Managing Supply Chain Risk for Critical Minerals Using Probabilistic Graphical Models

Mineral supply chains, especially for critical resources like copper, lithium, and rare earth elements, are increasingly vulnerable to disruption Geopolitical tension, volatile demand, declining ore grades, and environmental regulation are converging to create unpredictable dynamics.

To proactively manage these risks, we implemented a Probabilistic Graphical Model (PGM) that translates the core dynamics of the influential Ryter et al. copper system models into a Bayesian framework. This PGM draws directly from the economics-informed system structure and parameter behaviors described in:

- Ryter et al. (2022): Assessing recycling, displacement, and environmental impacts using an economics-informed material system model.

- Ryter et al. (2024): Understanding key mineral supply chain dynamics using economics-informed material systems.

The result is a flexible, interpretable, and uncertainty-aware tool for assessing and forecasting risk across the mineral supply chain.

Probabilistic Graphical Models combine statistical inference with domain knowledge. They are ideal for modeling complex systems where:

- Variables interact in nonlinear ways (e.g., price and demand feedback),

- Uncertainty is fundamental (e.g., future supply or policy direction),

- Transparent reasoning is needed (e.g., policy decisions and impact explanation).

In this context, a PGM enables:

- Risk propagation modeling: How do changes in recycling policy ripple through to emissions or mine output?

- Scenario simulation: What’s the likely outcome of a global tax on mining operations?

- Causal inference: Which variables most influence refinery throughput or emissions?

We designed a Bayesian network of several nodes, each representing a key concept from the Ryter material system models. The structure is based on conditional dependencies between variables in the copper supply chain and its surrounding economic system.

Copper Price Index – Reflects global copper pricing dynamics, influenced by supply and demand

Mine Production Volume – Driven by price, ore grade, regulatory costs, and capital conditions

Refinery Throughput – Influenced by scrap supply, copper price, and refining cost

Scrap Supply Ratio – Governs the proportion of secondary vs. primary copper

Recycling Efficiency – Determined by collection rates, sorting tech, and policy support

Composite Economic Pressure – Aggregates economic, political, and market factors impacting system behavior

Carbon Emission Rate – A function of ore grade, production intensity, and refinery performance

Ore Grade – Declines over time, increasing energy use and emissions per unit of metal

Export Policy Impact – Captures trade restrictions or tariffs affecting supply reliability

Refining Cost Index – Includes energy prices, labor, input costs, and regulatory compliance burdens

1. Rebound-Aware Recycling Policy Modeling:

Simulates how increased recycling impacts demand, pricing, and ultimately mining activity, a core challenge noted in Ryter et al. (2022, 2024).

2. Probabilistic Emissions Forecasting:

Carbon Emission Rate is modeled as a function of ore grade and production decisions, enabling scenario-based CO2e emission forecasts.

3. Mine Incentive Tracing:

Copper Price Index and Export Policy Impact influence Mine Production Volume, capturing supply latency and thresholds.

4. Scenario-Based Resilience Analysis:

Policy shifts (e.g., carbon taxes) affect multiple downstream variables like Refining Cost Index and Scrap Supply Ratio.

This PGM implementation offers a transparent, probabilistic, and extensible representation of the complex copper supply chain dynamics developed by Ryter et al. It transforms a rich, economics-informed material system model into an inference-ready Bayesian tool for strategy and risk management.

By doing so, we enable:

- Decision-makers to test interventions,

- Analysts to simulate scenarios under uncertainty,

- Stakeholders to understand systemic vulnerabilities and trade-offs.

This approach is particularly relevant to policymakers, sustainability leads, and industry strategists navigating the fragile landscape of mineral resource security.