Optimal harvesting time in a size-heterogeneous population

This paper analyzes the optimal harvesting time for husbanded biological assets consisting of individuals of different sizes. In contrast to previous works which include a random variable in the growth function, it is assumed that the heterogeneity is caused by differences in the initial sizes of the planted culture. Therefore, the evolution of the population with a given growth pattern is described by a size-structured dynamic model. An optimality condition is obtained and compared with the one known in the size-homogeneous case. If the size heterogeneity is taken into account, then under appropriate natural conditions for the biological and economic factors, the resource should be maintained longer compared with the recommendations obtained from the homogeneous models of the same culture. The theoretical findings are confirmed by numerical experiments with a hypothetical culture, and an application to the tilapia farming in Mexico.