Harvesting Policies with Stepwise Effort and Logistic Growth in a Random Environment

Abstract

Recently, we have developed optimal harvesting policies based on profit optimization in random varying environments. Namely, we have considered a logistic stochastic differential equation growth model, with the purpose of discussing the use of variable versus constant effort harvesting policies in terms of the expected accumulated discounted profit during a finite time interval. Using realistic parameters, we have concluded that there is only a slight reduction in profit when choosing the applicable constant effort policy instead of the variable effort policy, which presents strong disadvantages. Here, we apply a logistic growth model and a more general profit structure to present alternative policies based on variable effort, named stepwise policies, where the harvesting effort is determined, under the optimal variable effort policy, at the beginning of each year (or of each biennium) but is kept constant during that year (biennium). Replacing the optimal variable effort policy by these stepwise non-optimal policies has the advantage of applicability but, at best, considerably reduces the already small profit advantage the optimal variable effort policy has over the optimal constant effort sustainable policy.