Mathematical Modeling of Feed Rations Using Solver Software

Ancuta Simona ROTARU, Mihai BENTEA, Ioana POP, Anamaria VATCA, Luisa ANDRONIE


Animal nutrition is a very large area of study where mathematical modeling is a success, as in many areas. In addition to shaping the main physiological processes underlying the farm animals yielding, the objective function optimization issue (i.e. total expenditure on fodder) arises both in terms of protein and vitamin's intake of nutrients and in terms of their cost. Optimising feed rations through mathematical modeling monitors the amount of food an animal needs throughout the day, so that the objective function (also called goal function of efficiency function) be minimum or maximum depending on the problem requirements. In order to solve mathematical model one needs fodder varieties that are part of the fodder basis and this feed (in kg) must be purchased or produced, and the solving method we use is the Solver tool of Microsoft Office Excel software . In order to optimize the objective function one should observe the following restrictions concerning the provisioning of total feed expressed in nutrients: provisioning of the necessary fodder by groups of fodder, observing proportions in fodder structure by groups of fodder, complying with fodder plants culture technologies and taking into account the availability of land designated for the forage and fodder crops. The mathematical model consists of three parts: the system of restrictions, non-negativity conditions and objective function. This paper shows the effectiveness of the Solver IT tools solver in dealing with many linear programming issues, including the establishment of feed rations as ensuring a good and well balanced food in terms of nutrition ensures both a good maintenance of the animals and an increased production.


feed rations, mathematical models,objective function, optimization, Solver

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