dynamic programming

In the livestock industry around the world, most decisions are about increasing profitability per head, which is not an independent process and is affected by the interactions of biological functions such as (production, reproduction and health) and prices that are changed by policy. Replacement and breeding affect profitability (Nasre Esfahani, 2018). Issues such as feed price fluctuations and the lack of coherent policies to support the dairy industry in the country have made the profession one of the most risky jobs in the economy. When a producer wants to make the decision to remove or replace a cow, it is best to compare the future benefits and expected benefits of keeping a cow or replacing an animal with another. The most important objective of a livestock unit is to maximize the profit of the herd, one of the issues affecting this profit is the criteria and rate of elimination (Rogers et al,1988). If culling and replacement are not optimal, the cows are removed sooner or later than the optimal deadline, the profitability of the herd decreases. The need to determine the optimal time to remove cows requires simultaneous consideration of several biological and economic variables (De Vries,2006). The removal decision must be based on the anticipated future earnings of the cow. The longer the livestock has a livelihood in the herd, the more profit the livestock earns. The decision to properly, optimally and reasonably eliminate livestock is made by comparing the present value of the future cash flow of the cow present in the herd to the present value of the future cash flow of its replacement heifers, ultimately occupying the most valuable animal in the present (Groenendall et al,2005). The application of dynamic programming in the animal sciences is more on animal substitution issues. The optimal policy at each stage represents the best decision from that stage to the final stage. This method calculates an expected value for each of the situations that can be faced and the decision maker selects the best decision based on the expected value based on the situations ahead. Several dynamic programming models for optimal replacement decision making in dairy herds have been proposed by (De Vries,2004) and (Van Arendonk,1985). (Cardoso et al,1999) reported optimizing replacement and inoculation policies in dairy cows by calculating monthly income, costs and probability of elimination.

In this study, using raw data collected from industrial dairy farms of Ardabil between 2015 and 2018, the biological parameters of the herd, such as the shape of the lactation curve, the risk of forced removal and the possibility of pregnancy in different lactation periods and Different months after calving were estimated. The financial information of the herd was also obtained in the form of an economic questionnaire from the studied units. It was further developed by incorporating biological parameters and financial information into a bio economic model in Dairy Vip software. The feature of this software is that it simulates the livestock over time and also calculates the performance of the herd based on breeding and replacement decisions with the goal of maximizing profitability. Milk production was evaluated using daily milk production records and fitting the incomplete gamma curve (Wood). Dairy Vip software defined average daily milk production levels in the herd by entering lactation data (raw milk quantity, incremental milk slope to peak production and milk slope decrease until peak production). Mean milk yield of 305 days at first to third lactation and peak lactation was reported in Table 1.The mean 21-day inoculation rate and cattle breeding rate were 49.3% and 37%, respectively. By default Dairy Vip software, a maximum livestock can be in the herd 24 months after calving. The risk of fetal loss from the second to the eighth month was 6.24, 4.16, 2.08, 1.11, 0.45, 0.19, and 0.19 percent, respectively. A Dynamic programming model was developed to determine the optimal replacement policy for cows in dairy farms and in economic conditions in Ardabil province. The objective function investigated in this study was to maximize the present value of net income from current cows and alternative heifers. Markov chain simulation was used to estimate the expected statistics under optimal policy.

The implications of the decision policies for optimum and non-optimum removal using Dairy Vip software are presented in Table 3. With the implementation of optimal policies, the overall annual removal rate increased from 30.11% to 43.8%. However, the forced removal rate fell by 2.3%. Pregnancy rate increased from 18/15 to 18.2% and increased by 2.89%. Based on the above results, it can be inferred that the economic importance of increasing the pregnancy rate is more urgent in herds with poorer reproductive performance. Also, the non-optimal catch rate dropped from 33.9% to 37%, indicating an increased likelihood of livestock being pregnant in different months. The 21-day inoculation rate ranged from 47.6 to 49.3%, indicating appropriate cow inoculation. By reducing the days of gestation in dairy cows can increase milk production, which in this study reduced the optimal days of gestation from 139 days to 132 days, which resulted in a significant 7-day decrease in milk production and finally annual. Open days are the interval from birth to the next gestation period, from 167 days to 161 days. With the decline in pregnancy, the rate of pregnancy increased. Calving distance also decreased from 13.6 to 13.3, which was reduced to 0.3 per month, which in turn increased annual milk production. As shown in Table 3, the optimal daily milk yields were increased from 41.4 to 44.2 by the optimal policies, which increased the daily milk yield by 3 kg per cow. And the annual yield of milk increased from 12548 to 13483 kg per cow. Reducing the average days of lactation increased the daily and annual production of productive cows by 3 and 935 kg, respectively.

Decisions to optimize voluntary removal and estimation of livestock value by computer simulation in Dairy VIP software enable improved economic returns. This improvement is due to the decrease in average lactation days in the herd resulting in increased milk production, cattle sales and calf production. Although the implementation of optimal policies is associated with increased livestock removal and replacement costs and increased feed costs, however, the increased revenue from implementing these policies could well offset the increased costs. In general, it can be concluded that increasing milk production in medium-sized cows is the most important factor in increasing economic profit. The results of this study showed that low-yielding animals showed their least future benefit in early lactation, indicating that they should be eliminated sooner.

