Determining the most appropriate age of replacement for dairy cows in Ardabil Province using Stochastic dynamic programming

Background and goal: the objective of this study is to determine the most appropriate time to replacing dairy cows using dynamic programming model in the state of uncertainty of production system. One of the most important management decisions affecting the livestock profitability is timely replacement of dairy cow with young heifers. The base for deciding to replace a dairy cow, which produces several lactation in herd, with a heifer, which have recently passed its first calving and started lactation, is comparing the current value of these two choices. If the expected present value of dairy cow in cattle is less than a heifer we decide to replace. Otherwise, the dairy cow remains in the cattle at least another term to be decided at the beginning of the next period. In probabilistic dynamic programming the direction is in a side which could eventually involve the uncertainties of the analysis in the decision-making process effectively.
using system analysis method, the economic system of cow herd is decomposed to income and expenses components and each of these components were also divided into sub-sections. Then by using mathematical models and MATLAB programming language, the simulation of a bio-economic model was done. The income component including income from selling milk, selling surplus heifers, bull calves and costs including nutrition, management and fixed costs. Management costs also include health care, human resources and reproduction costs which used as input parameters. In order to optimal decision to maintenance or replacement of dairy cows, the probabilistic dynamic programming method was used. The objective function is to maximize net present value in a planning horizon of 10 lactation period. The dairy cow was defined through state variables including lactation period, milk production capacity and different kinds of delay in pregnancy. At each stage, the dairy cows were classified using condition variables including production power in three levels (low, medium and full production) and reproductive performance in 4 levels with a calving interval of 410, 450, 490 and 530 days.
the results showed that for a dairy cow for delays of 40, 80 and 120 days in pregnancy compared with ideal situation of 410 days, economic losses were 3549666.4, 6020255.8 and 10382976.3 Rials respectively. The model results in uncertainty state of production system showed that maintenance of high producing dairy cows until the eighth pregnancy is economic and maintenance of low and average producing dairy cows is not recommended. Optimal life determined by dynamic programming using Markov simulation was 4.75 years and replacement rate was 21%.
in many farms, the annual replacement rate is measured and the percentage of removed cows is determined. If a prospective study is needed to improve removing decisions which can lead to different remove decisions by manufacturers in which to determining optimal time of cow removal we should calculate multiple biological and economic variables at same time. By applying optimal replacement strategy of livestock in addition to achieving more profits we can offer more suitable management patterns to livestock unit managers in order to better deciding which lead to increase productivity in production units.