Mathematical Methods Applied to the Problem of Dairy Cow Replacements: A Scoping Review
Simple Summary
Abstract
1. Introduction
2. Materials and Methods
2.1. Research Questions
2.2. Identify Relevant Studies
2.3. Selection Criteria
3. Results and Discussion
3.1. Identify Relevant Studies and Selection Criteria
3.2. Chart the Data
3.3. Results Related to Specific Research Questions
3.4. Gaps in the Literature and Future Outlook
4. Conclusions
Author Contributions
Funding
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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Publication Number in Paper New | Title | Reference |
---|---|---|
1 | Preliminary model to investigate culling and replacement policy in dairy herds | [20] |
2 | Replacement policy in dairy herds on farms where heifers compete with cows for grassland. 2. Experimentation | [21] |
3 | Operational replacement decision model for dairy herds | [14] |
4 | Beef production from a dairy farm a linear programming simulation approach | [22] |
5 | Optimal replacement policy for multicomponent systems: An application to a dairy herd | [23] |
6 | An economic comparison of 4 insemination and culling policies in dairy herds, by method of stochastic simulation | [24] |
7 | Recursive stochastic programming applied to dairy cow replacement | [15] |
8 | Ranking of dairy cows for replacement | [25] |
9 | Optimizing model-insemination, replacement, seasonal production, and cash flow | [13] |
10 | Optimal replacement in the dairy herd a multi component system | [26] |
11 | Dynamic probabilistic simulation of dairy herd management practices. i. model description and outcome of different seasonal calving patterns | [27] |
12 | Dynamic probabilistic simulation of dairy herd management practices. ii. comparison of strategies in order to change a herds calving pattern | [28] |
13 | A survey of markov decision programming techniques applied to the animal replacement problem | [29] |
14 | Optimizing the herd calving pattern with linear programming and dynamic probabilistic simulation | [30] |
15 | Technical and economic effects of culling and reproduction strategies in dairy cattle herds estimated by stochastic simulation | [31] |
16 | Technical and economic effects of feeding one vs. multiple total mixed rations estimated by stochastic simulation under different dairy herd and management characteristics | [32] |
17 | Evaluation of a stochastic dynamic replacement and insemination model for dairy cattle | [33] |
18 | Modeling the relationship between reproductive performance and net-revenue in dairy herds | [34] |
19 | A linear programming formulation of the Markovian decision process approach to modelling the dairy replacement problem | [35] |
20 | A stochastic model simulating the feeding-health-production complex in a dairy herd | [36] |
21 | Optimizing replacement decisions for Finnish dairy herds | [37] |
22 | Optimizing breeding decisions for Finnish dairy herds | [38] |
23 | Interactions between optimal replacement policies and feeding strategies in dairy herds | [39] |
24 | Comparison of economically optimized culling recommendations and actual culling decisions of Finnish Ayrshire cows | [40] |
25 | Economics of delayed replacement when cow performance is seasonal | [11] |
26 | The cost of generic clinical mastitis in dairy cows as estimated by using dynamic programming | [41] |
27 | Optimal replacement policy and economic value of dairy cows with diverse health status and production capacity | [7] |
28 | Determining the optimum replacement policy for Holstein dairy herds in Iran | [2] |
29 | A large Markovian linear program to optimize replacement policies and dairy herd net income for diets and nitrogen excretion | [6] |
30 | A multi-level hierarchic Markov process with Bayesian updating for herd optimization and simulation in dairy cattle | [1] |
31 | Optimal culling strategy in relation to biological and economic efficiency and annualized net revenue in the Japanese Black cow calf production system | [42] |
32 | The effect of reproductive performance on the dairy cattle herd value assessed by integrating a daily dynamic programming model with a daily Markov chain model | [43] |
33 | A simple formulation and solution to the replacement problem: A practical tool to assess the economic cow value, the value of a new pregnancy, and the cost of a pregnancy loss | [44] |
34 | Effects of sex control and twinning on economic optimization of culling cows in Japanese Black cow calf production systems | [45] |
35 | Short communication: Prediction of retention pay-off using a machine learning algorithm | [46] |
36 | Stochastic economic evaluation of dairy farm reproductive performance | [47] |
37 | A robust statistical model to predict the future value of the milk production of dairy cows using herd recording data | [4] |
38 | Using decision trees to extract patterns for dairy culling management | [48] |
39 | Enhancing culling decisions in swiss dairy farms: introducing a tool for improved replacement choices | [5] |
40 | Economic impacts of constrained replacement heifer supply in dairy herds | [3] |
Application | Methodology | |||||||
---|---|---|---|---|---|---|---|---|
Optimization | Simulation | Other | ||||||
