# Optimal Decisions for Resource Extraction under Uncertainty

CSIRO is developing methodologies and software for determining the switching boundaries to help mineral companies to make optimal sequential decisions under economic and geological uncertainties. The methodology is based on novel regression Monte Carlo techniques. It requires the optimal control solution constructed using large number of Monte Carlo simulations of the main uncertainties (e.g. commodity prices, interest rates, exchange rates, the quality and amount of ore, etc).

Visualizing the switching boundaries makes it easier to understand how the optimal strategies change under different market conditions and different project settings. It provides a simple and intuitive decision support tool for identifying optimal operational strategies and for optimal management of resources projects. It also helps in evaluating the financial benefits of using dynamic strategies.

### Example: Optimal Decisions for Copper Extraction under Market Uncertainty

We illustrate the approach by using a classical example of a copper mine operation with flexibility to delay, temporarily close, restart and permanently abandon the mine in response to changes in the commodity price. The features of the problem are 3 possible operating regimes:

1. Open;
2. Temporarily closed; and
3. Abandoned;

Changing the operating regime incurs switching costs. The cash flow at each time step depends on the current copper price, production rate, operating costs and taxes. At each decision time, the optimal operating regime is chosen so as to maximize the mine value over the entire planning horizon. Decisions are based on the expected future cash flow conditional on the current decision and copper price, using the information from a large number of simulated future copper prices.

Figure 1 shows that operational flexibility can significantly increase the project value. The difference between the Net Present Value (NPV) of the optimal flexible strategy (dark blue) and the fixed strategy (light blue) is especially large for smaller initial copper prices. A considerably improved risk profile of the optimal dynamic strategy, with increased probability of profits and significantly decreased probability of losses, is illustrated in Fig. 2.

Figure 1: Comparison of the NPV of mine with fixed and optimal operational strategies

Figure 2: Comparison of distributions of expected discounted cash flow.

Determining the optimal strategy as a function of the copper price and the remaining reserves is a complex task. The project value has to be optimized over the whole planning horizon (here 60 years in our example). CSIRO is developing a methodology and software to construct switching boundaries for optimal flexible management of natural resource projects under uncertainty.

### Switching Boundaries

The switching boundaries give the critical copper prices when the mine should change from one operating regime to another. In our example, the boundaries depend on both the remaining mine life and the remaining reserves, and are represented by two-dimensional surfaces (see Fig. 3). They also depend on the costs involved in changing from one regime to another. For example, the company has to pay maintenance costs when a project is closed temporarily. It also has to pay workers and staff when they are laid off. If a mine is abandoned, the company has to pay decommissioning costs.

Figure 3: Switching surfaces for 60-year time horizon.

At each decision time, there are 4 possible switching boundaries (see Fig. 4):

1. from open to closed (→),
2. from closed to open (→) ,
3. from open to abandoned (→), and
4. from closed to abandoned (→).

These boundaries split the plane into 6 regions of optimal decisions:

1. open the mine;
2. close the mine;
3. abandon if currently closed;
4. abandon if currently open;
5. abandon unconditionally; and finally
6. a hysteresis band where no switching occurs, that appears due to the switching costs.

Figure 4: Switching boundaries at a decision time (t = 45).

Figure 5 illustrates the evolution of the switching boundaries with time, which provides insight into the changes in the optimal operating strategy over the mine life. Towards the end of planning horizon, the ’abandon’ region increases, while the operating region ’open’ decreases. Besides, the switching boundary from ’open’ to ’close’ disappears, which means that it is no longer optimal to close the mine temporarily. Also, there is a sharp increase in the switching boundary towards the end of planning horizon, as the reserves are near depletion. This indicates that much higher commodity prices are required for reopening the mine when the reserve is low and toward the end of the time horizon.

Figure 5: Evolution of switching boundaries with time.

Determining the switching boundaries for such problems remains a challenging task. The new efficient regression Monte Carlo techniques developed by CSIRO make it possible to tackle realistic high dimensional dynamic optimization problems under combined market and geological uncertainties.