Application of resource allocation optimisation to provide profitable options for dairy production systems


1Institute of Veterinary, Animal and Biomedical Sciences, Massey University, Private Bag 11-222, Palmerston North 4442, New Zealand

2142 Ballantyne Road, Poraiti, RD 2, Napier 4182, New Zealand

*Corresponding author:


A linear program (LP) model analysed resource use on a 100 ha dairy farm. A single optimum-profit combination was established for resources which were either optimised or constrained. It was found that, with a fixed herd of 320 milking cows, when production increased from 305 kg milksolids per cow (kg MS/cow) to

415 kg MS/cow, cash profit increased by 65%. This required additional supplements. If, however, feed demand and supply were optimised at 415 kg MS/cow, the LP reduced milking cow number rather than buy in feed to meet the increased feed demand from higher production per cow. At all production levels chosen between 305 and 415 kgMS/cow, it was most economic to dry off and cull cows early in dry summers to optimise feed demand vs. feed grown; use nitrogen (N) fertiliser to avoid a feed deficit only when response rates of better than 10 kgDM to 1 kg N could be expected; not use N for growing supplements to harvest. Pasture cover, within defined constraint levels, provided a  buffer for  feed  demand and  supply  fluctuations. The study highlights the importance of assessing production, income and cost in an integrated framework to identify the point at which individual resources become limiting.

Keywords: dairy farm systems; computer model; simulation; optimise; resource allocation.


The use of computerised modelling is common in New Zealand agriculture. Examples include, Grazing   Systems   (GSL,   Ridler   et   al.,   2001), Farmax, UDDER (Larcombe, 1988) and Dexcel Whole Farm Model (Wastney et al., 2002), with the developed models having varying levels of impact on farmer behaviour (Woodward et al., 2008). Linear programming (LP) has been used mainly to simulate particular aspects of farm production systems (Stott,

2008) with few used to simulate farm systems (McCall & Clark, 1999), especially where the emphasis  is  on  the  marginal  productivity  of  the system being investigated (Santarossa et al., 2004).

Models  are  flexible  and  respond  rapidly  to input changes. These features enable users to examine in detail situations ranging from the individual animal to the whole-farm, depending on the  model  structure  and  parameters.  This  paper reports on the results of a linear programming model (GSL LP) which integrates the physical and financial environments in which farmers operate. It includes receipts for products and costs of operating a farm.

This LP model allocates resources according to energy relationships derived from controlled experiments. The  user  defines  inputs  which  then apply to a unique situation that the LP model is analysing. For example, the average pasture growth rate and availability, quantity and quality of all forages expressed as Megajoules of metabolisable energy  (MJME)  per  kg  of  dry  feed,  herd  age

structure and production, addition of nitrogen, crops or irrigation and all other resources are initially specified but can then be varied as required for each two-week period of a year. The resources in the LP model used in this investigation were for predominantly  pasture-fed  dairy  cows  reflecting New         Zealand’s   main   production   system.   “In principle, efficient milk production on grassland involves, as a prerequisite, the best possible fit between the varying curve of pasture production and the much more stable curve of cow and herd requirements” (McMeekan, 1960).

As the LP model has the ability to add, replace or modify in quantity and output the resources being used in  a  controlled stepwise manner (Figure 1), these functions allow incremental addition of resources    after    initially    constraining    selected resources.

The stepwise application of constraints by the LP model provides the means to investigate change, then to modify or optimise each resource in order to understand the response of the system to a specific change. Although the change is ultimately driven by its financial outcome, it depends primarily on feed- energy relationships and the cost of the energy. Interpretation of solutions in this context is not complex and is aided by reporting of forage status, animal  production and  cash  flows  in  two-weekly intervals.

Roche and Newman (2008) advised against investigating total extra product from total extra input, defined as “Margin over Feed”, but did not

FIGURE 1:  a  model representing the  relationship between feed supply, feed demand and production economics in a grazed livestock production system. MJME = Megajoules of metabolisable energy; MC = Marginal cost; MR = Marginal revenue; DM = Dry matter; PKE = Palm kernel expellar.

