Determing the effectiveness and factors Affecting optimal Herd Life In Dairy cows by dynamic programming and DEA model

One surefire way to increase income and profit is to pay attention to the viability of the dairy cow and increase the efficiency of each livestock unit. The purpose of this study was to determine the efficiency and effective factors on optimal herd life in dairy cows with dynamic data envelopment analysis and planning model in Ardabil city.

The data of this study were related to 1397 time series of dairy farms in Ardebil city which were analyzed by system analysis method, economic system of dairy herd and income and cost components, and each of these components was subdivided into other sections. Then, using mathematical models, we simulated a bioeconomic model and optimized it with the help of the Matlab software Compecon toolkit. The dairy cattle were described with state variables including lactation period, milk production capacity and different gestation states. In order to design data envelopment analysis model, several inputs and outputs in the production process were studied. The main variables used in the study included, herd size by apex, feed and concentrate in kg, manpower by day, health by Frequency of milk, milk production and livestock manure production per kg and total income were determined. And Deap 2.1 software based on minimizing the amount of input per unit of product was used for performance calculations.

Optimal herd life (from first calving to elimination) was 4.55 years under optimum conditions. The results also showed that the technical efficiency with constant return to scale is 0.719 and with variable return to scale equal to 0.899 and scale efficiency was calculated to be 0.888. The overall technical efficiency value was 0.99, allocative efficiency 0.583 and economic efficiency 0.579.

The effect of heifer price, milk price and discount rate on optimum lifespan showed that with increasing heifer price, milk price decrease and discount rate increase elimination percentage decreased and optimum lifespan increased. The results of data envelopment analysis showed that in terms of variability of efficiency relative to scale, increase in herd size and health costs and decrease in forage, concentrate and labor costs, respectively, 14.18, 0.83 , 2.8% and 5% result in inefficient herds being maintained by maintaining levels. Therefore, in order to make an inefficient unit effective, changes must be made to the inputs and outputs of that unit. By specifying the differences between the inefficient and inefficient units, appropriate strategies are designed to eliminate the gap between them.