A Mathematical Programming Approach to Beef Feedlot Optimization

The efficient operation of a beef cattle feedlot is governed by the purchase and selling weights and prices of the animals and by the feeding system used. The optimal feeding system will involve feeding least cost rations to animals at every stage in the production process. A method is described for determining optimal feeding systems which meet the nutrient standards recommended by the US National Research Council. The approach involves first using linear programming (LP) to determine least cost rations to produce specified liveweight gains in animals of known liveweight. Dynamic programming (DP) is then used to determine the optimal sequence of rations to feed in order to produce animals of specified liveweight from animals of known initial weight at minimum cost, using the least cost rations determined from the LP model. The results from this new DP model can then be used to determine the optimal combination of purchase weight, selling weight and feeding system. It is shown that in order to use the DP model, the LP model must be solved a large number of times and a new method is developed to produce these solutions more efficiently. The approach is applied to a representative problem and the computational experience is presented.