Invasive species constitute a major economic and ecological threat. They produce billions of dollars in damages annually and are considered on of the top five factors causing the loss of biodiversity. Hence the prevention, control and elimination of invasive species are major objectives for government agencies. While ecological and biological research can identify effective treatment measures, the implementation of these methods is inevitably limited by fiscal constraints. Thus, ecological data needs to be incorporated into economic cost-minimization models to find the optimal balance of alternative approaches subject to budget limitations. We present a stochastic dynamic optimization model that analyzes the optimal choices for invasive species management: the optimal levels of search intensity to detect established species and the optimal degree of control of a detected species. The model illustrates how the optimal strategy for a single species depends on the interactions among three factors: the speed of the invasive species invasion, the distributions of random biological processes, and the specific parameters pertaining to that species.