Image 4

explain   how   a   marginal   analysis   should   be conducted to  investigate the  effects of  individual increments of inputs on the incremental output and subsequent extra revenue. The law of diminishing marginal returns (DMR) (Kay et al., 2008) states that as additional units of a variable input are used in combination with one or more fixed inputs, marginal extra physical product will eventually decline. Examples of fixed inputs are land and buildings.   “DMR   is   based   on   the   biological processes  found  in   agricultural  production  and results from the inability of plants and animals to provide the same response indefinitely to successive increases in nutrients or some other input” (Kay et al., 2008).

If a program does not simultaneously account for financial factors, DMR and physical constraints on resources, it lacks the accuracy and efficiency required   for   modern   dairy   production   systems (Ferris  &  Malcolm,  1999).  Models  that  consider financial  resources  after  the  physical  calculations are complete usually fail to fully account for DMR because the process must include the ability to select the most economic mix based on marginal return to each  possible resource  within  a  dynamic  system. The  LP  methodology  of  continual  analysis  of
multiple resource use based on productive and economic combinations ensures this occurs. Some analysts use averaging procedures such as a gross margin of   total   revenue   minus   variable costs; a  partial  budget where only the part of the business deemed to be affected by a change is analysed;

a benchmarking system where properties and businesses with similar characteristics are compared to identify differences in production, farm performance and profitability; or feed budgeting. These techniques do not generally allow one to comprehensively assess the effect of integration of farm resources on the adjusted for any combination of resources. When this has been established, feed-back loops which include   the   economics   of   each aspect of production can be constructed to more accurately allocate resources profitably. If a LP optimisation routine is used to calculate total feed supply and the explain   how   a   marginal   analysis   should   be conducted to  investigate the  effects of  individual increments of inputs on the incremental output and subsequent extra revenue. The law of diminishing marginal returns (DMR) (Kay et al., 2008) states that as additional units of a variable input are used in combination with one or more fixed inputs, marginal extra physical product will eventually decline. Examples of fixed inputs are land and buildings.   “DMR   is   based   on   the   biological processes  found  in   agricultural  production  and results from the inability of plants and animals to provide the same response indefinitely to successive increases in nutrients or some other input” (Kay et al.,
If a program does not simultaneously account for financial factors, DMR and physical constraints on resources, it lacks the accuracy and efficiency required   for   modern dairy production systems (Ferris  &  Malcolm,  1999).  Models  that  consider financial  resources  after  the  physical  calculations are complete usually fail to fully account for DMR because the process must include the ability to select the most economic mix based on marginal return to each  possible resource  within  a  dynamic  system. The  LP  methodology  of  continual  analysis  of pattern of feed supply, feed demand from specific animals can be exactly matched. If this feed demand can be met from existing pasture production alone, this sets a base from which other options can be compared.

Manipulation of animal number and performance, and pasture type and supplement availability can be used to provide a wide variety of management options with varying financial outcomes, management constraints and risk profiles.


The LP model objective in this study was ultimately the best economic return. The LP model allowed selected resources to be constrained, primarily cow number and production per cow, but it allowed the addition of other resources such as supplementary feeds, nitrogen and grazing off. The model  depended  primarily  on  relationships involving feed energy and its cost. Interpretation of solutions was aided by reporting of forage, animal production and cash flows in two-weekly intervals.

Costs  and  prices  for  2010  were  applied, for example $6.15/kg milksolids (MS). Expenses included only variable costs such as farm-working

TABLE 1: Expected production, profit and the resource requirements of a pasture-based, spring-calving, seasonal-supply, 100-ha New Zealand dairy farm at specified numbers of cows and/or per-cow production levels. MS = Milksolids.

Image 1

TABLE 2: The effect of different herd sizes at one per-cow milk-production level on the resources required, expected production and profit of a pasture-based, spring-calving, seasonal-supply, 100 ha New Zealand dairy farm. MS = Milksolids.

