An Algebraic Optimization Model to Conserve Water Environment by Distributing Manure for Harvesting

Abstract

Abstract An overuse of manure on farmland creates a major environmental problem. When dumping more manure than the crops need as fertilizer, it causes an excess of manure in those fields. Rainwater drains these excessive amounts from the surface into the water reservoirs (rivers and lakes), where they pollute the water, nourish algae, and harm the fish. We develop an algebraic optimization model to formulate for the selection of the right field at the right time so that the environmental damage is limited. We gather instance data from a region of topologically connected reservoirs in northern Senegal and their adjacent farmlands. This mathematical problem then can be tackled by standard solvers for linear optimization problems. When applied in practice, this solution can improve the water quality by reducing the amount of manure and its main components, Nitrogen, Phosphorus, and Potassium.