Paper Number | Herd | Individual | Markov Chains | Markov Decision Process | Linear Programming | Deterministic | Stochastic | |
1 | X | X | X | |||||
2 | X | X | ||||||
3 | X | X | ||||||
4 | X | X | ||||||
5 | X | X | X | |||||
6 | X | X | ||||||
7 | X | Recursive Stochastic Programming | ||||||
8 | X | X | X | |||||
9 | X | X | ||||||
10 | X | X | X | |||||
11 | X | X | ||||||
12 | X | X | X | |||||
13 | X | X | X | |||||
14 | X | X | X | |||||
15 | X | X | X | |||||
16 | X | X | ||||||
17 | X | X | ||||||
18 | X | X | X | |||||
19 | X | X | X | |||||
20 | X | X | ||||||
21 | X | X | ||||||
22 | X | X | ||||||
23 | X | X | ||||||
24 | X | X | ||||||
25 | X | X | X | |||||
26 | X | X | X | |||||
27 | X | X | Logistic regression | |||||
28 | X | X | ||||||
29 | X | X | ||||||
30 | X | Multilevel Markov hierarchical process | ||||||
31 | X | X | ||||||
32 | X | X | X | |||||
33 | X | X | X | |||||
34 | X | X | ||||||
35 | X | X | ML decision trees | |||||
36 | X | X | ||||||
37 | X | Exponential smoothing, linear regression, and logistic function | ||||||
38 | X | Decision trees | ||||||
39 | X | X | ||||||
40 | X | X | X |
Response Variables | Economic Indicator | Main Production Type | Type of Extensive Production | ||||||||
---|---|---|---|---|---|---|---|---|---|---|---|
Number Publication in Paper | Milk Production | Diseases | Other | Benefit | Income | Cost | Other | Beef | Milk | Grazing | Barn |
1 | X | Genetic improvement in performance per cow. | X | X | X | ||||||
2 | X | X | X | X | |||||||
3 | Present net value (NPV) | X | |||||||||
4 | Beef production. Replacement rate. Breed. | X | X | ||||||||
5 | Expected value of keeping a cow in the herd | X | |||||||||
6 | X | Interval between calvings, the rate of discarding, and the rate of detection of estrus and conception. | X | X | |||||||
7 | X | X | X | ||||||||
8 | X | X | |||||||||
9 | X | X | X | ||||||||
10 | X | ||||||||||
11 | X | X | |||||||||
12 | X | X | X | ||||||||
13 | Optimal replacement policies, and herd statistics. | Present net value (NPV) | X | ||||||||
14 | X | X | X | ||||||||
15 | X | X | X | ||||||||
16 | X | X | |||||||||
17 | X | X | X | ||||||||
18 | X | X | |||||||||
19 | X | X | X | ||||||||
20 | X | Food intake, food utilization, conception, slaughter, involuntary elimination, and death. | X | X | |||||||
21 | X | X | X | ||||||||
22 | X | The replacement rate, the structure of the herd. | X | X | |||||||
23 | X | Average herd lifespan, calving interval, replacement rate, feed intake, and body weight change. | X | X | X | ||||||
24 | X | Risk of discarding, open days (pregnancy), lactation stage (days in milk), and month of delivery. | X | X | |||||||
25 | X | X | |||||||||
26 | mastitis | X | X | X | |||||||
27 | X | X | |||||||||
28 | X | Retention value (RPO). | X | X | |||||||
29 | X | Herd structure, replacement policy, dry matter intake (DMI), and nitrogen excretion (N). | X | X | |||||||
30 | X | Productive herd life. Interval between calvings. Annual discard rate. Proportion of voluntary discards. Feed intake capacity. Energy requirement. Forage and concentrate intake. Monthly Revenue and Costs. Monthly and lifetime net income. | X | X | X | ||||||
31 | Biological efficiency (BE), the live weight of discarded cows and their calves, metabolizable energy consumption (ME), and economic costs and revenues. | Economic efficiency (EE) and annualized net income (AN). | X | ||||||||
32 | Retention value (RPO) | X | X | ||||||||
33 | X | The value of a new pregnancy, the cost of a pregnancy loss, the pregnancy rate, the discard rate, and the structure of the herd. | Present net value (NPV) | X | |||||||
34 | X | X | X | ||||||||
35 | Retention value (RPO) | X | X | ||||||||
36 | X | Feed costs, calf sales revenues, discard costs, reproductive costs, herd structure (parity, days in milk, days open), and pregnancy and discard rates. | X | X | |||||||
37 | X | Somatic cell count, survival, and correlation structures between these herd-level measures. | X | ||||||||
38 | X | X | X | ||||||||
39 | X | Expected lifespan of the cow. Average monthly income per cow. Average monthly costs per cow. State transitions (lactation, month in milk, month of pregnancy). Lactation curves (milk production, protein and fat content). | X | Cow value | X | X | |||||
40 | X | X |
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Palma, O.; Plà-Aragonés, L.M.; Mac Cawley, A.; Albornoz, V.M. Mathematical Methods Applied to the Problem of Dairy Cow Replacements: A Scoping Review. Animals 2025, 15, 970. https://doi.org/10.3390/ani15070970
Palma O, Plà-Aragonés LM, Mac Cawley A, Albornoz VM. Mathematical Methods Applied to the Problem of Dairy Cow Replacements: A Scoping Review. Animals. 2025; 15(7):970. https://doi.org/10.3390/ani15070970
Chicago/Turabian StylePalma, Osvaldo, Lluis M. Plà-Aragonés, Alejandro Mac Cawley, and Víctor M. Albornoz. 2025. "Mathematical Methods Applied to the Problem of Dairy Cow Replacements: A Scoping Review" Animals 15, no. 7: 970. https://doi.org/10.3390/ani15070970
APA StylePalma, O., Plà-Aragonés, L. M., Mac Cawley, A., & Albornoz, V. M. (2025). Mathematical Methods Applied to the Problem of Dairy Cow Replacements: A Scoping Review. Animals, 15(7), 970. https://doi.org/10.3390/ani15070970