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Markov Decision Processes to Model Livestock Systems

  • Lars Relund NielsenEmail author
  • Anders Ringgaard Kristensen
Part of the International Series in Operations Research & Management Science book series (ISOR, volume 224)

Abstract

Livestock farming problems are often sequential in nature. For instance at a specific time instance the decision on whether to replace an animal or not is based on known information and expectation about the future. At the next decision epoch updated information is available and the decision choice is re-evaluated. As a result Markov decision processes (MDPs) have been used to model livestock decision problems over the last decades. The objective of this chapter is to review the increasing amount of papers using MDPs to model livestock farming systems and provide an overview over the recent advances within this branch of research. Moreover, theory and algorithms for solving both ordinary and hierarchical MDPs are given and possible software for solving MDPs are considered.

Keywords

Optimal Policy Milk Yield Markov Decision Process Policy Iteration Average Reward 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Notes

Acknowledgements

The authors are grateful to Dr. Anna-Maija Heikkilä, MTT Economic Research, for her valuable information about several of the Finnish models referenced.

This chapter has been compiled with support from The Danish Council for Strategic Research (The PigIT project, Grant number 11-116191).

References

  1. Allore H, Schruben L, Erb H, Oltenacu P (1998) Design and validation of a dynamic discrete event stochastic simulation model of mastitis control in dairy herds. J Dairy Sci 81(3):703–717. DOI 10.3168/jds.S0022-0302(98) 75626-7CrossRefGoogle Scholar
  2. van Arendonk J (1985a) A model to estimate the performance, revenues and costs of dairy cows under different production and price situations. Agr Syst 16(3):157–189. DOI 10.1016/0308-521X(85)90010-1CrossRefGoogle Scholar
  3. van Arendonk J (1985b) Studies on the replacement policies in dairy cattle. ii. optimum policy and influence of changes in production and prices. Livest Prod Sci 13(2):101–121. DOI 10.1016/0301-6226(85)90014-4CrossRefGoogle Scholar
  4. van Arendonk J (1986) Studies on the replacement policies in dairy cattle. iv. influence of seasonal variation in performance and prices. Livest Prod Sci 14(1):15–28. DOI 10.1016/0301-6226(86)90093-XCrossRefGoogle Scholar
  5. van Arendonk J (1988) Management guides for insemination and replacement decisions. J Dairy Sci 71(4):1050–1057. DOI 10.3168/jds.S0022-0302(88) 79651-4CrossRefGoogle Scholar
  6. van Arendonk J, Dijkhuizen A (1985) Studies on the replacement policies in dairy cattle. iii. influence of variation in reproduction and production. Livest Prod Sci 13(4):333–349. DOI 10.1016/0301-6226(85)90025-9CrossRefGoogle Scholar
  7. van Asseldonk M, Huirne R, Dijkhuizen AA, Beulens A (1999) Dynamic programming to determine optimum investments in information technology on dairy farms. Agr Syst 62(1):17–28. DOI 10.1016/S0308-521X(99) 00051-7CrossRefGoogle Scholar
  8. Bar D, Tauer L, Bennett G, Gonzalez R, Hertl J, Schukken Y, Schulte H, Welcome F, Groehn Y (2008a) The cost of generic clinical mastitis in dairy cows as estimated by using dynamic programming. J Dairy Sci 91(6):2205–2214. DOI 10.3168/jds.2007-0573CrossRefGoogle Scholar
  9. Bar D, Tauer L, Bennett G, Gonzalez R, Hertl J, Schulte H, Schukken Y, Welcome F, Grohn Y (2008b) Use of a dynamic programming model to estimate the value of clinical mastitis treatment and prevention options utilized by dairy producers. Agr Syst 99(1):6–12. DOI 10.1016/j.agsy.2008. 09.001CrossRefGoogle Scholar
