Game Theory Meets Solar Trash: A Two-Level Model Turns Retired Panels Into Profit

Solar power has spent two decades basking in its reputation as the world’s cleanest energy success story, but a quieter crisis is mounting on rooftops and in solar parks. Photovoltaic panels last roughly 25 to 30 years, which means the earliest large installations, particularly in Indian states such as Rajasthan and Gujarat, are now approaching the end of their working lives. According to a joint report by the International Renewable Energy Agency and the IEA Photovoltaic Power Systems Programme, cumulative PV panel waste could reach between 1.7 and 8 million tonnes by 2030. The Global E-waste Monitor 2024 estimates that around 600,000 metric tonnes of panels were discarded globally in 2022, a figure projected to quadruple. A new study published in Cleaner Engineering and Technology proposes a mathematically rigorous answer to the question the solar boom has long deferred: what happens when the panels come down?

The stakes are both environmental and economic. Decommissioned crystalline silicon modules contain lead, cadmium and tin, substances linked to brain disorders, cancers and damage to the lungs, liver, kidneys and prostate if they leach from improper dumps. Yet the same panels are also a treasure chest of recoverable material. IRENA estimates that recycling end-of-life PV panels could unlock roughly 450 million dollars in recoverable value by 2030 and 15 billion dollars by 2050. The problem, the study’s authors Shikha Tiwari, Eshwar Dayal and Lakshay argue, is that existing waste management systems simply fail to capture this stream, because of economic and logistical constraints. Solar installations range from sprawling utility-scale parks to scattered urban rooftops, and that geographic fragmentation drives up the cost of collecting heavy, fragile freight from thousands of dispersed points.

The core of the new work is a bi-level optimization model, a mathematical structure designed for situations where two decision-makers with conflicting goals interact. In this formulation, the collection centre operator acts as the leader, seeking to minimise total cost, which includes fixed facility costs, vehicle routing expenses and the incentives paid out. The end users of solar panels act as followers, rationally choosing whether to hand their retired panels to the formal recycling system and, if so, whether to request a home pickup or deliver the panels themselves to a drop-off point. The lower level of the model maximises the incentives users receive, while the upper level minimises the operator’s total cost. The authors frame this as a Stackelberg game, a classic game-theoretic construct in which the leader anticipates the follower’s best response before committing to its own decision.

What makes the framework distinctive is that it stitches together, in a single model, four elements that previous studies treated largely in isolation: forecasting of future waste volumes, optimisation of facility locations, vehicle routing, and financial incentives. The authors’ comparative analysis of the literature shows that most prior works incorporated at most two of these dimensions. Some optimised facility placement but ignored routing; others modelled incentives but lacked any mathematical backbone for reverse logistics. By contrast, the new model makes incentives endogenous, meaning the payment levels themselves are decision variables that respond to waste volumes and costs, rather than fixed assumptions plugged in from outside.

The forecasting component is built on the Weibull distribution, a statistical function widely used to model failure rates over time. Rather than assuming every panel dies at exactly year 25, the Weibull approach produces a probabilistic retirement curve that rises during operational degradation and accelerates near end of life, which the authors argue is far closer to real-world behaviour than a fixed-lifespan model in which all panels retire simultaneously. The study runs two scenarios: a regular-loss baseline with a shape factor of about 2.49, and an early-loss pessimistic scenario with a shape factor of 5.38, reflecting premature failures from harsh weather or handling damage. Future installed capacity is projected using segmented linear growth rates, declining from 7.8 percent in 2021-2025 to 3.5 percent by 2036-2040, a deliberate choice to avoid the overestimation that exponential extrapolation produces over a 20-year horizon.

That overestimation problem is vividly demonstrated in the results. When an exponential growth assumption with a 14 percent compound annual growth rate is applied to Jaipur district, the model projects more than 2,300 megawatts of installed capacity in a single district by 2040, and a cumulative capacity overestimate of more than 100 percent. Such inflated numbers would lead planners to open unnecessary collection centres, oversize their fleets and set incentive levels for waste that will never materialise. The segmented linear approach, by contrast, produces projections that the authors consider implementable, and it feeds district-level waste estimates for Jaipur from 2021 to 2040, a spatial resolution fine enough to support actual facility location and routing decisions, unlike the national or state-level estimates that dominate the existing literature.

