Integrating the use of linear and dynamic programming methods for dairy cow diet formulation

Despite many refinements that have been made to the basic Linear Programming model used to find economically optimal diets for dairy cows, the sequential nature of the physical and physiological changes that a cow goes through during lactation have not been incorporated into the modelling process satisfactorily. This paper demonstrates how it can be achieved by integrating the use of both Linear and Dynamic Programming methods to optimise the economic performance of a dairy cow over its entire lactation. Linear Programming generates solutions for each potential liveweight change occurring during each of eleven four week periods over the lactation, then the use of DP allows both the selection of the optimal sequence of liveweight changes during the lactation and the specification of rations associated with this optimal path.