# Profitability Optimization of Dairy Farms: The Effect of Pregnancy Rate and Culling Decision

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## Abstract

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## Simple Summary

## Abstract

## 1. Introduction

## 2. Materials and Methods

#### 2.1. The Investigated Dairy Farms and the Method of Data Collection

#### 2.2. Choosing a Statistical Model

#### 2.3. The Distribution of the Calving to First Service Interval (CFSI)

- Johnson su: $f\left(x\right)=\frac{b}{\sqrt{{x}^{2}+1}}\varphi (a+b\mathrm{log}(x+\sqrt{{x}^{2}+1}))$
- genextreme: $f\left(x\right)=\mathrm{exp}(-{(1-cx)}^{1/c}){(1-cx)}^{1/c-1})$
- mielke: $f\left(x\right)=\frac{k{x}^{k-1}}{{(1+{x}^{s})}^{1+k/s}}$
- burr: $f\left(x\right)=cd\frac{{x}^{-c-1}}{{(1+{x}^{-c})}^{d+1}}$
- invgamma: $f\left(x\right)=\frac{{x}^{-a-1}}{\Gamma \left(a\right)}\mathrm{exp}(-\frac{1}{x}).$

#### 2.4. Length of Gestation

#### 2.5. Time between Successive Inseminations

#### 2.6. Effective Fertility

#### 2.7. Model Verification

## 3. Results and Discussion

#### 3.1. Model Parameters

#### 3.2. Profitability

#### 3.3. Milk Yield Trends

#### 3.4. Considering All Simulated Individuals

#### 3.5. Considering Only Pregnant Individuals

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**Plot of the evolution of the CFSI as a function of density and the first five distributions fitted by the AIC value.

**Figure 3.**Normal distribution fitted to real data on gestation length (the markers represent the real data, while the solid lines represent the fitted data series).

**Figure 4.**Real and multi-Gaussian model fitting of time intervals between unsuccessful inseminations.

**Figure 5.**Probability density values calculated for the pregnant herd only and for the whole herd as a function of the number of inseminations (the solid line is the real data, the dashed line is the linear fitted data).

Distribution | AIC Value | Distribution | BIC Value | Distribution | Sum of Squared Differences | |
---|---|---|---|---|---|---|

1 | Johnson su | 301,879.4457 | Johnson su | 301,912.905 | Johnson su | 0.002377 |

2 | genextreme | 302,003.1927 | genextreme | 302,028.2872 | exponnorm | 0.002388 |

3 | mielke | 302,009.5675 | mielke | 302,043.0269 | burr12 | 0.002433 |

4 | burr | 302,010.1332 | burr | 302,043.5925 | invweibull | 0.002488 |

5 | invgamma | 302,040.148 | invgamma | 302,065.2425 | burr | 0.002495 |

Distribution | Weights | Averages | Standard Deviations |
---|---|---|---|

1. | 0.50 | 22.32 | 2.62 |

2. | 0.32 | 41.68 | 9.03 |

3. | 0.14 | 72.75 | 16.07 |

4. | 0.03 | 126.02 | 30.68 |

5. | 0.01 | 208.51 | 94.69 |

1. Farm | 2. Farm | 3. Farm | 4. Farm | 5. Farm | 6. Farm | |
---|---|---|---|---|---|---|

January | 0.290288 | 0.427578 | 0.362306 | 0.320567 | 0.460518 | 0.320567 |

February | 0.297108 | 0.40757 | 0.363591 | 0.326293 | 0.445264 | 0.326293 |

March | 0.271527 | 0.416369 | 0.372992 | 0.315096 | 0.443843 | 0.315096 |

April | 0.309963 | 0.390013 | 0.363683 | 0.308043 | 0.446775 | 0.308043 |

May | 0.272847 | 0.346596 | 0.334951 | 0.293084 | 0.439539 | 0.293084 |

June | 0.23063 | 0.340537 | 0.310934 | 0.253014 | 0.391304 | 0.253014 |

July | 0.173338 | 0.336765 | 0.246849 | 0.224691 | 0.360628 | 0.224691 |

August | 0.187857 | 0.32552 | 0.259133 | 0.225623 | 0.392649 | 0.225623 |

September | 0.22706 | 0.36502 | 0.31304 | 0.248262 | 0.409018 | 0.248262 |

October | 0.299523 | 0.383095 | 0.381153 | 0.28819 | 0.444978 | 0.288103 |

November | 0.320073 | 0.405457 | 0.369177 | 0.299295 | 0.432553 | 0.299295 |

December | 0.302183 | 0.395085 | 0.369365 | 0.294806 | 0.440601 | 0.294806 |

**Table 4.**Milk yield data for all herds as a function of success rate (20–50%) and milk production decline (300 days–400 days).