  10. Bellman R (1957) Dynamic programming. Princeton University Press, PrincetonGoogle Scholar
  11. Ben-Ari Y, Gal S (1986) Optimal replacement policy for multicomponent systems—an application to a dairy-herd. Eur J Oper Res 23(2):213–221. DOI 10.1016/0377-2217(86)90240-7CrossRefGoogle Scholar
  12. Ben-Ari Y, Amir I, Sharar S (1983) Operational replacement decision model for dairy herds. J Dairy Sci 66:1747–1759. DOI 10.3168/jds. S0022-0302(83)82002-5CrossRefGoogle Scholar
  13. Boichard D (1990) Estimation of the economic value of conception rate in dairy cattle. Livest Prod Sci 24(3):187–204. DOI 10.1016/0301-6226(90) 90001-MCrossRefGoogle Scholar
  14. Bono C, Cornou C, Kristensen A (2012) Dynamic production monitoring in pig herds I: modeling and monitoring litter size at herd and sow level. Livest Sci 149(3):289–300. DOI 10.1016/j.livsci.2012.07.023CrossRefGoogle Scholar
  15. Cabrera V (2010) A large markovian linear program to optimize replacement policies and dairy herd net income for diets and nitrogen excretion. J Dairy Sci 93(1):394–406. DOI 10.3168/jds.2009-2352CrossRefGoogle Scholar
  16. Cabrera V (2012) 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. J Dairy Sci 95(8):4683–4698. DOI 10.3168/jds.2011-5214CrossRefGoogle Scholar
  17. Cardoso V, Nogueira J, van Arendonk J (1999a) Optimum replacement and insemination policies for crossbred cattle (holstein friesian x zebu) in the south-east region of brazil. Livest Prod Sci 58(2):95–105. DOI 10.1016/ S0301-6226(98)00205-XCrossRefGoogle Scholar
  18. Cardoso V, Nogueira J, Van Arendonk J (1999b) Optimal replacement and insemination policies for holstein cattle in the southeastern region of brazil: the effect of selling animals for production. J Dairy Sci 82(7):1449–1458. DOI 10.3168/jds.S0022-0302(99)75372-5CrossRefGoogle Scholar
  19. Cha E, Hertl J, Bar D, Groehn Y (2010) The cost of different types of lameness in dairy cows calculated by dynamic programming. Prev Vet Med 97(1):1–8. DOI 10.1016/j.prevetmed.2010.07.011CrossRefGoogle Scholar
  20. Cha E, Bar D, Hertl J, Tauer L, Bennett G, Gonzalez R, Schukken Y, Welcome F, Groehn Y (2011) The cost and management of different types of clinical mastitis in dairy cows estimated by dynamic programming. J Dairy Sci 94(9):4476–4487. DOI 10.3168/jds.2010-4123CrossRefGoogle Scholar
  21. Dekkers J (1991) Estimation of economic values for dairy cattle breeding goals: bias due to sub-optimal management policies. Livest Prod Sci 29(2–3):131–149. DOI 10.1016/0301-6226(91)90062-UCrossRefGoogle Scholar
  22. Dekkers JCM, Ten Hag JH, Weersink A (1998) Economic aspects of persistency of lactation in dairy cattle. Livest Prod Sci 53(3):237–252. DOI 10.1016/S0301-6226(97)00124-3CrossRefGoogle Scholar
  23. Delorenzo M, Spreen T, Bryan G, Beede D, van Arendonk J (1992) Optimizing model: insemination, replacement, seasonal production, and cash flow. J Dairy Sci 75(3):885–896. DOI 10.3168/jds.S0022-0302(92) 77829-1CrossRefGoogle Scholar
  24. Demeter R, Kristensen A, Dijkstra J, Lansink AO, Meuwissen M, van Arendonk J (2011) A multi-level hierarchic markov process with bayesian updating for herd optimization and simulation in dairy cattle. J Dairy Sci 94(12):5938–5962. DOI 10.3168/jds.2011-4258CrossRefGoogle Scholar
  25. Fisher W, Schruben L (1953) Linear programming applied to feed-mixing under different price conditions. J Farm Econ 35(4):471–483. URL http://www.jstor.org/stable/1233362
  26. Ge L, Kristensen A, Mourits M, Huirne R (2010a) A new decision support framework for managing foot-and-mouth disease epidemics. Ann Oper Res. DOI 10.1007/s10479-010-0774-2Google Scholar
