The rapid global expansion of photovoltaic (PV) power generation has positioned solar energy as a cornerstone of the clean energy transition. Consequently, the volume of end-of-life (EOL) solar panels is projected to increase exponentially in the coming decades. The recycling and remanufacturing of these decommissioned solar panels not only hold significant socio-economic value by recovering precious materials but are also critically important for environmental protection and the sustainable development of the solar industry. To address the operational challenges within this emerging reverse supply chain, this paper designs and constructs a two-stage supply chain network specifically for solar panel recycling and remanufacturing. The model incorporates key members including the solar panel manufacturer, domestic PV power plants, a remanufacturer, and the overseas market. With the objective of maximizing the overall supply chain profit, decision optimization models for different stages are established. The corresponding optimal pricing decisions and profit outcomes for each member are derived. Furthermore, the impact of the recycling rate on these decisions is analyzed. Numerical experiments are conducted to validate the rationality and effectiveness of the proposed model and its solutions.
1. The Two-Stage Solar Panel Recycling and Remanufacturing Supply Chain Network
Considering the lifecycle characteristics of solar panels and the evolving landscape of the industry, a two-stage closed-loop supply chain network is designed, as illustrated in the conceptual framework. The operation is divided into two distinct phases:
Stage 1 (Initial Production and Deployment): This phase represents the early stage of the solar industry. All solar panels are manufactured by the producer using virgin raw materials. The output is distributed to two channels: a portion is sold to the overseas market, and another portion is supplied to domestic PV power plants for electricity generation. To incentivize the adoption and scale-up of solar power, a subsidy policy is implemented for the domestic PV power plants. This subsidy, often a governmental measure, aims to lower the effective procurement cost for power plants, thereby stimulating demand and supporting the growth of the solar panel manufacturing sector.
Stage 2 (Recycling and Remanufacturing): As the first batch of solar panels installed in domestic power plants approaches its end-of-life, the supply chain transitions into a closed-loop system. A key challenge is the high cost and technical complexity associated with solar panel recycling, which can hinder the development of a circular economy for solar panels. To encourage the remanufacturer to engage in collection and processing, a subsidy strategy is introduced. The subsidy for the remanufacturer is defined as $S_r = \mu \cdot q_{r2}$, where $\mu$ is the subsidy per unit and $q_{r2}$ is the quantity of solar panels collected.
The remanufacturer collects EOL solar panels with a collection rate $\theta$ ($0 < \theta < 1$). Upon collection, the panels are sorted based on their remaining quality $\alpha$, which is assumed to be uniformly distributed between a lower bound $\alpha_L$ and an upper bound $\alpha_H$. A proportion $\beta$ of the collected panels are classified as high-quality, while the remaining $(1-\beta)$ are low-quality. Low-quality panels have minimal value for direct reuse and are thus dismantled to extract recycled materials. High-quality panels undergo minimal reprocessing and are then sold to the overseas market.
Considering the demand characteristics of the overseas market, it purchases a fraction $\gamma$ of the available high-quality recycled solar panels. The remaining high-quality panels $(1-\gamma)$ are also directed to the material recovery stream. The recycled materials from both streams are then used in the manufacturing of new solar panels, with a remanufacturing yield rate of $\lambda$ ($0 < \lambda < 1$).
To further incentivize the manufacturer to use recycled materials and reduce reliance on virgin raw materials, a penalty fee is imposed on the use of virgin materials. The manufacturer pays an environmental fee $f \cdot q_{n2}$, where $q_{n2}$ is the quantity of new panels produced using virgin materials and $f$ is the unit environmental fee. Consequently, the market demand in Stage 2 is satisfied by panels made from both recycled and virgin materials.
The key parameters and decision variables for modeling this supply chain are summarized below.
| Parameter | Description |
|---|---|
| $\gamma$ | Sales ratio of high-quality recycled solar panels to the overseas market |
| $C_m$ | Cost of raw material (virgin) per solar panel |
| $\mu$ | Unit subsidy for the remanufacturer in Stage 2 |
| $M_{pvi}$ | Potential market size of the overseas market in stage $i$ |
| $\alpha_L, \alpha_H$ | Lower and upper bounds of remaining quality for recycled solar panels |
| $R_{pv}$ | Revenue per solar panel for the PV power plant |
| $\lambda$ | Remanufacturing yield rate of recycled materials into new solar panels |
| $q_{pvi}$ | Demand for solar panels from the domestic PV plant in stage $i$ |
| $f$ | Unit environmental fee for using virgin materials |
| $C_n$ | Utility (effective value) per unit of solar panel for the overseas market |
| $C_{pv}$ | Manufacturing cost per solar panel (excluding material cost) |
| $\eta$ | Subsidy rate for the domestic PV power plant |
| $C_r$ | Remanufacturing/processing cost per recycled solar panel |
| $\theta$ | Collection rate of end-of-life solar panels |
| $p_i$ | Market price of a new solar panel in stage $i$ (Decision Variable) |
| $p_{su2}$ | Market price of a recycled (high-quality) solar panel in Stage 2 (Decision Variable) |
| $p_{dsc2}$ | Collection price paid for an EOL solar panel in Stage 2 (Decision Variable) |
To simplify the model analysis, the following assumptions are made:
