Principles of Dynamic Optimization in Resource Management

The type of resource problem amenable to static analysis is distinguished from that requiring dynamic analysis. Possibly due to the apparent complexity of optimal control theory methods, often dynamic models have not been applied where they would be appropriate. In this article dynamic programming arguments are used to derive optimality conditions directly and simply. They are derived for a renewable resource such as a fishery, but they have application to resource management in general. The approach is illustrated by examples to the extraction of a depletable resource, to feeding for weight gain, and to applying fertilizer when some fertilizer carriers over from one crop season to another. Conditions for the optimal replacement of biological units are also considered.