Markov decision process: Case example Optimal management of - - PowerPoint PPT Presentation

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Mar 03, 2023 44 likes •415 views

Markov decision process: Case example Optimal management of replacement heifers in beef herd Anna Helena Stygar Department of Department of Veterinary and Animal Sciences University of Copenhagen Polish beef industry Advanced quantitative

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Markov decision process: Case example Optimal management of replacement heifers in beef herd

Anna Helena Stygar Department of Department of Veterinary and Animal Sciences University of Copenhagen

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Polish beef industry

Advanced quantitative methods in herd management

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Where is a problem??

Advanced quantitative methods in herd management

3

?

Early breeding Late breeding Age, body weight, season

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The goal of work

The objective of this study was to develop a multi-level hierarchic Markov model to determine the economically

  • ptimal management strategy for the replacement beef

heifers.

Advanced quantitative methods in herd management

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Material and methods – data

Advanced quantitative methods in herd management

The mean and limit values were estimated on the basis of the empirical data representing the Limousin cattle population in Poland (33 521 Limousin heifers born between 1991 and 2008) and on the literature review. The main data set, used for the estimation of model parameters, was obtained from the Polish Association of Beef Cattle Breeders and Producers (PABCBP).

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Material and methods – data from the herd

Advanced quantitative methods in herd management

The following data were collected: heifer identification number, date of birth, birth weight, standardized on 210th day body weight, body weight at first calving, date of first and subsequent calvings, calves' sex, birth weight and standardized on 210th day body weight of the first and subsequent calves.

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Empirical data

Advanced quantitative methods in herd management

Age (months) Number of heifers 10 15 20 25 30 35 40 1000 2000 3000 4000 5000 Body weight (kg) Number of heifers 200 300 400 500 600 700 800 1000 2000 3000 4000 5000

  • Fig. 1. The distribution of the age and body weight at conception of the Limousin heifers

born in Poland between 1991 and 2008, based on data from PABCBP

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Empirical data

Advanced quantitative methods in herd management

Season 1 Season 2 Season 3 Season 4 Percentage 10 20 30 40 50 60 70

Heifers born between 1991 and 2008

Season 1 Season 2 Season 3 Season 4 Percentage 10 20 30 40 50 60 70

Cows and heifers in 2010

Season 1: February, March, April; Season 2: May, June, July; Season 3: August, September, October; Season 4: November, December, January.

  • Fig. 2. The distribution of the conception seasons of Limousin females in Poland, based on data from PABCBAP
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Advanced quantitative methods in herd management

Stages and states in the model

Stage I State I Stage II State II Stage III State III Stage IV State IV

Age, body weight, season

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Heifer management as a sequential problem

Advanced quantitative methods in herd management

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Model structure

Advanced quantitative methods in herd management

The optimized decisions concerned:

  • feeding level during the pre-puberty period,
  • time of weaning,
  • feeding level during the reproductive period and
  • age, body weight and season at conception.
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Model structure

Advanced quantitative methods in herd management

The uncertainty in the model was represented by

  • the involuntary disposal probability,
  • the probability of attaining body weight gain,
  • the probability of onset of puberty and
  • the probability of conception.
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Model structure

Advanced quantitative methods in herd management

The objective function was set to maximise the average net returns per heifer inserted.

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Model structure

Advanced quantitative methods in herd management

Revenues were derived either from the predicted future profitability of a replacement (pregnant) heifer or from the value of culled heifer sold on a live weight basis.

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Model structure

Advanced quantitative methods in herd management

The costs in heifer rearing included: the cost of replacement, feeding costs, breeding and veterinary treatment costs, direct labor costs.

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MLHMP Platform

Advanced quantitative methods in herd management

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MLHMP Platform in JAVA

Advanced quantitative methods in herd management

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Sensitivity analyses

Advanced quantitative methods in herd management

The value of objective function and the values of decision variables (e.g. age at weaning and breeding, body weight at breeding) were observed for different:

  • weaning strategies,
  • varied breeding costs,
  • probability of conception,
  • feed costs,
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Sensitivity analyses

Advanced quantitative methods in herd management

  • slaughter prices,
  • varied rearing conditions:
  • decrease in ADG during the pre-puberty period
  • traditional target breeding weight - breeding decision only

for heifers that exhibit estrus and reached 65% of mature body weight,

  • the alternative use of breeding methods (AI, NS) throughout

a year

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Short break !!!

Advanced quantitative methods in herd management

After the break we will be downloading model and working with it

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Downloading beef heifer model

Advanced quantitative methods in herd management

Model can be dowloaded from: http://www.prodstyr.ihh.kvl.dk/software/mlhmp.html

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Downloading beef heifer model

Advanced quantitative methods in herd management

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Installing and removing plug-in

Advanced quantitative methods in herd management

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How it could look on your computer

Advanced quantitative methods in herd management

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How it could look on your computer

Advanced quantitative methods in herd management

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How it could look on your computer

Advanced quantitative methods in herd management, 07-10-2015

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Tasks after installing :

Advanced quantitative methods in herd management, 07-10-2015

  • Calculate optimal policy
  • Find average net return per heifer
  • Check the result table
  • Calculate sub-optimal strategy
  • Breeding possible only for heifers with BW > 330kg
  • Simulation
  • Calculate average BW at conception
  • Calculate average age at conception
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Time to look on results!!