  27. Ge L, Mourits M, Kristensen A, Huirne R (2010b) A modelling approach to support dynamic decision-making in the control of fmd epidemics. Prev Vet Med 95(3–4):167–174. DOI 10.1016/j.prevetmed.2010.04.003CrossRefGoogle Scholar
  28. Giaever H (1966) Optimal dairy cow replacement policies. Ph.D. thesis, University of California, Berkeley, University Microfilms, Ann ArborGoogle Scholar
  29. Giordano J, Kalantari A, Fricke P, Wiltbank M, Cabrera V (2012) A daily herd markov-chain model to study the reproductive and economic impact of reproductive programs combining timed artificial insemination and estrus detection. J Dairy Sci 95(9):5442–5460. DOI 10.3168/jds.2011-4972CrossRefGoogle Scholar
  30. Glenn J (1983) A dynamic programming model for pig production. J Oper Res Soc 34:511–519. DOI 10.1057/jors.1983.118CrossRefGoogle Scholar
  31. Grohn Y, Rajala-Schultz P, Allore H, DeLorenzo M, Hertl J, Galligan D (2003) Optimizing replacement of dairy cows: modeling the effects of diseases. Prev Vet Med 61(1):27–43. DOI 10.1016/S0167-5877(03)00158-2CrossRefGoogle Scholar
  32. Haran P (1997) Markov decision processes in the optimisation of culling decisions for irish dairy herds. Master’s thesis, School of Computer Applications, Dublin City UniversityGoogle Scholar
  33. Harris B (1990) Recursive stochastic programming applied to dairy cow replacement. Agr Syst 34(1):53–64. DOI 10.1016/0308-521X(90)90093-6CrossRefGoogle Scholar
  34. Heikkila A, Nousiainen J, Jauhiainen L (2008) Optimal replacement policy and economic value of dairy cows with diverse health status and production capacity. J Dairy Sci 91(6):2342–2352. DOI 10.3168/jds.2007-0736CrossRefGoogle Scholar
  35. Heikkila A, Nousiainen J, Pyorala S (2012) Costs of clinical mastitis with special reference to premature culling. J Dairy Sci 95(1):139–150. DOI 10. 3168/jds.2011-4321Google Scholar
  36. Houben E, Huirne R, Dijkhuizen A, Kristensen A (1994) Optimal replacement of mastitis cows determined by a hierarchic Markov process. J Dairy Sci 77:2975–2993. DOI 10.3168/jds.S0022-0302(94)77239-8CrossRefGoogle Scholar
  37. Huirne R, Hardaker J (1998) A multi-attribute utility model to optimise sow replacement decisions. Eur Rev Agric Econ 25(4):488–505. DOI 10.1093/ erae/25.4.488CrossRefGoogle Scholar
  38. Huirne R, Hendriks T, Dijkhuizen A, Giesen G (1988) The economic optimisation of sow replacement decisions by stochastic dynamic programming. J Agric Econ 39:426–438. DOI 10.1111/j.1477-9552.1988. tb00602.xCrossRefGoogle Scholar
  39. Huirne R, Dijkhuizen A, Renkema JA (1991) Economic optimization of sow replacement decisions on the personal computer by method of stochastic dynamic programming. Livest Prod Sci 28:331–347. DOI 10. 1016/0301-6226(91)90014-HGoogle Scholar
  40. Huirne R, van Beek P, Hendriks T, Dijkhuizen A (1993) An application of stochastic dynamic programming to support sow replacement decisions. Eur J Oper Res 67:161–171. DOI 10.1016/0377-2217(93)90059-VCrossRefGoogle Scholar
  41. Jalvingh A, Dijkhuizen A, van Arendonk J, Brascamp E (1992a) Dynamic probabilistic modelling of reproductive and replacement in sow herds. general aspects and model description. Agr Syst 39:133–152. DOI 10.1016/ 0308-521X(92)90105-WCrossRefGoogle Scholar
  42. Jalvingh A, Dijkhuizen A, van Arendonk J, Brascamp E (1992b) An economic comparison of management strategies on reproduction and replacement in sow herds using a dynamic probabilistic model. Livest Prod Sci. 32:331–350. DOI 10.1016/0301-6226(92)90004-NCrossRefGoogle Scholar