1. The quality $\alpha$ of recycled solar panels follows a uniform distribution.
2. The price of a recycled solar panel is linearly and positively correlated with its quality.
3. The market demand functions are known.
4. All solar panels are of identical specification.
2. Decision Models and Optimal Outcomes
2.1 Stage 1 Decision Model
In Stage 1, all solar panels are new and produced from virgin materials. The subsidy for the domestic PV power plant is $S_{pv1} = \eta \cdot p_1$. The demand from the overseas market is modeled as a function of the panel’s price and utility:
$$ Q_f = M_{pv1} \left(1 – \frac{p_1}{C_n}\right) $$
This implies demand is positive only when the panel’s utility $C_n$ exceeds its price $p_1$. The total market demand is:
$$ q_1 = q_{n1} = Q_f + q_{pv1} = M_{pv1}\left(1 – \frac{p_1}{C_n}\right) + q_{pv1} $$
The total supply chain profit $\pi_{tol}$ is the sum of the manufacturer’s profit $\pi_{m1}$ and the power plant’s profit $\pi_{pv1}$:
$$ \pi_{tol} = \pi_{m1} + \pi_{pv1} = q_{n1}(p_1 – C_m – C_{pv}) + q_{pv1}(R_{pv} – p_1 + \eta p_1) $$
Substituting $q_1$ into the profit function yields a concave quadratic function in $p_1$:
$$ \pi_{tol} = -\frac{M_{pv1}}{C_n} p_1^2 + \left( \frac{M_{pv1}(C_m + C_{pv})}{C_n} + M_{pv1} + \eta q_{pv1} \right)p_1 – (M_{pv1} + q_{pv1})(C_m + C_{pv}) + q_{pv1}R_{pv} $$
Taking the first-order condition $\frac{\partial \pi_{tol}}{\partial p_1} = 0$, the optimal new solar panel price is:
$$ p_1^* = \frac{M_{pv1}(C_m + C_{pv} + C_n) + C_n \eta q_{pv1}}{2 M_{pv1}} $$
The corresponding maximum total supply chain profit is:
$$ \pi_{tol}^* = \frac{[M_{pv1}(C_m + C_{pv} + C_n) + C_n \eta q_{pv1}]^2}{4 C_n M_{pv1}} – (M_{pv1} + q_{pv1})(C_m + C_{pv}) + q_{pv1}R_{pv} $$
The optimal profits for the manufacturer and the power plant can be derived by substituting $p_1^*$ into their respective profit functions.
| Member | Optimal Pricing | Optimal Profit |
|---|---|---|
| Manufacturer | $p_1^* = \frac{M_{pv1}(C_m + C_{pv} + C_n) + C_n \eta q_{pv1}}{2 M_{pv1}}$ | $\pi_{m1}^* = \frac{[M_{pv1}(C_m+C_{pv}+C_n) +C_n\eta q_{pv1}]^2 -2[M_{pv1}(C_m+C_{pv}+C_n)]^2 -2\eta C_n^2 q_{pv1}^2}{-4C_n M_{pv1}} + \frac{1}{2}(C_m+C_{pv}+C_n)q_{pv1}(1+\eta) – (M_{pv1}+q_{pv1})(C_m+C_{pv})$ |
| PV Power Plant | – | $\pi_{pv1}^* = \frac{q_{pv1}[M_{pv1}(2R_{pv} + (C_m+C_{pv}+C_n)(\eta-1)] + C_n \eta q_{pv1}(\eta-1)}{2M_{pv1}}$ |
2.2 Stage 2 Decision Model
In Stage 2, the quantity of collected EOL solar panels is $q_{r2} = \theta q_{pv1}$. Based on the quality distribution, the quantities are: $q_{h2} = \beta q_{r2}$ (high-quality), $q_{l2} = (1-\beta) q_{r2}$ (low-quality).
The quantity of new panels made from recycled materials is:
$$ q_{old2} = \lambda ( q_{l2} + q_{h2}(1-\gamma) ) = \lambda \theta q_{pv1} (1 – \beta \gamma) $$
Assuming a linear relationship between price and quality, the average collection price is $p_{dsc2} = \frac{\alpha_H + \alpha_L}{6} p_2$. The average quality of sold recycled panels is $Q_{pv} = \frac{1}{2}(2\alpha_H – \gamma \beta (\alpha_H – \alpha_L))$, hence their price is $p_{su2} = Q_{pv} p_2$.