In order to optimally use the inputs, the efficiency of economic units is of great importance. The purpose of this study is to investigate the technical efficiency and economic value of some traits of production, reproduction, survival and growth of Holstein cows in Pars agro-industry. For this purpose, required information including: manpower, cattle population, feed consumption and milk production quantities were collected from Pars Livestock Unit by documentary study, observation and face-to-face interview and their efficiency was calculated based on production and economic performance. The variables used in the research include herd size in terms of head, feed and concentrate in terms of weight, manpower in terms of men per day, health in terms of number of days per day, milk production and production of manure in terms of kilograms and incomes in Rials, which include Income from milk sales, Rial value of livestock manure produced, income from sales of voluntary and forced elimination of livestock, income from sales of bulls and heifers in dairy farms were examined. Deap 2.1 software was used for performance calculations. Optimal decision was calculated numerically by a iterative method using compecon toolbox in MATLAB program. Probability of pregnancy in the first, second, third and higher lactation periods based on data analysis and using logistic regression and GenMod procedure of SAS software Obtained, the results showed that the average of technical efficiency with constant efficiency compared to the scale was 0.83; the average efficiency with variable efficiency compared to the scale was 0.86 The scale efficiency of this company was estimated to be 0.96. The amount of technical efficiency in general was 0.83, allocation efficiency was 0.87 and economic efficiency was 0.72. This unit was efficient in March in terms of types of efficiency, which means that during this month, in addition to consuming a certain amount of product produced with a minimum of inputs, the minimum costs are also considered in the composition of inputs, so the unit in this month was technically, allocative, economically and economically efficient and has a constant return on scale. Also, the highest economic value in non-optimal conditions in survival, reproductive, productive and growth traits, and also for survival rate after weaning, first calving age, milk fat and body weight of adult animals was equal to 234297.30, -41835.16, 128664.12 and 454227.93 Rials, respectively. In optimal conditions, the highest economic value for survival, reproduction, production and growth traits was related to the set of traits of production lifespan, and the calving interval, milk fatproduction and daily weight gain before weaning were estimated at 4594.88,9084.67, 1582264.09 and -1464.87 Rials, respectively. The reason for the difference in economic values of traits in optimal conditions compared to non-optimal conditions is due to the application of optimal livestock replacement strategy, so that the farmer's policy in eliminating and replacing, affect herd profit.

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.

The purpose of this study was to determine the removal rate under the optimal alternative milking strategy for different production and health conditions in dairy cattle of Ardabil province. One of the most important management decisions that affect livestock production is the timely replacement of dairy cattle with young heifers. Using the system analysis method, the economic system of the dairy cattle was split into income and cost components and each of these components was subdivided into other parts. Then, using the existing models and using the Compecon Combinator tool kit, Matlab programming language was used to simulate a bioeconomic model. The objective function was to maximize the net present value of the livestock in a planning horizon with 10 lactation periods. Dairy cattle were defined by state variables including lactation period, milk production capacity, and different mastopathic outbreaks..In each stage, dairy cattle were classified by state variables including production capacity in 3 levels (low production, moderate and high production), and health status in 3 levels (non-disease, treatable disease, and disease that eliminated livestock). he results of the model analysis showed that the maintenance of dairy cows up to the sixth stomach and the average cows production until the fourth stomach is economically justified and the maintenance of low production cows is not recommended.

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.

The objective of this study was to estimate the economic value of productive and reproductive traits in Holstein dairy cattle in the North West, based on data collected from eight large herds of three provinces (Ardabil, East Azerbaijan and West Azerbaijan) under sub-optimal and optimal manufacturing system based on market conditions in 2011, was based. In this study, economic values for some production and reproductive traits including milk, milk fat, birth weight, mature cow weight, age at first calving and calving interval, were calculated using a deterministic bio-economic model according and the weighted average revenues and costs of different age groups. Economic value of each trait was estimated as the amount of change in the annual profit of production system resulted by one unit increase in the mean of the trait while the means of other traits were hold constant. Economic values for these traits were 7297.86, 85301.68, -126286.29, -11785.38, -80752.14 and -197416.81 Rials, respectively. Production systems for the culling and replacement policies were assumed as optimal herd. Then calculation of the economic value of a trait by one unit increase of mean of the trait of the change of the system was re-optimized. System’s profit in optimal condition before and after the change was calculated from the difference between the obtained economic values. Economic values for some production and reproductive traits including milk, milk fat, birth weight, mature cow weight, age at first calving and calving interval, were 20833.51,147887.78,-53606.09,-5002.665,-34277.73,-6450.21 Rials, respectively. Sub-optimized production systems to estimate the economic value of the biased is therefore better estimate the economic values of the optimized systems.

The objective of this study was to determine the optimal herd life of dairy cows in North West of Iran based on data collected from nine large herds of three provinces (Ardabil, East Azerbaijan and West Azerbaijan) and to assess its affecting factors using data on costs and revenues in 2012 and by stochastic dynamic programming. Variables used to describe the state of cows included lactation number at 10 levels, production ability at 3 levels and reproductive performance at 4 levels. Markov chain was used to incorporate the probability for each level of factors in determining the status of a cow. The objective function was the expected net present value of a cow in a 10-years horizon and the optimization criterion was to maximize this function. Using dynamic programming the optimal combination of the state variables was realized and hence the optimum herd life of the cows was estimated to be 4.99 years. Examination of optimal objective function in different states revealed that increasing the production level and reducing the calving interval resulted in higher expected net present value of cows. The effect of changes in price of heifers, milk and discount rates on optimal herd life was examined and it was found that by increasing heifer price, lowering milk price and increasing the discount rate, the culling rate was decreased and optimal herd life was increased.