Modelowanie matematyczne we wspomaganiu procesów decyzyjnych w opasie buhajków
AbstractThe present study shows some applications of mathematical modelling as a tool for gaining a valuable insight into the factors that determine the efficiency of the fattening process of young bulls. Such knowledge may be useful in taking informed production decisions that would lead to optimal economic results. In constructing the theoretical models of bull fattening, the available experimental and literature data were used, and two decision problems, namely how to determine the composition of feeding rations and how to design an optimal fattening strategy, were considered. The strategy focused on the sequence of daily gains, the end-point of fattening and the time of possible replacement of one bull-calf with another in varying technical and economic conditions. Analyses were performed for bulls of late- and early-maturing beef breeds and of dairy breeds. The strategy was optimised by adopting the following approaches: (i) fattening to the assumed slaughter weight, (ii) fattening with the assumed duration, and (iii) cyclic fattening with the replacement option. The fattening was modelled as a separate farming activity that starts after weaning and is split into several stages. Depending on the kind of the approach, the length of the stage was fixed or varied. At each stage, the state of the process (body weight) was observed and the decision (daily gain or daily gain x stage length) affecting the process was made. The optimal daily gains were selected from among the admissible daily gains defined by the growth rates assumed in the French, American and Dutch feeding standards and by the expected growth rates of the bull breeds under study, estimated by means of Richard's growth model. The technical parameters of the models included initial body weight, slaughter weight, width of the body weight class interval in the optimisation process, percentage deviation from the expected daily gains, length of the fattening period, length of a stage in the fattening period (length of the planning horizon in the cyclic fattening), and body weight of a replacement bull-calf. The economic parameters comprised prices of feeds, cost of a calf, cost of a replacement bull-calf, non-feed costs, and live weight price of young bulls. Nutrient requirements were determined according to the INRA and NRC feeding standards, assuming 20 kg-wide class intervals of body weight and 100 g-wide class intervals of daily gain. For all the combinations of body weights with daily gains, feeding rations were compiled by linear programming with a simplex method. This made it possible to minimise the cost of the ration that ensures adequate levels of both energy and protein at a specified dry matter intake. Three types of feeding rations were considered: A — maize silage, concentrate, B — wilted grass silage, concentrate, and C —maize silage, wilted grass silage, concentrate. The optimal strategy of fattening was devised by using a dynamic programming method. The optimisation criterion (the objective function) was defined as maximisation of the expected direct surplus* from the whole fattening process. The direct surplus from fattening determined at the end of each stage was calculated by subtracting the direct costs borne from the beginning of the fattening process from the actual value of live weight production. The effects of the optimal fattening strategy designed were evaluated by estimating such indicators as feed and nutrient conversion, direct surplus, direct cost of 1 kg of live weight production, and economic efficiency of fattening. The efficiency of fattening was defined as a percentage ratio of the value of live weight production to the direct costs of fattening. The input variables for the models can easily be modified and adapted so as to reflect the conditions of various production systems. Hence, the software designed by the author on the basis of the models has the potential to become a useful decision-making tool for beef producers and agricultural extension professionals. However, the solutions obtained may only be treated as a suggestion to be considered when taking production decisions. At the same time, it seems that gaining information on the critical components of bull fattening by means of sensitivity analysis was even more important than predicting precise figures. The results of modelling were as follows. With the feeding rations fulfilling the nutrient requirements of the INRA standards and with the slaughter weights assumed to be 600 vs. 700 kg for the bulls of latematuring beef breeds and 500 vs. 600 kg for the bulls of dairy breeds, the mean optimal intensity of fattening was higher for the lower slaughter weight. This resulted from the relatively high optimal daily gains at the early stages of fattening, and indicates that intensive feeding of young bulls is the most efficient. In contrast, when the nutrient requirements of the NRC standards were adopted, the resulting optimal daily gains were higher in the fattening to the greater slaughter weight. This may be associated with the differences in the nutrient requirements for the defined body weight and daily gain of the fattened bulls between the two systems studied. Extending the assumed fattening period caused a decrease in the expected mean optimal daily gains. Unlike the expected direct surplus, the expected economic efficiency was highest for the shortest fattening period (180 days). The efficiency decreased with increasing duration of fattening. In the model of cyclic fattening with one rotation allowed and the price of 1 kg of calf live weight equal to that of 1 kg of young bull live weight (5.0 PLN), the optimal replacement time always fell in the middle of the assumed planning horizon. The sequence of daily gains in the two cycles was the same. A slightly lower economic efficiency can be expected for a longer (18 months) than shorter (12 months) planning horizon. At the same cost of a bull-calf in both cycles, the optimal fattening strategy was independent of body weight. At the price of 1 kg of bull-calf live weight set at 8.0 PLN and the price of 1 kg of young bull live weight at 5.0 PLN, bull replacement appeared to be unprofitable in the 12-month planning horizon both for the late-maturing beef breeds and dairy breeds. In the 18-month planning horizon the replacement was more profitable than the continuation of fattening of the previous bull only for the dairy breeds. Regardless of the assumed slaughter weight or the length of the fattening period, the expected economic efficiency of the optimal fattening strategies was higher for the INRA system than the NRC system. For both feeding systems, the highest economic efficiency can be expected when the animals are fed with maize and wilted grass silage supplemented with concentrates, and slightly lower when the ration consists of maize silage supplemented with concentrates. At higher daily costs of feeding with the ration composed of maize silage, wilted grass silage and concentrates, the optimal slaughter weight decreased, as did the optimal length of the fattening period, while the optimal daily gains usually increased. In the option with the assumed slaughter weight, the optimal daily gains usually fell slightly, however, the expected economic efficiency of the process was noticeably lower. The optimal fattening strategies developed did not display great sensitivity to the changes in the production and economic variables. However, alteration of these variables considerably influenced the expected economic efficiency of fattening. There were no distinct differences in the economic efficiency of the optimal strategies between the models with the assumed slaughter weight and the assumed fattening duration (under similar production and economic conditions). Therefore, when the optimisation criterion (the objective function) is maximisation of the direct surplus, the choice of the type of the decision model should mostly be driven by technological considerations or the possibilities for selling the live weight produced.
|Other language title versions||Mathematical modelling to support decision-making processes in the fattening of young bulls|
|Publisher||Uniwersytet Rolniczy im. Hugona Kołłątaja w Krakowie, MNiSW |
|Publishing place (Publisher address)||Kraków|
|Book series /Journal (in case of Journal special issue)||Zeszyty Naukowe Uniwersytetu Rolniczego im. Hugona Kołłątaja w Krakowie. Rozprawy, ISSN 1899-3486, (0 pkt)|
|Publication size in sheets||12.5|
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