Feed formulation problem in Peruvian aquaculture: A mathematical programming approach

The aquaculture industry in Peru, in recent years, has been growing by 14.4% between 1998 and 2018, and has become popular among small entrepreneurs due to the climate conditions and extensions of water offered by the Peruvian territory. Feeding represents between 40 and 60% of the total costs and this figure is increases by 80% in small-scale or family productions, therefore, there is a need to implement an adequate feeding program for aquaculture. The objective of this research is to develop a linear programming (LP) model that allows the optimization of the fish feed formulation by manufacturing a balanced meal using locally available inputs. Authors like V.O. Oladokun and A. Jhonson (2012) have managed to make a similar model in the poultry sector, achieving a 9% reduction in feed costs. Information was collected from scientific articles and journals on nutritional content, ingredients, and alternatives fish feed consumption; the cost of the ingredients has been obtained using current market information. The mathematical model contains 10 decision variables and 11 restrictions, which was conducted with Solver on Excel. The fish farm used in the case study allowed us to collect the necessary information for the resolution of the model and the analysis of the optimal results. The optimal solution of the PL model reveals a reduction in feed costs with the new formulation compared to the feed used by fish farmers. The analysis of the optimal results allowed us to see how the total feed costs could be affected by the implementation of the sensitivity analysis with the Monte Carlo simulation.