Linear Programming in dairy farms: use no traditional

Abstract

ABSTRACT: A real case of a dairy cooperative was modeled using linear programming to address difficulties in achieving the proper operation of its processing plant. The cooperative requires constant volumes of milk with specific quality levels, depending on the products being processed in each case. To demonstrate the usefulness of the Linear Programming (LP) tool in organizing the dairy industry, a model was developed that includes the feasible production capacity of the cooperative’s members, as well as the possibility of external milk purchases (for times when the required quality cannot be achieved). The so-called “base” model minimizes the cost of raw milk. Considering the importance of what the industry refers to as “useful solids” (US), an additional constraint was later incorporated into the model to quantify them. This modification did not alter the conclusions and is straightforward to formulate. Subsequently, the same model was reformulated to maximize the useful solids constraint, given the relevance of this factor in determining milk prices. In this version, the constraint was transformed into the objective function, while prices became a capital constraint. It is noteworthy that this modification results in a different allocation of resources. The results presented to veterinarians raised significant concerns. Furthermore, the study shows that the quality indicator known as “useful solids” presents important limitations, and therefore, it might not be the most appropriate metric for designing a quality-based bonus system.