Total allowable catch for managing squat lobster fishery using stochastic nonlinear programming

The authors’ work on lobster fishery in Chile is summarized in this paper. The paper presents the formulation and algorithmic resolution of a two-stage stochastic nonlinear programming model with recourse. The proposed model considers a long-term planning horizon and specifically allows an optimal total allowable catch quota to be obtained for the first planning period. This model takes into account biomass dynamics, the conditions guaranteeing sustained species management and uncertain parameters such as growth rate and species carrying capacity. These parameters are explicitly incorporated via a discrete random variable (scenarios). The proposed model is solved by Lagrangian decomposition using the algebraic modeling software AMPL, in combination with the solver MINOS to solve the nonlinear models resulting from the scenario decomposition. The article also presents the results obtained with this methodology and the conclusions drawn from the work.