Combination of linear and weighted goal programming with penalty function in optimisation of a daily dairy cow ration

https://doi.org/10.17221/2601-AGRICECONCitation:Žgajnar J., Juvančič L., Kavčič S. (2009): Combination of linear and weighted goal programming with penalty function in optimisation of a daily dairy cow ration. Agric. Econ. – Czech, 55: 492-500.
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The aim of the paper is to present a developed spreadsheet tool for the formulation of a daily dairy cow ration. It is constructed on the basis of two linked sub-models developed on the MS Excel platform. It merges the common linear programming model and the weighted-goal programming model with a penalty function. The first sub-model is included in the tool to make an estimate of the least-cost magnitude that might be expected. The obtained result is entered into the second sub-model as the goal that should be met as closely as possible. The tool was tested at two different values of preferential weights for dairy cows with a 25 kg daily milk yield. The results obtained confirm the benefits of the applied approach. In contrast to the common linear program tools, which terminate at formulation of the least-cost ration, our tool provides more efficient rations (in both economic and nutritive terms) by fine-tuning the nutritive goals and by allowing for harmless deviations from these goals by application of penalty functions.
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