Optimal Exploitation of a Mineral Resource under Stochastic Market Prices

In this chapter, we study the operation and optimal exploitation of a mining project. We model the project as a collection of minimal extraction units or blocks, each with its own mineral composition and extraction costs. The decision maker’s problem is to maximize the economic value of the project by controlling the sequence and time of extraction, as well as investing in costly capacity expansions. We use a real options approach based on contingent claim analysis and risk-neutral valuation to solve the problem for a fixed extraction sequence, taking as an input the stochastic process that regulates the time dynamics of futures prices. Our solution method works in two steps. First, we consider a fixed production capacity and use approximate dynamic programming to compute upper and lower bounds on the value function in terms of the spot price and mineralogical characteristics of the blocks. We use these bounds to obtain an operating policy that is asymptotically optimal as the spot price grows large. In the second step, we extend this asymptotic approximation to handle capacity expansion decisions. Our numerical computations suggest that the proposed policy is near optimal. Finally, we test our methodology in a setting based on data from a real project at Codelco (the world’s largest copper producer).