Summary notes for:

Symposium on Modelling.

13 April 2012


Prepared by


Barrie Ridler
Grazing Systems Ltd

GSL Systems Modelling.

Modelling Real Farm Systems; The use of LP.


Farm systems are complex and function as an interaction of many components. Although often perceived as being stable they are more often on the edge of change due to undefined constraints in critical resources.

The key to systems success is being able to identify any constraint (time, quantity, quality) and provide a viable substitute or alter the system mix to minimise its effect.

New Zealand agriculture has simplified the concept of systems by reporting ratios such as production per hectare and stock/ha. that average data, then use these ratios as a means to compare between farms or farm systems.

Obviously, averaging data destroys detail, and detail is required to identify and overcome constraints yet this “benchmarking” is a major contributor to extension efforts. Averaging results in a less efficient allocation of resources at the margin, which can in turn lead to systems collapse if not recognised in time.

Massey University’s Agricultural Economics and Farm Management Department developed a number of linear programming models through the period 1970-1985 in order to better handle the marginal changes that occur within biological systems. Production Economics was part of this modelling effort and resulted in models of pasture growth with additional nitrogen, modelling forage crops in dairy systems in Northland, dairy farm systems and bull beef systems.

Of these models, the dairy farm systems model (“No. 4 Dairy LP model” -used to run the Massey No.4 Dairy farm from 1980-84 and reported to Ruakura Dairy Farmers Conference 1984) was improved as computers and LP became more sophisticated. This more general model was also used for optimising lamb sales, mixed dairy/bull beef and was further adapted by Ruakura in the 1990’s.

The knowledge gained from this work was incorporated into a different model (Grazing Systems Ltd.) in the 1990’s. These models suffered from varying levels of inflexibility due to the need to establish some fixed rules for solving. This somewhat obscured the marginal productivity edge of the models although they were generally an improvement on simple gross margin and partial budget analysis as they allowed substitution (to a limited extent) of resources based on the diminishing returns of selected resources. LP allows allocation of resources through an iterative process, ideally using a constant re-evaluation of the production and economics of the system.

Rather than isolating resources into discrete components, calculating their effect outside of the system then returning the “better” component back into the same resource mix, LP ensures the inter-relationships that effect the quantity and substitution of each resource is continually calculated in a full systems context. The early models were restricted in their ability to complete this process due to the boundaries required by the input data.

By 2002 this inflexibility demanded a new approach to how LP methodology could be best used. Much had been learnt about systems response from previous modelling and farm results. This knowledge and experience was used as the basis for change.

All the previous modelling structures were discarded in favour of new programming techniques that enhanced the ability of the LP process and allowed simple relationships to evolve into quite complex combinations and provide a new insight into what systems were really possible. (The “GSL” LP.) But this in itself created problems because of industry perceptions of just what farm systems should look like and what they should report.

Model acceptance had encountered the often contradictory field of attitudes and beliefs currently held by farmers and their advisors

The “New Zealand condition”.

Throughout the period from 1960 to 1990, researchers such as McMeekan, During and Brougham provided the knowledge to increase farm production at minimal cost. But even in the early 1960’s, Massey University agricultural economist Professor Will Candler was pointing out the economic limitations of increasing biological production (Candler W, 1962).

This advice was largely ignored by animal, plant and industry productionists while farmers and sharemilkers increased cow numbers as a means to progress profitability.

This emphasis on production has now become part of the intuitive process in all farming business, from farming through service industry to bankers and researchers.

What we have is a belief that is apparently oblivious to the distinction between biological and economic efficiency. This belief is aided by the simplistic use of comparative processes such as benchmarks and KPI’s, which conspire to obscure the reality of how real farm systems work.

The reality is that systems exhibit diminishing returns.

The Importance of Diminishing Returns and Marginal Productivity.

GSL Model Examples:

Response to nitrogen is a critical factor in both the economic and environmental outcome of many dairy farm systems. (It is of limited value for other farm types except in specialist circumstances.)Yet data on nitrogen response in New Zealand is sparse.

The first Table and graphs in the Appendix relate to one trial with bull beef. The actual returns from adding nitrogen are summarised in both production and economic return.

When Table 1 is studied many will conclude that nitrogen should be added up to about 85 kgN per hectare as it is still “making money” ($150.70 cost vs. $162.70 return).

The reality of the marginal analysis shows that any nitrogen added beyond 45 kgN/ha is actually uneconomic ($MC vs. $MR). Return should not be calculated using average response rates and total return less total cost, but on marginal productivity.

Fig 1 shows how the response to nitrogen diminishes and Fig 2 shows where the cost of nitrogen (MC) and the $ return for each additional kgN cross over (when MC=MR) compared to the total revenue vs. total cost lines.

This process is a crucial requirement for any farm systems model in order to identify when to cease adding input. Without LP it is difficult (perhaps impossible?) to identify this point for each individual system and the use of average response rates invariably encourages overuse of resources, reduces profit and increases environmental damage.

The marginal productivity analysis is able to be handled within LP. Each iteration of the LP model moves the solution closer to an optimal mix of resources until a best mix “optimum” is reached. Provided the time period is short enough (2 weekly seems accurate enough under most circumstances) efficient allocation of a variety of inputs can be accurately calculated to ensure the most economic outcome.

An emissions framework has been added to the GSL model and can accurately calculate GHG based on the resources actually employed within the LP. This adds another dimension to systems analysis; the ability to solve for a specified level or range of GHG output. CO2 emissions can be constrained in a similar way to other outputs or inputs yet the LP still solves for the best economic result despite the restrictions.

