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A Mathematical Optimisation Model of a New Zealand Dairy Farm: The Integrated Dairy Enterprise (IDEA) Framework


  • Graeme J. Doole

    () (University of Waikato)

  • Alvaro J. Romera

    () (Dairy New Zealand)

  • Alfredo A. Adler

    () (Dairy New Zealand)


Optimisation models are a key tool for the analysis of emerging policies, price sets, and technologies within grazing systems. A detailed nonlinear optimisation model of a New Zealand dairy farming system is described. The framework is notable for its rich portrayal of pasture and cow biology that add substantial descriptive power to standard approaches. Key processes incorporated in the model include: (1) pasture growth and digestibility that differ with residual pasture mass and rotation length, (2) pasture utilisation that varies by stocking rate, and (3) different levels of intake regulation. Model output is shown to closely match data from a more detailed simulation model (deviations between 0 and 5 per cent) and survey data (deviations between 1 and 11 per cent), providing confidence in its predictive capacity. Use of the model is demonstrated in an empirical application investigating the relative profitability of production systems involving different amounts of imported feed under price variation. The case study indicates superior profitability associated with the use of a moderate level of imported supplement, with Operating Profit ($NZ ha-1) of 934, 926, 1186, 1314, and 1093 when imported feed makes up 0, 5, 10, 20 and 30 per cent of the diet, respectively. Stocking rate and milk production per cow increase by 35 and 29 per cent, respectively, as the proportion of imported feed increases from 0 to 30 per cent of the diet. Pasture utilisation increases with stocking rate. Accordingly, pasture eaten and nitrogen fertiliser application increase by 20 and 213 per cent, respectively, as the proportion of imported feed increases from 0 to 30 per cent of the diet.

Suggested Citation

  • Graeme J. Doole & Alvaro J. Romera & Alfredo A. Adler, 2012. "A Mathematical Optimisation Model of a New Zealand Dairy Farm: The Integrated Dairy Enterprise (IDEA) Framework," Working Papers in Economics 12/01, University of Waikato.
  • Handle: RePEc:wai:econwp:12/01

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    References listed on IDEAS

    1. Kingwell, Ross S., 2011. "Managing complexity in modern farming," Australian Journal of Agricultural and Resource Economics, Australian Agricultural and Resource Economics Society, vol. 55(1), pages 1-23.
    2. Graeme J. Doole & David J. Pannell, 2008. "Optimisation of a Large, Constrained Simulation Model using Compressed Annealing," Journal of Agricultural Economics, Wiley Blackwell, vol. 59(1), pages 188-206, February.
    3. Berentsen, P. B. M. & Giesen, G. W. J., 1995. "An environmental-economic model at farm level to analyse institutional and technical change in dairy farming," Agricultural Systems, Elsevier, vol. 49(2), pages 153-175.
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    Cited by:

    1. Dowson, Oscar & Philpott, Andy & Mason, Andrew & Downward, Anthony, 2019. "A multi-stage stochastic optimization model of a pastoral dairy farm," European Journal of Operational Research, Elsevier, vol. 274(3), pages 1077-1089.
    2. Notte, Gastón & Cancela, Héctor & Pedemonte, Martín & Chilibroste, Pablo & Rossing, Walter & Groot, Jeroen C.J., 2020. "A multi-objective optimization model for dairy feeding management," Agricultural Systems, Elsevier, vol. 183(C).
    3. Notte, Gastón & Pedemonte, Martín & Cancela, Héctor & Chilibroste, Pablo, 2016. "Resource allocation in pastoral dairy production systems: Evaluating exact and genetic algorithms approaches," Agricultural Systems, Elsevier, vol. 148(C), pages 114-123.
    4. David A Fleming & Kate Preston, 2018. "International Agricultural Mitigation Research and the Impacts and Value of Two SLMACC Research Projects," Working Papers 18_11, Motu Economic and Public Policy Research.

    More about this item


    dairy production; mathematical optimisation; whole-farm model;

    JEL classification:

    • Q12 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - Agriculture - - - Micro Analysis of Farm Firms, Farm Households, and Farm Input Markets
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis

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