Dynamic Decision-making Model for Stochastic Population Management with Scheduled Inspections

Controlling animal population in natural environment, such as fishery resources, their preys and predators, and some invasive species, is a main part of environmental management. In the real world, both continuous and impulsive interventions are carried out for controlling the population; the latter is scheduled at pre-determined time and is subject to deterioration. Finding the most cost-effective interventions can be mathematically formulated as a mixed optimal control problem whose solution reduces to solving recursive Hamilton-Jacobi-Bellman (HJB) equations. However, such an approach has not been made so far. In this paper, we present a primitive mathematical formulation of the population control problem and derives the recursive HJB equations to be solved based on a dynamic programming principle. A demonstrative computational example on a predatory bird population control problem is also presented. The computational results give an instruction when the overhead lines should be installed to repel the bird and when and how much they should be shot.