  43. Jalvingh A, van Arendonk J, Dijkhuizen A (1993a) Dynamic probabilistic simulation of dairy-herd management-practices.i. model description and outcome of different seasonal calving patterns. Livest Prod Sci 37(1–2):107–131. DOI 10.1016/0301-6226(93)90067-RCrossRefGoogle Scholar
  44. Jalvingh A, van Arendonk J, Dijkhuizen A, Renkema J (1993b) Dynamic probabilistic simulation of dairy-herd management-practices. ii. comparison of strategies in order to change a herds calving pattern. Livest Prod Sci 37(1–2):133–152. DOI 10.1016/0301-6226(93)90068-SCrossRefGoogle Scholar
  45. Jalvingh A, Dijkhuizen A, van Arendonk J (1994) Optimizing the herd calving pattern with linear-programming and dynamic probabilistic simulation. J Dairy Sci 77(6):1719–1730. DOI 10.3168/jds.S0022-0302(94) 77113-7CrossRefGoogle Scholar
  46. Jørgensen E (1992) Sow replacement: reduction of state space in dynamic programming model and evaluation of benefit from using the model. Dina Research Report 6, National Institute of Animal ScienceGoogle Scholar
  47. Jørgensen E (1993) The influence of weighing precision on delivery decisions in slaughter pig production. Acta Agric Scand 43(3):181–189. DOI 10. 1080/09064709309410163Google Scholar
  48. Kalantari A, Cabrera V (2012) 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. J Dairy Sci 95(10):6160–6170. DOI 10.3168/jds.2012-5587CrossRefGoogle Scholar
  49. Kalantari A, Mehrabani-Yeganeh H, Moradi M, Sanders A, de Vries A (2010) Determining the optimum replacement policy for holstein dairy herds in iran. J Dairy Sci 93(5):2262–2270. DOI 10.3168/jds.2009-2765CrossRefGoogle Scholar
  50. Kennedy J (1986) Dynamic programming. Applications to agriculture and natural resources. Elsevier Applied Science Publishers, London/New YorkGoogle Scholar
  51. Kennedy J, Stott A (1993) An adaptive decision-making aid for dairy cow replacement. Agr Syst 42(1–2):25–39. DOI 10.1016/0308-521X(93) 90066-BCrossRefGoogle Scholar
  52. Killen L, Kearney B (1978) Optimal dairy cow replacement policy. Ir J Agric Econ Rural Sociol 7:33–40. URL http://www.jstor.org/stable/25556435
  53. Kristensen A (1987) Optimal replacement and ranking of dairy cows determined by a hierarchical markov process. Livest Prod Sci 16(2):131–144. DOI 10.1016/0301-6226(87)90015-7CrossRefGoogle Scholar
  54. Kristensen A (1988) Hierarchic Markov processes and their applications in replacement models. Eur J Oper Res 35(2):207–215. DOI 10.1016/ 0377-2217(88)90031-8CrossRefGoogle Scholar
  55. Kristensen A (1989) Optimal replacement and ranking of dairy-cows under milk quotas. Acta Agric Scand 39(3):311–318. DOI 10.1080/ 00015128909438523CrossRefGoogle Scholar
  56. Kristensen A (1992) Optimal replacement in the dairy-herd: a multicomponent system. Agr Syst 39(1):1–24. DOI 10.1016/0308-521X(92)90002-6CrossRefGoogle Scholar
  57. Kristensen A (1993) Bayesian updating in hierarchical Markov-processes applied to the animal replacement-problem. Eur Rev Agric Econ 20(2):223–239CrossRefGoogle Scholar
  58. Kristensen A (1994) A survey of Markov decision programming techniques applied to the animal replacement-problem. Eur Rev Agric Econ 21(1):73–93. DOI 10.1093/erae/21.1.73CrossRefGoogle Scholar
  59. Kristensen A (2003) A general software system for Markov decision processes in herd management applications. Comput Electron Agric 38(3):199–215. DOI 10.1016/S0168-1699(02)00183-7CrossRefGoogle Scholar
  60. Kristensen A, Jørgensen E (2000) Multi-level hierarchic Markov processes as a framework for herd management support. Ann Oper Res 94:69–89. DOI 10.1023/A:1018921201113CrossRefGoogle Scholar
