be made available upon request to the corresponding author.