Image 2expenses and excluded fixed costs and capital expenditure.

In Table 1 are shown successive runs of the LP model. A base performance was established for the model farm of 100 ha effective growing 12,026 kg pasture dry matter  (DM). In  the first row of  the table, herd size was set at 320 cows of mixed ages, including     first-calving     two-year-old     heifers. Production was set at 305 kg MS per cow based on a herd profile of 25% replacement rate; live-weight gain in replacements; a maximum of six years in the herd; live-weight variation between seasons as cows lost and regained condition; and intake and production of younger cows proportionate to mature cows. The nitrogen (N) fertiliser available to  the model was constrained to set dates of application, and the amounts available were also discrete, not continuously variable, in line with typical on-farm practice.  The  amounts  showing  in  Table  1  were those indicated by the model to supply the required feed at least cost for the specified conditions. Other factors determined by the model were the amount of silage made and supplements purchased; concentrates required (Table 1) and pasture covers carried   forward,   subject   to   upper   and   lower constraint levels for each period; and financial performance. The model had user-defined or default values for two-weekly feed quality and also feed quality/cow-intake constraints.

In the second row of the table, a base level of 305 kg MS per cow was set and the farm system was then allowed to optimise itself (“Base optimise”). The third run, on Row 3, had fixed herd size, but the model was allowed to dry-off cows early and cull some of the herd. In Rows 4 to 10, average production per cow was set and where indicated, numbers of cows were also set.

To establish the relationship between stocking rate, production and profitability for the conditions on this farm the number of cows was set in all but one of the LP model runs, as was per-cow production. In that one run, the model was allowed to  determine the  optimum  cow  number.  Per-cow production was held constant. Outputs from these scenarios are given in Table 2.


The effects of setting stocking rate and per-cow milksolids production, or allowing the LP model to optimise within one of these constraints are shown in  Table 1. In  general it  was found that  a  high- producing herd was more profitable than a lower- producing herd, notwithstanding the need for extra feed for the former. The LP model showed that, with a fixed herd of 320 milking cows grazing the 100ha,  profit  increased  65%  from  $166,091  to $273,443 when production was increased from 305 kg  MS  per  cow  to  415  kg  MS  per  cow.  This required additional supplements of 152 t DM if the cows averaged 305 kg MS per cow or 452 t DM plus some concentrate, if the cows averaged 415 kg MS per cow.

If feed demand and feed supply were optimisedthrough resource allocation, the LP model reduced milking  cow  number  and  fed  them  with  an  all pasture   diet,   rather   than   buying   in   feed   to compensate for the increased feed demand from the higher producing cows (286 cows producing 305 kg MS per cow returning $187,254 versus 243 cows producing 415 kg MS per cow returning $316,924).

At the four production levels chosen of 305; 332; 366; and 415 kg MS per cow, it was most economic to dry off and cull cows in dry summers to  optimise   feed   demand   versus   feed   grown (Table 1). The model used nitrogen (N) fertilizer to avoid a  feed deficit  only when response rates of better than 10 kg DM to 1 kg N could be expected. It did not use N for growing supplements to harvest. Pasture cover rose or fell, within defined constraint levels, to provide a buffer for periods of low or high feed demand.

The analysis of the effect of progressively reducing the number of cows producing 305 kg MS per  cow determined that  the  optimum profit was generated with 286 cows grazing the 100 ha. It should be noted that there were marked differences between each run of the model in the amounts of resources used. It was found that, as cow stocking rate  declined, it  became more profitable to graze some, or all, of the replacement heifers on the model farm than to pay fees to graze them elsewhere.