  61. Kristensen A, Søllested T (2004a) A sow replacement model using Bayesian updating in a three-level hierarchic Markov process I. Biological model. Livest Prod Sci 87(1):13–24. DOI 10.1016/j.livprodsci.2003.07.004CrossRefGoogle Scholar
  62. Kristensen A, Søllested T (2004b) A sow replacement model using Bayesian updating in a three-level hierarchic Markov process, II. optimization model. Livest Prod Sci 87(1):25–36. DOI 10.1016/j.livprodsci.2003.07.005CrossRefGoogle Scholar
  63. Kristensen A, Thysen I (1991a) Economic value of culling information in the presence and absence of a milk quota. Acta Agric Scand 41(2):129–135. DOI  10.1080/00015129109438594 CrossRefGoogle Scholar
  64. Kristensen A, Thysen I (1991b) Ranking of dairy-cows for replacement—alternative methods tested by stochastic simulation. Acta Agric Scand 41(3):295–303. DOI  10.1080/00015129109439912 CrossRefGoogle Scholar
  65. Kristensen A, Nielsen L, Nielsen M (2012) Optimal slaughter pig marketing with emphasis on information from on-line live weight assessment. Livest Sci 145(1–3):95–108. DOI 10.1016/j.livsci.2012.01.003CrossRefGoogle Scholar
  66. Kure H (1997a) Marketing management support in slaughter pig production. Ph.D. thesis, The Royal Veterinary and Agricultural University. URL http://www.prodstyr.ihh.kvl.dk/pub/phd/kure_thesis.pdf
  67. Kure H (1997b) Optimal slaughter pig marketing. In: Proceedings of the dutch/danish symposium on animal health and management economics, Copenhagen, January 23–24 1997. Dina Notat No. 56, 39-47. URL http://www.prodstyr.ihh.kvl.dk/pub/symp/hk/Kure97a.pdf
  68. Kure H (1997c) Slaughter pig marketing management: utilization of highly biased herd-specific data. In: Kure et al. (eds.) Proceedings of the first european conference for information technology in agriculture, Copenhagen, June 15–18Google Scholar
  69. Langford F, Stott A (2012) Culled early or culled late: economic decisions and risks to welfare in dairy cows. Anim Welf 21(1):41–55. DOI 10.7120/ 096272812X13345905673647CrossRefGoogle Scholar
  70. Lien G, Kristensen A, Hegrenes A, Hardaker J (2003) Optimal length of leys in an area with winter damage problems. Grass Forage Sci 58(2):168–177. DOI 10.1046/j.1365-2494.2003.00367.xCrossRefGoogle Scholar
  71. McArthur A (1973) Application of dynamic programming to the culling decision in dairy cattle. Proc N Z Soc Anim Prod 33:141–147Google Scholar
  72. Mccullough D, Delorenzo M (1996a) Effects of price and management level on optimal replacement and insemination decisions. J Dairy Sci 79(2):242–253. DOI 10.3168/jds.S0022-0302(96)76357-9CrossRefGoogle Scholar
  73. Mccullough D, Delorenzo M (1996b) Evaluation of a stochastic dynamic replacement and insemination model for dairy cattle. J Dairy Sci 79(1):50–61. DOI 10.3168/jds.S0022-0302(96)76333-6CrossRefGoogle Scholar
  74. Mourits M, Huirne R, Dijkhuizen A, Galligan D (1999a) Optimal heifer management decisions and the influence of price and production variables. Livest Prod Sci 60(1):45–58. DOI 10.1016/S0301-6226(99)00037-8CrossRefGoogle Scholar
  75. Mourits M, Huirne R, Dijkhuizen A, Kristensen A, Galligan D (1999b) Economic optimization of dairy heifer management decisions. Agr Syst 61(1):17–31. DOI 10.1016/S0308-521X(99)00029-3CrossRefGoogle Scholar
  76. Nielsen B, Kristensen A (2007) Optimal decisions in organic beef production from steers effects of criterion of optimality and price changes. Livest Sci 110(1–2):25–32. DOI 10.1016/j.livsci.2006.09.024CrossRefGoogle Scholar
  77. Nielsen B, Kristensen A, Thamsborg S (2004) Optimal decisions in organic steer production—a model including winter feed level, grazing strategy and slaughtering policy. Livest Prod Sci 88(3):239–250. DOI 10.1016/j. livprodsci.2003.11.010CrossRefGoogle Scholar
