A Pearson-network Approach to Animals’ Feed Formulation

Ration formulation plays a crucial role in the profitability and sustainability of animal farming, particularly in developing economies like Nigeria, where feed costs can account for 60-80% of production expenses. Traditional methods such as the Pearson Square and matrix techniques are limited in flexibility, scope, and ability to handle multiple constraints. This study introduces a novel approach by integrating graph theory (network models) with the Pearson Square method to develop diverse, cost-effective, and nutritionally balanced animal feed rations. Using secondary data from agricultural by-products sourced predominantly from Benue State, Nigeria, a directed multi-stage network was constructed with 50 vertices (ingredients) and 237 edges (ingredient interactions), representing nine stages of feed formulation, ranging from energy and protein sources to vitamins and minerals. The developed model generated over 30,000 unique feed formulations. Analytical results showed average nutritional outputs of metabolizable energy at 28g 6.86 kcal/kg, crude fibre at 8.13%, dry matter at 80.75%, nitrogen at 34.33%, and calcium at 0.28%, all within acceptable ranges for animal nutrition. The model offers flexibility to accommodate cultural and regional ingredient restrictions and addresses feed preservation concerns. This research demonstrates the potential of network optimization techniques in enhancing ration formulation processes in animal agriculture.