Advanced quantitative methods in herd management

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Results

Advanced quantitative methods in herd management

Month of birth I II III IV V VI VII VIII IX X XI XII

Average

Optimal month and age (mo) at weaning X (9) XI (9) XII (9) I (9) II (9) III (9) X (3) V (9) VI (9) VII (9) VIII (9) IX (9)

  • (9)

Optimal age at conception (mo) 14,4 13,0 12,9 12,8 12,8 13,4 11,0 18,2 15,6 15,2 16,7 14,5

13,2

Optimal body weight at conception (kg) 343 359 356 353 352 368 360 395 357 352 373 343 361,7 ADG from birth to conception (g) 700 820 810 810 810 820 970 650 680 690 660 700

810

Average net return per heifer (PLN) 1226 1284 1324 1368 1411 1323 1229 1114 1130 1129 1119 1182 1296 Average net return per heifer (EUR) 294 308 318 328 339 318 295 267 271 271 269 284

311 Results:

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Results

Advanced quantitative methods in herd management

Season 1 Season 2 Season 3 Season 4 Percentage 10 20 30 40 50 60 70 Season 1: February, March, April; Season 2: May, June, July; Season 3: August, September, October; Season 4: November, December, January.

  • Fig. 5. The distribution of heifer breeding seasons under the optimal rearing strategy
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Sensitivity analyses

Advanced quantitative methods in herd management

Baseline ADG decreased by 200 g/d Breeding weight ≥ 65% of average mature body weight AI scenario NS scenario Average age at conception (mo) 13,2

15,7 16,5

13,5 13,5 Average body weight at conception (kg) 361,7 352,0 446,6 367,5 347,6 ADG during rearing period (g) 810 730 820 810 760 Average net return / heifer (PLN) 1296

1216 1065 1 249 1 325

Average net return / heifer (EUR) 311 292 256 300 318 Average breeding costs (PLN) 183,5 183,6 181,5 208,5 178,7 Average breeding costs / heifer (EUR) 44,1 44,1 43,6 50,1 43,0 Average rearing costs (PLN) 2264,4 2373,8

2510,9

2 383,5 2 350 Average rearing costs / heifer (EUR) 544,3 570,6 603,6 573,0 564,9

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Sensitivity analyses

Advanced quantitative methods in herd management

Baseline The feed costs The slaughter prices +20%

  • 20%

+20%

  • 20%

Average age at conception (mo) 13,2 13,0 13,2 13,2 13,0 Average body weight at conception (kg) 361,7 352,6 367,9 368,1 350,9 ADG during rearing period (g) 810 800 830 830 800 Average net return / heifer (PLN) 1296

688 1916 2513 95

Average net return / heifer (EUR) 311,6 165,6 460,8 604,3 22,9 Average breeding costs (PLN) 183,5 193,6 177,0 177,2 193,2 Average breeding costs / heifer (EUR) 44,1 46,5 42,5 42,6 46,4 Average rearing costs(PLN) 2264,4 2575,3 1857,5 2190,7 2233,0 Average rearing costs / heifer (EUR) 544,3 619,1 446,5 526,6 536,8

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Sensitivity analyses

Advanced quantitative methods in herd management

1324.87 PLN (318.5 EUR) 1311.85 PLN (315.3 EUR) 1368.17 PLN (328.9 EUR) 1346.28 PLN (323.6 EUR) 1411.55 PLN (339.3 EUR) 1383.18 PLN (332.5 EUR)

1250 1300 1350 1400 1450 March April May

Average net return in PLN (EUR)/ heifer

Strategies Non-optimal - weaning at the beginning of November Optimal - weaning after 9 months of suckling

Comparison of average net return per heifer under the optimal (weaning after 9 months of suckling) and non optimal strategy (weaning at the beginning of November)

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Conclusions

Advanced quantitative methods in herd management

The economic efficiency of beef cattle operations can be considerably improved by breeding heifers as yearlings, however the optimal age at breeding depends on feeding intensity which determines reaching optimal body weight and sufficient body development. Breeding heifers at the body weight lower then 65% body weight of mature cow can be economically beneficial.

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Conclusions

Advanced quantitative methods in herd management

Commonly practised weaning at the end of pasture season is economically justified as indicated by only slightly better economic results for optimal rearing period (lasting 9 months) compared to weaning at the end of pasture season. The net return per heifer is primarily subject to changes in slaughter prices and feed costs.

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Conclusions

Advanced quantitative methods in herd management

The replacement beef heifer model is an effective tool that can be used to support farmers’ decisions by determining the economically optimal management strategy for the replacement heifers. By changing the key variables and parameters as well as the production conditions the model allows an insight into the critical components of heifer rearing.

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Any questions ??

Advanced quantitative methods in herd management