  78. Nielsen L (2011) Markov decision processes (MDPs) in R. URL https://r-forge.r-project.org/projects/mdp/
  79. Nielsen L, Jørgensen E, Kristensen A, Østergaard S (2010) Optimal replacement policies for dairy cows based on daily yield measurements. J Dairy Sci 93(1):77–92. DOI 10.3168/jds.2009-2209Google Scholar
  80. Nielsen L, Jørgensen E, Højsgaard S (2011) Embedding a state space model into a markov decision process. Ann Oper Res 190(1):289–309. DOI 10.1007/s10479-010-0688-zCrossRefGoogle Scholar
  81. Niemi J (2006) A dynamic programming model for optimising feeding and slaughter decisions regarding fattening pigs. Ph.D. thesis, MTT Agrifood Research FinlandGoogle Scholar
  82. Noordegraaf A, Buijtels J, Dijkhuizen A, Franken P, Stegeman JA, Verhoeff J (1998) An epidemiological and economic simulation model to evaluate the spread and control of infectious bovine rhinotracheitis in the netherlands. Prev Vet Med 36(3):219–238. DOI 10.1016/S0167-5877(98)00081-6CrossRefGoogle Scholar
  83. Pihamaa P, Pietola K (2002) Optimal beef cattle management under agricultural policy reforms in finland. Agric Food Sci Finl 11(1):3–12. URL http://jukuri.mtt.fi/handle/10024/452290
  84. Pla L, Pomar C, Pomar J (2003) A Markov decision sow model representing the productive lifespan of herd sows. Agr Syst 76(1):253–272. DOI 10. 1016/S0308-521X(02)00102-6Google Scholar
  85. Pla L, Pomar C, Pomar J (2004) A sow herd decision support system based on an embedded markov model. Comput Electron Agric 45(1):51–69. DOI 10.1016/j.compag.2004.06.005CrossRefGoogle Scholar
  86. Powell W (2011) Approximate dynamic programming solving the curses of dimensionality. Wiley, HobokenCrossRefGoogle Scholar
  87. Puterman M (1994) Markov decision processes. Wiley series in probability and mathematical statistics. Wiley, New YorkGoogle Scholar
  88. Rajala-Schultz P, Grohn Y (2001) Comparison of economically optimized culling recommendations and actual culling decisions of finnish ayrshire cows. Prev Vet Med 49(1–2):29–39. DOI 10.1016/S0167-5877(01)00180-5CrossRefGoogle Scholar
  89. Rajala-Schultz P, Grohn Y, Allore H (2000a) Optimizing breeding decisions for finnish dairy herds. Acta Vet Scand 41(2):199–212Google Scholar
  90. Rajala-Schultz P, Grohn Y, Allore H (2000b) Optimizing replacement decisions for finnish dairy herds. Acta Vet Scand 41(2):185–198Google Scholar
  91. Rodriguez S, Jensen T, Pla L, Kristensen A (2011) Optimal replacement policies and economic value of clinical observations in sow herds. Livest Sci 138(1–3):207–219. DOI 10.1016/j.livsci.2010.12.026CrossRefGoogle Scholar
  92. Rogers G, van Arendonk J, McDaniel B (1988a) Influence of involuntary culling on optimum culling rates and annualized net revenue. J Dairy Sci 71(12):3463–3469. DOI 10.3168/jds.S0022-0302(88)79952-XCrossRefGoogle Scholar
  93. Rogers G, van Arendonk J, McDaniel B (1988b) Influence of production and prices on optimum culling rates and annualized net revenue. J Dairy Sci 71(12):3453–3462. DOI 10.3168/jds.S0022-0302(88)79951-8CrossRefGoogle Scholar
  94. Smith B (1971) The dairy cow replacement problem. An application of dynamic programming, Bulletin 745. Florida Agricultural Experiment Station, GainesvilleGoogle Scholar
  95. Smith B (1973) Dynamic programming of the dairy cow replacement problem. Am J Agric Econ 55(1):100–104. DOI 10.2307/1238671Google Scholar
  96. Sørensen J, Kristensen E, Thysen I (1992) A stochastic model simulating the dairy herd on a pc. Agric Syst 39(2):177–200. DOI 10.1016/0308-521X(92) 90107-YCrossRefGoogle Scholar
