Optimization of Profit for Pasture-Based Beef Cattle and Sheep Farming Using Linear Programming: Model Development and Evaluation

A linear programming optimization tool is useful to assist farmers with optimizing resource allocation and profitability. This study developed a linear programming profit optimization model with a silage supplement scenario. Utilizable kilograms of pasture dry matter (kg DM) of the total pasture mass was derived using minimum and maximum pasture mass available for beef cattle and sheep and herbage utilization percentage. Daily metabolizable energy (MJ ME/head) requirements for the various activities of beef cattle and sheep were estimated and then converted to kg DM/head on a bi-monthly basis. Linear programming was employed to identify the optimum carrying capacity of beef cattle and sheep, the most profitable slaughtering ages of beef cattle, the number of prime lambs (sold to meat processing plants), and sold store lambs (sold to other farmers for finishing). Gross farm revenue (GFR) and farm earnings before tax (EBT) per hectare and per stock unit, as well as total farm expenditure (TFE), were calculated and compared to the average value of Taranaki-Manawatu North Island intensive finishing sheep and beef Class 5 farming using Beef and Lamb New Zealand (B+LNZ) data. The modeled farm ran 46% more stock units (a stock unit consumed 550 kg DM/year) than the average value of Class 5 farms. At this stocking rate, 83% of the total feed supplied for each species was consumed, and pasture supplied 95% and 98% of beef cattle and sheep feed demands, respectively. More than 70% of beef cattle were finished before the second winter. This enabled the optimized system to return 53% and 188% higher GFR/ha and EBT/ha, respectively, compared to the average values for a Class 5 farm. This paper did not address risk, such as pasture growth and price fluctuations. To understand this, several additional scenarios could be examined using this model. Further studies to include alternative herbages and crops for feed supply during summer and winter are required to expand the applicability of the model for different sheep and beef cattle farm systems.

[1]  W. J. Anderson,et al.  The effect of dairy farm intensification on farm operation, economics and risk: a marginal analysis , 2017 .

[2]  T. Ramilan,et al.  Quantifying sheep enterprise profitability with varying flock replacement rates, lambing rates, and breeding strategies in New Zealand , 2020 .

[3]  A. Ashfield,et al.  Bioeconomic modelling of male Holstein-Friesian dairy calf-to-beef production systems on Irish farms , 2014 .

[4]  A. Ashfield,et al.  Simulation modelling of temperate grassland based dairy calf to beef production systems , 2013 .

[5]  Frederick V. Waugh,et al.  The Minimum-Cost Dairy FeedAn Application of “Linear Programming” , 1951 .

[6]  K. E. McClure,et al.  Sheep Production , 1929, Nature.

[7]  A. J. Romera,et al.  A model for simulating rule-based management of cow–calf systems , 2004 .

[8]  Val Snow,et al.  Modelling pastoral farm agro‐ecosystems: A review , 2008 .

[9]  E. B. Burnside,et al.  Beef production from a dairy farm: A linear programming simulation approach , 1984 .

[10]  Graeme J. Doole,et al.  Detailed description of grazing systems using nonlinear optimisation methods: A model of a pasture-based New Zealand dairy farm , 2013 .

[11]  G. Dean,et al.  Production Functions and Linear Programming Models for Dairy Cattle Feeding , 1972 .

[12]  Is there an association between dam live weight and litter structure in a flock of grazing Perendale sheep , 2011 .

[13]  J E Annetts,et al.  Multiple objective linear programming for environmental farm planning , 2002, J. Oper. Res. Soc..

[14]  P. Kenyon,et al.  Breeding ewe lambs successfully to improve lifetime performance , 2014 .

[15]  P. Kenyon,et al.  Intensive sheep and beef production from pasture--a New Zealand perspective of concerns, opportunities and challenges. , 2014, Meat science.

[16]  Graeme J. Doole,et al.  Improving the profitability of Waikato dairy farms: Insights from a whole-farm optimisation model , 2015 .

[17]  J. W. Wilton,et al.  A LINEAR PROGRAMMING MODEL FOR BEEF CATTLE PRODUCTION , 1974 .

[18]  Ross Kingwell,et al.  Dryland pasture improvement given climatic risk , 1994 .

[19]  G. Jansen,et al.  Linear Programming in Selection of Livestock , 1984 .

[20]  S. Thamsborg,et al.  Optimal decisions in organic steer production—a model including winter feed level, grazing strategy and slaughtering policy , 2004 .

[21]  A. Pleasants,et al.  Associations of body condition score and change in body condition score with lamb production in New Zealand Romney ewes , 2019 .

[22]  W. Rossing,et al.  A multi-objective optimization model for dairy feeding management , 2020 .

[23]  David Scobie,et al.  Optimisation of the Resource of Land-Based Livestock Systems to Advance Sustainable Agriculture: A Farm-Level Analysis , 2020 .

[24]  G. Doole,et al.  The role and value of diverse sward mixtures in dairy farm systems of New Zealand: An exploratory assessment , 2017 .

[25]  J. Zgajnar,et al.  OPTIMIZATION OF BULLS FATTENING RATION APPLYING MATHEMATICAL DETERMINISTIC PROGRAMMING APPROACH , 2008 .

[26]  Graeme J. Doole,et al.  Optimising the interrelationship between intake per cow and intake per hectare , 2015 .

[27]  P. H. Robinson,et al.  A linear programming model to optimize diets in environmental policy scenarios. , 2012, Journal of dairy science.

[28]  L. Killen,et al.  A linear programming model of grassland management , 1987 .

[29]  P. Tozer,et al.  The Impact of Hogget and Mature Flock Reproductive Success on Sheep Farm Productivity , 2020, Agriculture.

[30]  T. Rehman,et al.  Unravelling the rationale of `overgrazing' and stocking rates in the beef production systems of Central Brazil using a bi-criteria compromise programming model , 2005 .

[31]  Optimal choice of dairy forages in eastern Australia. , 2007, Journal of dairy science.

[32]  David J. Pannell,et al.  MIDAS, a bioeconomic model of a dryland farm system. , 1987 .

[33]  David J. Pannell,et al.  Lessons from a Decade of Whole-Farm Modelling in Western Australia , 1996 .

[34]  Leon S. Lasdon,et al.  Design and Use of the Microsoft Excel Solver , 1998, Interfaces.

[35]  R. Dewhurst,et al.  A bio-economic model for cost analysis of alternative management strategies in beef finishing systems , 2020, Agricultural Systems.

[36]  T. Ramilan,et al.  The effect of ewe wastage in New Zealand sheep and beef farms on flock productivity and farm profitability , 2019, Agricultural Systems.

[37]  David J. Pannell,et al.  Debugging Mathematical Programming Models: Principles and Practical Strategies , 1996 .

[38]  Michael Robertson,et al.  Climate change impacts and farm-level adaptation: Economic analysis of a mixed cropping–livestock system , 2017 .

[39]  Michael Wallace,et al.  The development of a mathematical model to investigate Irish beef production systems , 2006 .

[40]  N. López-Villalobos,et al.  Carcass characteristics and meat quality of Hereford sired steers born to beef-cross-dairy and Angus breeding cows. , 2016, Meat science.

[41]  D. Mccall,et al.  Optimized dairy grazing systems in the northeast United States and New Zealand. I. Model description and evaluation. , 1999, Journal of dairy science.

[42]  Guy M. Trafford,et al.  The usefulness and efficacy of linear programming models as farm management tools , 2013 .