Increasing the cow number from 286 to 305 by the  addition  of  34  cows  reduced  “profit”  from
$187,254 to $166,091, a drop of $21,163. Reducing   cow   number   by   36   below   the “optimal”  of  286  to  250,  reduced  the  profit  by $5,692. As each additional cow above optimal was added, there was an increasingly large drop in profit, emphasising   the    importance   of    a    “marginal analysis”,    comparing    marginal    revenue    and marginal costs (Kay et al., 2008). The LP model indicated that there was less financial risk, with reduced profit, associated with being slightly under-stocked than with being highly stocked, provided that the control of feed enabled the maintenance of pasture growth rate and quality. When moving from the  LP  run  with the  highest number  of  cows  towards  that  with  the  lowest number and the model was able to eliminate all the bought-in feed and began to allocate resource use from cheaper feed options such as N fertilizer and grazed-off stock, it eliminated the next most expensive  feed  source  which,  in  this  case  was grazing one- to two-year-old replacement heifers off of the model farm. Then it moved to 4-month to 1 year-old stock before using N fertilizer at a >10:1 response rate, calculated as kg DM:kg N, or grazing mature cows on the farm over winter.

Table 2 presents but one set of scenarios. New scenarios could be generated by changing the level of per cow production, cost structure, product price or feed supply curve.


It is generally accepted that supplementation of dairy cows is most profitable when used to fill a short-term deficit in pasture so as to ensure continuation of lactation. However, if an accurate pasture-demand profile can be established and adjustments to this demand can be made at critical times, this will  prove to  be more profitable than supplementation within established farm systems.

Resource allocation can determine the most profitable  option  when  supplementary  feeds  are being  evaluated.  Rather  than  debating  the differences between kinds of  supplements, or  the response and substitution rate of each supplement when  being  fed,  it  should  first  be  established whether  supplementation  is  merited.  This  study found it was most profitable to have fewer, high- producing cows, fully-fed on pasture. Macdonald et al. (2008) reported over 415 kg MS per cow can be achieved from all-pasture feeding. Pasture production,  quality  and  utilisation  can  be manipulated by altering grazing interval for individual paddocks and by adjusting daily stocking rate through herd size and area grazed (Ridler & Hurley, 1984).

If the farm experiences regular poor spring growth and frequent dry summers, it was found that it is usually better to dry off and cull cows in dry summers.

On the model farm, N fertilizer was of limited benefit  unless  response  rates  of  better  than  10:1 were achieved at the time of the feed deficit. Ironically, the time when extra pasture is most needed, the response rates to applied N fertilizer are poorest such as during a cold spring, or a dry summer/autumn period.
If the same deficits occur regularly, feed demand can be altered economically through
running fewer stock (with potentially better production per cow), altering calving date or more aggressive drying off and/or culling cows.
This study has shown the importance of integrated resource allocation optimisation when changing resource use to optimise profit on a seasonal supply dairy farm. With this objective, the LP model gave a practical management approach suitable for a commercial dairy farm offering the user an ability to innovate by evaluating multiple outcomes from changing the resources of an established base.
Management is characterized by the daily decisions needed to modify plans promulgated using the best knowledge at a time of imperfect knowledge. Too often, plans concentrate on production and financial targets without due regard to the quantity and quality of resources available. Such plans should not act as rigid frameworks within which management is constrained, particularly when the plans are based on single- factor or straight-line analyses such as gross margins, benchmarks, partial budgets, or response functions to supplementary feeds. These do not truly reflect the multitude of options and possible combinations from the continually changing mix of resources present on any farm. Due to the facility of the LP model to add single or multiple increases in available resources, a profile of likely options and their individual effect on profit within the framework of an existing farm with its unique resources was established.
This study showed that, for the model farm, profit was optimised where cows were fully-fed on good-quality pasture at a stocking rate that enabled high production in the region of 415 kg MS per cow. Supplementary feeding led to higher total profit if it led to increased per-cow production, not increased farm stocking rate. Early drying off/culling was the best option for the farm under summer-dry conditions. The effect of the pattern of feeding supplements to pasture-fed cows, supplement characteristics such as quality (MJME/kg) or cost, and the relationships between supplements, herd characteristics, and basic farm- management practices on the model farm warrant a further report.


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