# Optimization of Bulls Fattening Ration Applying Mathematical Deterministic Programming Approach

J. ZGAJNAR and S. KAVCIC
University of Ljubljana, Biotehnical Fac., Dept. of Animal Science, Groblje 3, SI-1230 Domzale, Slovenia

### Abstract

ZGAJNAR, J. and S. KAVCIC, 2008. Optimization of bulls fattening ration applying mathematical deterministic programming approach. Bulg. J. Agric. Sci., 14: 76-86

The more specialized beef farms demand the more precise management to achieve economically justified outcome. Undergoing CAP reform and market liberalisation are just some of numerous factors that are going to have significant impact especially on expenditures rise in the beef sector. Forage variable cost already range between 40 % and 70 % of total variable cost of bulls fattening in Slovenia. Ration formulation is therefore becoming fundamental lever of beef farms management. To support beef farmers we present a user friendly tool developed in Excel framework that utilizes mathematical deterministic programming techniques. Paper illustrates the supplementation of linear program by weighted goal program resulting in more efficient beef ration formulation. User can decide either to minimize forage costs, to achieve more balanced ration or to implement own weights about importance of both, always based on feed at his/her disposal. In this way the tool developed is applicable for practical decision making on beef farms, enabling cost-effective and nutrient-balanced beef production.

## Key words: linear programming, weighted goal programming, ration optimization, beef farming, beef economicsAbbreviations: aij - The quantity of the ith nutrient in one unit of jth feed; bi - The amount of the ith resource available – right hand side (RHS); C - Objective function (LP); CF - Crude fibre; cj - jth feed cost; di+ - Positive deviation variables including over achievement of the ith goal; di- - Negative deviation variables including under achievement of the ith goal; DM - Dry matter; gi - Expected daily requirement of the ith nutrient (goal); LP - Linear program; MCDM - Multi criteria decision making; ME - Metabolic energy (expressed in MJ - mega Joule); MP - Metabolisable proteins; MVM - Mineral-vitamin mixture; WGP I- Weighted goal programming, the first scenario; WGP II - Weighted goal programming, the second scenario; WGP - Weighted goal program; wi - Weight expressing the relative importance of achieving of the ith goal; Xj - The level of jth feed; Z - Objective function (WGP)

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