This type of analysis can be applied to an individual farm or regional groupings and can be replicated to provide a series based on single factor change, but with all other resources allowed to vary to ensure an optimal final resource mix (Fig.4). The analysis also provides an accurate analysis of the level of production/stocking rate at which farm profit will become compromised. Note however that such results reflect the mix of many inputs, not least of which is the influence of per cow production. In this example per cow production has been kept constant as herd number has increased.

The point to emphasise is that LP has the ability to identify constraints and to substitute inputs (sometimes output) based on the differing levels of performance of the resources. Data in the graphs therefore applies to only one unique set of circumstances. Changing any one resource (price, quantity, quality, and timing) will have a cascading effect on the system and may provide a slightly better or worse overall system result.

It is of interest that when the most limiting resource is constrained further in an LP, the entire process may be compromised and in certain cases may lead to economic collapse of the system (Fig 5 where nitrogen use is constrained and the LP system adjusts to reduce N leaching to lower levels.)

LP models when properly constructed are able to identify the “tipping point” after which economic performance will sometimes drastically decline (as shown in Figs.3, 4 and 5). Other forms of models cannot achieve this clarity. When models rely on averaged data (which removes detail) they are unable to perform marginal analyses.

Candler warned of trying to use such ratios for comparative purposes between farms and this warning has been renewed more recently. (Ferris 1999; Malcolm 2001).

The use of the GSL LP has emphasised the interactions that occur as production per cow alters. More production increases the complexities of change in feed demand, how best to adjust for this, the impact on fixed and variable costs if one option is selected over another, aspects of lumpy inputs such as labour and capital purchases; and the potential for insufficient feed quality as a new set of constraints grow in importance with the increasing animal performance. All these increase risk and complexity and the more complex the system, the more prone it is to collapse.

Similarly, when the issues that surround a change in replacement rate, herd longevity or varying performance of each age class in a herd are modelled using LP, it makes any attempt to compare farms by simple ratios appear at best, misguided.

A properly constructed model can use LP to solve all these interactions, often with new insights about the emergent systems that develop, or clues as to the likely constraints that will prevent further progress. The LP can then be used to investigate the best way to overcome these constraints.


The GSL LP now has flexibility and ability to evolve new combinations of resource uses that previously was not possible. This provides a new clarity of just what is involved in farm systems, how different combinations react and what constraints are likely to occur and when.

When “counterintuitive” results occur from LP an open mind is required to firstly acknowledge, and then process what must have occurred within the system. The report framework allows a rapid assessment of the full system and the process of substitution that must have occurred. The “what, when, how and why” that is so important for motivation and learning. All that is required is some thought, humility and systems knowledge (plus a smattering of economic understanding) to be of maximum benefit.

In effect the LP process can be made to provide a very precise report on the factors of production (production functions) involved in every outcome.

Compare this to the simplistic ratios and take home messages that are easy to digest but miss the point of farm systems. Productionists use simplified ratios without seeming to comprehend the depth of understanding farm systems really require.

Each resource reacts differently to each new situation. Marginal analysis is required to identify what best to use and to what extent. Concise reports detailing these data are then required to implement and manage change successfully.

Benchmarks cannot fulfil this role as the basis for their calculation precludes the concept of diminishing returns and therefore any ability to economically distinguish between differing resource use, what resource is best suited to a particular system, whether another option will be more beneficial and most importantly, identify at what point adding more input becomes uneconomic.


Biological efficiency can be striven for but does not miraculously result in the best profits. In New Zealand, the very best high-input systems struggle to perform as profitably as efficient pasture systems because high input costs at the margin are making a negative contribution to profit; the same process as the nitrogen example for pasture.
LP modelling holds hope for change, innovation and emergent ideas. To date, none of this is encouraging farming leaders to question the relevance of benchmarking in an environment that is undergoing continual change. Disregarding the many ways that a resource can respond within a system is putting the farmers and the environment in danger of collapse.
The recent adoption of a new production system at LUDF based upon a full LP systems appraisal of the farm, including limiting the GHG emissions, may be a first step towards providing more credibility for systems modelling. As always, management must be a participant in the process and is the key to the final success of any system. Without management buy in, even the best resources can be wasted.
So models need to be realistic enough to not only provide options, but convince the management that they offer a better (more profitable /simpler/ less risky or all three) option. This requires management to be provided with the means to understand and assess the fundamental message that fusion of production efficiency and production economics through LP modelling can provide a viable and reliable farm management system.


  • LP provides the key to allow thinking to break out of the current time warp orientation focus on farm production.
  • The LP process must be designed to allow emergent systems to evolve rather than be constrained to current perceptions of what farm systems are.
  • There needs to be a change in the manner in which farm management advice is conveyed with more emphasis on efficient resource allocation rather than simple messages and “comparative ratios” which provide poor indicators for resource efficiency or R&D investment.
  • The current entrained thinking results in deterioration of both the economic and environmental outcomes of real farms.
  • A major change in the belief structure of all involved in the industry is required.
  • Unfortunately some beliefs now appear so embedded as to have become attitudes which will be far more difficult to successfully alter.


Table 1: Marginal Cost and Marginal Return Table:

The Relationship between Input (Nitrogen) and Production (pasture and beef)

input production

Fig.1: Diminishing Returns Curve. Pasture Dry Matter response to added
Nitrogen (from Table 1 data).

fig 1

Fig.2: Total Revenue vs. Cost of added Nitrogen (from Table 1 data).

fig 2

Fig.3: Marginal Cost and Marginal Return to additional nitrogen (from Table 1 data).

fig 3

Fig. 4 Marginal Cost of milksolids when supplements fed.

fig 4

Fig 5. Constraining N use.
Impact on economic surplus on 3 different dairy farms.
$/ha vs. level of N leach/ha.

fig 5

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