For the case study, Jaipur, the district with the highest installed solar capacity in India’s top solar state, was divided into 95 equal square grids, with each grid centroid serving as a waste generation site. Thirty-seven authorised e-waste collection centres provided the pool of candidate facilities. The routing side of the model is a capacitated vehicle routing problem, solved with Miller-Tucker-Zemlin subtour elimination constraints to ensure that every collection route is a single continuous loop returning to its depot, rather than a set of disconnected fragments. Haversine distances between grid centroids and centres ground the routing calculations in real geography. The model also enforces a profitability rule: revenue from selling collected panels to recyclers must exceed total operating cost by at least 10 percent, a threshold reflecting administrative overhead, price volatility in recovered materials and the need to fund infrastructure investment.

The results reveal an elegant adaptive behaviour. Under regular loss, the model keeps just two collection centres open until 2035, then adds one per year, reaching six by 2039. Under early loss, where cumulative waste over 2021-2030 is roughly 31 times higher than in the regular scenario, the network scales to as many as 14 centres. Crucially, the model remains profitable in every year of both scenarios, adjusting centre counts and incentive levels without any structural redesign. The incentive dynamics are particularly telling: at low waste volumes, pickup incentives sit near their upper limit because door-to-door collection is cheap when there is little to collect, but as volumes surge, the model widens the gap between drop-off and pickup payments, effectively shifting the logistical burden onto end users and encouraging them to deliver panels themselves. Incentive values eventually stabilise at around 2,500 rupees per kilowatt for pickup and 3,500 for drop-off.

The study also derives four key performance indicators that translate the mathematics into measurable outcomes: cost per tonne collected, average haul distance per tonne, waste recovery rate, and carbon dioxide emissions per tonne. The recovery rate holds steady at about 84 percent across all years and scenarios, while emissions per tonne fall dramatically as waste density rises, dropping from over 35 kilograms of CO2 per tonne in the sparse early years to under 2 kilograms by 2039 in the regular-loss case. Sensitivity analysis shows that minimum collection rates above 70 percent yield a healthy profit-to-cost ratio, that collection centre capacities of 40,000 kilograms or more stabilise the network at two facilities, and that vehicle capacities of 4,000 kilograms or more minimise cost. Computationally, the framework scales gracefully: even at 132 grid cells, generating over four million variables, the solver converged in under 42 seconds with optimality gaps below 2.5 percent.

The implications reach well beyond Jaipur. The authors recommend that policymakers provide subsidies or extended producer responsibility funding during the low-volume window of 2026 to 2030, explicitly incentivise self-drop-off since full home pickup is fiscally unviable, and use the model’s quantified costs to set collection targets that are both ambitious and financially realistic. For operators, the message is that flat-rate incentives are inefficient; payments should be dynamically adjusted, centres should open in stages, and the pickup-drop-off gap should widen during waste surges. The framework is designed to be replicated across regions and time frames, and with modifications could extend to other e-waste streams. Future work, the authors note, could incorporate stochastic user behaviour, the informal recycling sector as a competitor, and real-time GIS integration. But the central insight stands: the coming wave of solar waste is not merely a liability to be buried, but a feedstock whose recovery can be engineered, optimised and made to pay for itself.

Subject of Research: Bi-level optimization modeling for sustainable end-of-life solar photovoltaic waste management and reverse logistics within a circular economy framework

Article Title: Development of a bi-level optimization model for sustainable Solar PV Waste management within a circular economy framework

Article References: Tiwari, S., Dayal, E., & Lakshay (2026). Development of a bi-level optimization model for sustainable Solar PV Waste management within a circular economy framework. Cleaner Engineering and Technology, 35, Article 101327. https://doi.org/10.1016/j.clet.2026.101327

Image Credits: AI Generated

DOI: 10.1016/j.clet.2026.101327

Keywords: solar PV waste, bi-level optimization, circular economy, reverse logistics, Weibull distribution, vehicle routing problem, Stackelberg game, recycling incentives, extended producer responsibility, Jaipur case study, e-waste management, renewable energy