The overseas demand for new panels is $q_{f2} = M_{pv2}(1 – \frac{p_2}{C_n}) – \gamma \beta \theta q_{pv1}$. Total demand for new panels is:
$$ q_2 = M_{pv2}\left(1 – \frac{p_2}{C_n}\right) + q_{pv2} – \gamma \beta \theta q_{pv1} $$
The quantity of panels made from virgin materials is:
$$ q_{n2} = q_2 – q_{old2} = q_2 – \lambda \theta q_{pv1} (1 – \beta \gamma) $$
The profit functions for Stage 2 are as follows:
Manufacturer Profit ($\pi_{m2}$):
$$ \pi_{m2} = q_2 p_2 – q_2 C_{pv} – q_{n2} C_m – q_{old2} C_m – f q_{n2} $$
Remanufacturer Profit ($\pi_r$):
$$ \pi_r = q_{old2} C_m + q_{su2} p_{su2} – q_{old2} C_r – q_{r2} p_{dsc2} + \mu q_{r2} $$
where $q_{su2} = \gamma \beta \theta q_{pv1}$.
PV Power Plant Profit ($\pi_{pv2}$):
$$ \pi_{pv2} = q_{pv2}(R_{pv} – p_2 + \eta p_2) + q_{r2} p_{dsc2} $$
Two scenarios are analyzed based on the risk profile of the domestic PV power plant.
Scenario A: Stable Power Plant (Non-Risky)
The supply chain objective is to maximize the combined profit of the manufacturer and remanufacturer: $\pi_b = \pi_{m2} + \pi_r$. This leads to a concave quadratic function in $p_2$. The optimal price $p_2^{a*}$ and total profit $\pi_b^{a*}$ are:
$$ p_2^{a*} = \frac{(C_m + f + C_{pv} + C_n)M_{pv2} + C_n\left[q_{pv2} + \theta q_{pv1}\left(\gamma\beta(Q_{pv}-1) – \frac{1}{6}(\alpha_H+\alpha_L)\right)\right]}{2M_{pv2}} $$
$$ \pi_b^{a*} = \frac{\left[(C_m + f + C_{pv} + C_n)M_{pv2} + C_n\left(q_{pv2} + \theta q_{pv1}\left(\gamma\beta(Q_{pv}-1) – \frac{1}{6}(\alpha_H+\alpha_L)\right)\right)\right]^2}{4 C_n M_{pv2}} + \lambda \theta q_{pv1}(1-\beta\gamma)(C_m – C_r + f) + \mu \theta q_{pv1} – (M_{pv2} + q_{pv2} – \gamma\beta\theta q_{pv1})(C_m + C_{pv} + f) $$
Scenario B: Risky Power Plant
The supply chain objective is to maximize the profit of all three domestic members: $\pi_b = \pi_{m2} + \pi_r + \pi_{pv2}$. The optimal solutions are:
$$ p_2^{b*} = \frac{(C_m + f + C_{pv} + C_n)M_{pv2} + C_n\left(\eta q_{pv2} + \theta q_{pv1} \gamma \beta (Q_{pv}-1)\right)}{2M_{pv2}} $$
$$ \pi_b^{b*} = \frac{\left[(C_m + f + C_{pv} + C_n)M_{pv2} + C_n\left(\eta q_{pv2} + \theta q_{pv1} \gamma \beta (Q_{pv}-1)\right)\right]^2}{4 C_n M_{pv2}} + \lambda \theta q_{pv1}(1-\beta\gamma)(C_m – C_r + f) + q_{pv2}R_{pv} + \mu \theta q_{pv1} – (M_{pv2} + q_{pv2} – \gamma\beta\theta q_{pv1})(C_m + C_{pv} + f) $$
3. Impact of the Solar Panel Collection Rate $\theta$ on Decisions
The collection rate $\theta$ is a crucial factor for the closed-loop operation in Stage 2. Analyzing its impact on the optimal profit and pricing is vital for supply chain management.
In Scenario A, the total profit $\pi_b^{a}$ is a quadratic function of $\theta$. Its behavior depends on the sign of a key composite parameter $\Delta^a$. Analysis shows that under most practical conditions where incentives ($\mu$, $f$) are sufficient, $\pi_b^{a}$ is maximized at $\theta = 1$. The corresponding optimal price becomes:
$$ p_{2}^{a*}|_{\theta=1} = \frac{(C_m + f + C_{pv} + C_n)M_{pv2} + C_n\left[q_{pv2} + q_{pv1}\left(\gamma\beta(Q_{pv}-1) – \frac{1}{2}(\alpha_H+\alpha_L)\right)\right]}{2M_{pv2}} $$
Only under very specific and unlikely parameter combinations would profit be maximized at $\theta=0$, indicating the clear economic benefit of high collection rates for the manufacturer-remanufacturer coalition.
