Optimal Resource Use Over Time with an Application to Ground Water

This paper is concerned with optimal allocation over time of a single resource which is either fixed in supply or only partially renewable at a point in time. Some resources which fall in this category are mineral deposits, ground water, petroleum, wildlife, and fish. A functional equation is obtained from a dynamic programming formulation of the problem. This functional equation is used to derive approximate decision rules for resource use as a function of current supply. The results are applied to ground water storage control and tested empirically by comparison with a decision rule obtained by detailed numerical methods.