  97. Stewart H, Burnside E, Wilton J, Pfeiffer W (1977) Dynamic-programming approach to culling decisions in commercial dairy herds. J Dairy Sci 60(4):602–617. DOI 10.3168/jds.S0022-0302(77)83908-8CrossRefGoogle Scholar
  98. Stewart H, Burnside E, Pfeiffer W (1978) Optimal culling strategies for dairy cows of different breeds. J Dairy Sci 61:1605–1615. DOI 10.3168/jds. S0022-0302(78)83772-2CrossRefGoogle Scholar
  99. Stott A (1994) The economic advantage of longevity in the dairy cow. J Agric Econ 45:113–122. DOI 10.1111/j.1477-9552.1994.tb00382.xCrossRefGoogle Scholar
  100. Stott A, Kennedy J (1993) The economics of culling dairy-cows with clinical mastitis. Vet Rec 133(20):494–499. DOI 10.1136/vr.133.20.494CrossRefGoogle Scholar
  101. Stott A, Jones G, Gunn G, Chase-Topping M, Humphry RW, Richardson H, Logue DN (2002) Optimum replacement policies for the control of subclinical mastitis due to s.aureus in dairy cows. J Agric Econ 53(3):627–644. DOI 10.1111/j.1477-9552.2002.tb00041.xCrossRefGoogle Scholar
  102. Stott A, Jones G, Humphry R, Gunn G (2005) Financial incentive to control paratuberculosis (Johne’s disease) on dairy farms in the United Kingdom. Vet Rec 156(26):825–831. DOI 10.1136/vr.156.26.825CrossRefGoogle Scholar
  103. Tijms H (2003) A first course in stochastic models. Wiley, West SussexCrossRefGoogle Scholar
  104. Toft N, Kristensen A, Jorgensen E (2005) A framework for decision support related to infectious diseases in slaughter pig fattening units. Agr Syst 85(2):120–37. DOI 10.1016/j.agsy.2004.07.017CrossRefGoogle Scholar
  105. Vargas B, Herrero M, van Arendonk J (2001) Interactions between optimal replacement policies and feeding strategies in dairy herds. Livest Prod Sci 69(1):17–31. DOI 10.1016/S0301-6226(00)00250-5CrossRefGoogle Scholar
  106. Verstegen J, Sonnemans J, Huirne R, Dijkhuizen A, Cox J (1998) Quantifying the effects of sow-herd management information systems on farmers’ decision making using experimental economics. Am J Agric Econ 80(4):821–829. DOI 10.2307/1244066CrossRefGoogle Scholar
  107. Viet A, Jeanpierre L, Bouzid M, Mouaddib A (2012) Using markov decision processes to define an adaptive strategy to control the spread of an animal disease. Comput Electron Agric 80:71–79. DOI 10.1016/j.compag.2011.10. 015CrossRefGoogle Scholar
  108. de Vries A (2004) Economics of delayed replacement when cow performance is seasonal. J Dairy Sci 87(9):2947–2958. DOI 10.3168/jds.S0022-0302(04) 73426-8CrossRefGoogle Scholar
  109. de Vries A (2006) Economic value of pregnancy in dairy cattle. J Dairy Sci 89(10):3876–3885. DOI 10.3168/jds.S0022-0302(06)72430-4CrossRefGoogle Scholar
  110. White W (1959) The determination of an optimal replacement policy for a continually operating egg production enterprise. J Farm Econ 41(5):1535–1542. URL http://www.jstor.org/stable/1235311
  111. Yalcin C, Stott A (2000) Dynamic programming to investigate financial impacts of mastitis control decisions in milk production systems. J Dairy Res 67(4):515–528. DOI 10.1017/S0022029900004453CrossRefGoogle Scholar
  112. Yates C, Rehman T (1998) A linear programming formulation of the Markovian decision process approach to modelling the dairy replacement problem. Agr Syst 58(2):185–201. DOI 10.1016/S0308-521X(98)00054-7CrossRefGoogle Scholar

Copyright information

© Springer Science + Business Media New York 2015

Authors and Affiliations

  • Lars Relund Nielsen
    • 1
    Email author
  • Anders Ringgaard Kristensen
    • 2
  1. 1.CORAL, Department of Economics and BusinessAarhus UniversityAarhusDenmark
  2. 2.Department of Large Animal SciencesUniversity of CopenhagenCopenhagenDenmark

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