In Scenario B, a similar analysis on $\pi_b^{b}$ reveals that it is typically a convex function of $\theta$, also maximized at $\theta=1$ under reasonable subsidy and fee settings. The optimal price at full collection is:
$$ p_{2}^{b*}|_{\theta=1} = \frac{(C_m + f + C_{pv} + C_n)M_{pv2} + C_n\left(\eta q_{pv2} + q_{pv1} \gamma \beta (Q_{pv}-1)\right)}{2M_{pv2}} $$
This confirms that a higher solar panel collection rate generally enhances overall supply chain profitability and helps stabilize optimal pricing, especially when the power plant is considered a strategic partner.
4. Numerical Experiment and Analysis
To validate the model, a numerical analysis is conducted with the following parameter values: $C_m=800$, $f=100$, $C_{pv}=200$, $C_r=100$, $R_{pv}=6000$, $C_n=4000$, $M_{pv1}=20000$, $M_{pv2}=40000$, $\alpha_H=0.85$, $\alpha_L=0.35$, $\beta=0.5$, $q_{pv1}=10000$, $q_{pv2}=20000$, $\gamma=0.8$, $\lambda=0.75$, $\mu=80$.
4.1 Impact of Subsidy Rate $\eta$ in Stage 1
Varying $\eta$ from 0 to 0.5, its impact on profits and the optimal new solar panel price $p_1^*$ is analyzed. The results show that the subsidy rate $\eta$ significantly increases the profit of the PV power plant (by approximately 29% at $\eta=0.5$) and also boosts the manufacturer’s profit. The optimal price $p_1^*$ increases monotonically with $\eta$. This demonstrates that subsidizing the power plant effectively stimulates upstream manufacturing and stabilizes the market.
4.2 Impact of Subsidy Rate $\eta$ in Stage 2 (Scenario B)
With $\theta=0.7$, the effect of $\eta$ in Stage 2 is examined. As expected, the power plant’s profit is most sensitive to $\eta$. The manufacturer’s profit increases modestly, while the remanufacturer’s profit is largely unaffected. The optimal prices for new, recycled, and collected solar panels all increase with $\eta$, with the collection price $p_{dsc2}$ showing the smallest increase. This indicates that the subsidy primarily supports the power plant and manufacturer nexus while maintaining stable recovery costs for the remanufacturer.
4.3 Impact of Collection Rate $\theta$ in Scenario A
With $\eta=0.4$, varying $\theta$ from 0 to 1 reveals distinct profit dynamics. The remanufacturer’s profit increases linearly with $\theta$. Conversely, the manufacturer’s profit decreases by up to 17% as $\theta$ increases because higher collection reduces demand for virgin-material-based new panels and diverts some overseas demand to recycled panels. The total supply chain profit remains relatively stable, indicating that $\theta$ effectively reallocates profit between the manufacturer and remanufacturer without harming the whole. Optimal prices for both new and recycled solar panels decrease slightly with increasing $\theta$, promoting market adoption.
4.4 Impact of Collection Rate $\theta$ in Scenario B
Including the power plant in the profit calculation changes the dynamic. While manufacturer profit still declines and remanufacturer profit rises with $\theta$, the power plant’s profit now shows a slight increase. Consequently, the overall supply chain profit experiences a net increase with higher $\theta$. All optimal prices (new, recycled, collected) exhibit a gentle, stable decline as $\theta$ increases. This highlights that a high solar panel collection rate, when managed in a coalition that includes the power plant, can create a win-win situation that boosts total profitability and maintains price stability across the supply chain.
5. Conclusion
The recycling and remanufacturing of solar panels present a critical opportunity for building a sustainable circular economy within the photovoltaic industry. This paper develops a two-stage supply chain network model incorporating solar panel manufacturers, PV power plants, remanufacturers, and the overseas market. Different subsidy strategies are designed for each stage to align incentives. Mathematical models are established to derive optimal pricing and profit decisions under various scenarios. The analysis confirms that subsidy strategies can significantly enhance the overall profit of the solar panel supply chain and improve the economic outcomes for individual members. Furthermore, the solar panel collection rate $\theta$ is identified as a powerful lever. It not only increases total supply chain profit but also facilitates the reallocation of profits among members, fostering cooperation. Importantly, a higher collection rate contributes to the stability of optimal pricing for both new and recycled solar panels, which is beneficial for long-term market health. The findings provide valuable theoretical insights and managerial guidance for designing and operating efficient and sustainable solar panel recycling and remanufacturing supply chains.