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 methods in herd management
Where is a problem?? Age, body weight, season Late breeding Early breeding ? 3 Advanced quantitative methods in herd management
The goal of work The objective of this study was to develop a multi-level hierarchic Markov model to determine the economically optimal management strategy for the replacement beef heifers. Advanced quantitative methods in herd management
Material and methods – data 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). Advanced quantitative methods in herd management
Material and methods – data from the herd 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. Advanced quantitative methods in herd management
Empirical data 5000 5000 4000 4000 3000 3000 Number of heifers Number of heifers 2000 2000 1000 1000 0 0 10 15 20 25 30 35 40 200 300 400 500 600 700 800 Age (months) Body weight (kg) 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 Advanced quantitative methods in herd management
Empirical data Heifers born between 1991 and 2008 Cows and heifers in 2010 70 70 60 60 50 50 40 40 Percentage Percentage 30 30 20 20 10 10 0 0 Season 1 Season 2 Season 3 Season 4 Season 1 Season 2 Season 3 Season 4 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 Advanced quantitative methods in herd management
Stages and states in the model Stage I Stage II Stage III State II Stage IV State I State III Age, body weight, season State IV Advanced quantitative methods in herd management
Heifer management as a sequential problem Advanced quantitative methods in herd management
Model structure 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. Advanced quantitative methods in herd management
Model structure 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. Advanced quantitative methods in herd management
Model structure The objective function was set to maximise the average net returns per heifer inserted. Advanced quantitative methods in herd management
Model structure 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. Advanced quantitative methods in herd management
Model structure The costs in heifer rearing included: the cost of replacement, feeding costs, breeding and veterinary treatment costs, direct labor costs. Advanced quantitative methods in herd management
MLHMP Platform Advanced quantitative methods in herd management
MLHMP Platform in JAVA Advanced quantitative methods in herd management
Sensitivity analyses 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, Advanced quantitative methods in herd management
Sensitivity analyses • 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 Advanced quantitative methods in herd management
Short break !!! After the break we will be downloading model and working with it Advanced quantitative methods in herd management
Downloading beef heifer model Model can be dowloaded from: http://www.prodstyr.ihh.kvl.dk/software/mlhmp.html Advanced quantitative methods in herd management
Downloading beef heifer model Advanced quantitative methods in herd management
Installing and removing plug-in Advanced quantitative methods in herd management
How it could look on your computer Advanced quantitative methods in herd management
How it could look on your computer Advanced quantitative methods in herd management
How it could look on your computer Advanced quantitative methods in herd management, 07-10-2015
Tasks after installing : • 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 Advanced quantitative methods in herd management, 07-10-2015
Time to look on results!! Advanced quantitative methods in herd management
Results: Results Month of birth I II III IV V VI VII VIII IX X XI XII Average - Optimal month and age X XI XII I II III X V VI VII VIII IX (9) (9) (9) (9) (9) (9) (3) (9) (9) (9) (9) (9) (mo) at weaning (9) Optimal age at 13,2 14,4 13,0 12,9 12,8 12,8 13,4 11,0 18,2 15,6 15,2 16,7 14,5 conception (mo) Optimal body weight at 343 361,7 343 359 356 353 352 368 360 395 357 352 373 conception (kg) ADG from birth to 810 700 820 810 810 810 820 970 650 680 690 660 700 conception (g) Average net return per 1182 1296 1226 1284 1324 1368 1411 1323 1229 1114 1130 1129 1119 heifer (PLN) Average net return per 311 294 308 318 328 339 318 295 267 271 271 269 284 heifer (EUR ) Advanced quantitative methods in herd management
Results 70 60 50 40 Percentage 30 20 10 0 Season 1 Season 2 Season 3 Season 4 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 Advanced quantitative methods in herd management
Sensitivity analyses Breeding weight ≥ ADG 65% of average Baseline decreased AI scenario NS scenario mature body by 200 g/d weight Average age at conception 15,7 16,5 13,2 13,5 13,5 (mo) Average body weight at 361,7 352,0 446,6 367,5 347,6 conception (kg) ADG during rearing period (g) 810 730 820 810 760 Average net return / heifer 1216 1065 1 249 1 325 1296 (PLN) Average net return / heifer 311 292 256 300 318 (EUR) Average breeding costs (PLN) 183,5 183,6 181,5 208,5 178,7 Average breeding costs / heifer 44,1 44,1 43,6 50,1 43,0 (EUR) 2510,9 Average rearing costs (PLN) 2264,4 2373,8 2 383,5 2 350 Average rearing costs / heifer 544,3 570,6 603,6 573,0 564,9 (EUR) Advanced quantitative methods in herd management
Sensitivity analyses The feed costs The slaughter prices Baseline +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) 810 800 830 830 800 688 1916 2513 95 1296 Average net return / heifer (PLN) 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 44,1 46,5 42,5 42,6 46,4 Average breeding costs / heifer (EUR) 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 Advanced quantitative methods in herd management
Sensitivity analyses 1450 Strategies Non-optimal - weaning at the beginning of November 1411.55 PLN Optimal - weaning after 9 months of suckling (339.3 EUR) 1383.18 PLN 1400 Average net return in PLN (EUR)/ heifer (332.5 EUR) 1368.17 PLN (328.9 EUR) 1346.28 PLN (323.6 EUR) 1350 1324.87 PLN (318.5 EUR) 1311.85 PLN (315.3 EUR) 1300 1250 March April May 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) Advanced quantitative methods in herd management
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