Optimization of Feed Ration Size in Aquatic System According to the Optimal Control Approach: Implications of Using the von Bertalanffy Growth Model

Rationing aquaculture farming feed is challenging for producers due to high feed costs, representing 30%–60% of the total operating costs. Therefore, optimal timing of feeding could lead to improved economic returns from an aquatic system. An optimal dynamic feeding model has been determined considering the von Bertalanffy growth model. A bioeconomic model of tilapia production in Mexico for specific markets was used for numerical illustration. The von Bertalanffy growth model was parameterized with experimental data from tilapia (Oreochromis niloticus) fed four ration sizes (50%, 80%, 100%, and satiety), in order to determine different optimal rationing for different fish sizes (200, 300, and 400 g), market prices (Monterrey, Cancún, Mexico City, and On site), and optimal harvesting times (OHT), considering the time value of money. The results of the modeled optimal feeding trajectories show a continuous decrease from stocking to reach a minimum value and then slightly approaching the harvest size. This result contrasts with the recommendations of the feed suppliers and with those found when a potential growth model was used. The results in the case study showed that the Monterrey market presented the highest present value of the benefits in the OHT and the different market sizes. The implications of the Bertalanffy model for optimal rationing trajectories are presented in the discussion.