Optimal resource extraction with uncertain reserves

The paper considers the problem of finding a plan that maximizes the expected discounted return when extracting a nonrenewable resource having uncertain reserves. An extraction plan specifies the rate at which the resource is extracted as a function of time until the resource is exhausted or the time horizon is reached. The return per unit of resource extracted may depend on the rate of extraction, time, and the amount of resource previously extracted. The paper applies a new method called the generalized search optimization technique to find qualitative features of optimal plans and to devise algorithms for the numerical calculation of optimal plans.