Day | Successful Insemination Experiment | ||||
---|---|---|---|---|---|

20% | 30% | 40% | 50% | ||

Total amount of milk (kg) | 300 | 7,403,579 | 7,396,329 | 7,383,544 | 7,370,866 |

350 | 7,427,995 | 7,411,954 | 7,393,707 | 7,378,133 | |

400 | 7,432,324 | 7,410,541 | 7,389,948 | 7,376,669 | |

Average length of lactation (days) | 300 | 346.69 | 342.14 | 333.45 | 324.21 |

350 | 370.61 | 359.31 | 343.01 | 329.57 | |

400 | 388.81 | 365.62 | 339.98 | 330.51 | |

Average daily milk yield/cow (kg) | 300 | 21.354 | 21.617 | 22.142 | 22.734 |

350 | 20.042 | 20.627 | 21.555 | 22.387 | |

400 | 19.115 | 20.267 | 21.736 | 22.318 |

**Table 5.**Development of data on herds that have undergone a successful insemination experiment as a function of success rate (20–50%) and milk production decline (300 days–400 days).

Day | Successful Insemination Experiment | ||||
---|---|---|---|---|---|

20% | 30% | 40% | 50% | ||

Number of cows in lactation | 300 | 768 | 888 | 949 | 979 |

350 | 841 | 929 | 971 | 989 | |

400 | 866 | 960 | 987 | 995 | |

Total amount of milk (kg) | 300 | 5,694,504 | 6,568,803 | 7,007,842 | 7,216,165 |

350 | 6,259,145 | 6,891,374 | 7,180,072 | 7,294,644 | |

400 | 6,443,755 | 7,113,913 | 7,291,722 | 7,337,053 | |

Average length of lactation (days) | 300 | 360.80 | 347.47 | 335.24 | 324.73 |

350 | 383.93 | 363.82 | 344.29 | 329.91 | |

400 | 401.40 | 367.32 | 339.49 | 329.65 | |

Average daily milk yield | 300 | 20.550 | 21.296 | 22.026 | 22.698 |

350 | 19.377 | 20.381 | 21.477 | 22.364 | |

400 | 18.536 | 20.173 | 21.7611 | 22.368 | |

Average calving intervals (days) | 300 | 426.24 | 412.84 | 400.55 | 389.90 |

350 | 439.78 | 425.16 | 407.62 | 394.21 | |

400 | 452.10 | 429.07 | 404.07 | 395.03 | |

Milk yield calculated for the days between two calving | 300 | 17.395 | 17.924 | 18.435 | 18.904 |

350 | 16.916 | 17.441 | 18.140 | 18.716 | |

400 | 16.458 | 17.270 | 18.283 | 18.666 |

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**MDPI and ACS Style**

Tóth, V.; Heinc, E.; Mikó, E.; Csendes, T.; Bánhelyi, B.
Profitability Optimization of Dairy Farms: The Effect of Pregnancy Rate and Culling Decision. *Animals* **2024**, *14*, 18.
https://doi.org/10.3390/ani14010018

**AMA Style**

Tóth V, Heinc E, Mikó E, Csendes T, Bánhelyi B.
Profitability Optimization of Dairy Farms: The Effect of Pregnancy Rate and Culling Decision. *Animals*. 2024; 14(1):18.
https://doi.org/10.3390/ani14010018

**Chicago/Turabian Style**

Tóth, Violetta, Emília Heinc, Edit Mikó, Tibor Csendes, and Balázs Bánhelyi.
2024. "Profitability Optimization of Dairy Farms: The Effect of Pregnancy Rate and Culling Decision" *Animals* 14, no. 1: 18.
https://doi.org/10.3390/ani14010018