Optimisation Models

MIDAS

In Western Australia, a whole-farm linear programming model, MIDAS (Model of an Integrated Dryland Agricultural System), has been developed to investigate how limited resources should be allocated to alternative enterprises (Morrison, 1986). A detailed description of the MIDAS model is given by Kingwell (1986). The MIDAS model has a joint emphasis on biology and economics. There are several versions for representative farms in different regions of Western Australia, but all include components for crops (cereal and legume), pastures, sheep, feed (crop residues, grains, pastures), machinery and finance. They are detailed in their representation of soil types and potential enterprise rotations, with different production figures for each phase of each rotation on each soil type (Pannell, 1996). The objective function represents profit maximisation. Although the original MIDAS model was deterministic, it has been adapted to account for risk. An example of an application of the MIDAS model is given by Young, Thompson, Curnow, and Oldham (2011) who investigate the impact of different liveweight profiles of Merino ewes on whole-farm profit. In comparison to simulation models such as Farmax, MIDAS allows for the calculation of optimal systems. However, like Farmax, the MIDAS model is a supply-driven model with animal production an output calculated in respect to a specific environmental context.

IDEA

The integrated dairy enterprise analysis (IDEA) model is a deterministic, steady-state optimisation model of pastoral dairy farming systems (Doole, Romera, & Adler, 2013). Unlike many other optimisation models, the IDEA model uses non-linear rather than linear programming techniques. The optimisation algorithm used is the CONOPT solver in the General Algebraic Modelling System (GAMS). The objective function involves the maximisation of operating profit or minimisation of GHG emissions (Doole, 2014).

Also, another unique feature of the IDEA optimisation model is that pasture intake is limited by herbage allowance and pasture growth and digestibility depends on defoliation intensity and the duration between grazing events (Doole and Romera 2013). The IDEA model therefore provides a detailed description of many of the key biophysical processes observed within grazing systems that are absent from other whole-farm models that utilise optimisation (Ludemann, 2009; McCall et al., 1999; Stott, Milne, Goddard, & Waterhouse, 2005).

A detailed description of the equations used in the model are presented in Doole et al. (2012). A central concept of the IDEA model is the balancing of energy supply and demand. The supply of energy is obtained from grazed pasture and supplements, while energy demand depends on individual cow attributes and herd structure. There are nine sub modules. The sub modules that define feed supply are the land use module (which specifies the area grazed, conserved and

cropped), the pasture module (which specifies the herbage mass available and the ME concentration of grass), the pasture utilisation module (defined by stocking intensity), the supplement module (which defines the amount of supplements used and the ME concentration of supplements), the substitution rate module, and the pad module (which specifies the time on pasture). The cow module determines feed demand and specifies the ME demand per cow type, the cow intake capacity, milk production per cow type, and the number of cows per type. The two remaining modules are the integration module (which ensures that the ME intake is greater to or equal to the ME demand and ensures that the potential intake is greater or equal to the DM intake) and the profit module (that sets revenues, operating costs and fixed costs).

Supplementary feeds that are available within the IDEA model include grass silage, maize silage, palm kernel expeller (PKE), and turnip crops. A large number of cow types (17,640) are defined in IDEA to allow a rich description of herd structure (Doole et al., 2012). Cow attributes that impact on feed demand include growth, conception, pregnancy, body condition, liveweight, intake, lactation length, and milk production. Herd structure decision variables include cull policy, age distribution, calving date and intake control.

An example of an application of the IDEA model, is given by Romera and Doole (2015) who use the model to investigate the interrelationship between intake per cow and intake per ha. Also, Adler, Doole, Romera, and Beukes (2013) show how the IDEA model can be adapted to investigate the impact of grazing systems on GHG emissions.

Albeit dairy, the IDEA model is a comprehensive farm-level model and is very relevant for the investigation of biological efficiency within livestock systems and is able to capture key biophysical processes within the grazing system. However, the model is also a supply-driven model and focuses on modelling livestock productivity in relation to a specified feed supply situation. For example, the model incorporates animal-plant-supplement dynamics and moderates production outcomes as a result of the impact of grazing mass, pasture growth, digestibility, rotation length, intake regulation, pasture utilisation and stocking rates on feed supply. This model is therefore suited to the

investigation of biological efficiency in relation to a particular farm scenario but is less suited to the strategic investigation of generalised drivers of livestock productivity across a range of contexts.

GSL

The Grazing Systems Ltd (GSL) linear programming model reported by Anderson and Ridler (2010) and reviewed by Hurley, Trafford, Dooley, and Anderson (2013) is a bio-economic model of a dairy grazing system. The GSL model is constructed by Jade software (Hurley et al., 2013) and is

deterministic (the model assumes that coefficients, costs and constraints are known with certainty). It optimises animal production against energy supply from pasture, crops and supplements. The model also allows for nitrogen applications and grazing off farm. Pasture supply constraints are specified as pasture covers through time. The objective function maximises cash surplus. Applications of the GSL model include an investigation of the optimum herd replacement rate (Ridler, Anderson, & McCallum, 2014) and an investigation on the optimal dairy system in a sensitive catchment (Sulzberger, Phillips, Shadbolt, Ridler, & McCallum, 2015).

Hurley et al. (2013) conclude that the GSL model does provide another useful addition to the “tool box” of farm system decision support and simulation programmes. However, like other models already discussed, the GSL linear programming model is a supply-driven model with the model outputs (and the associated recommendations on optimal livestock systems) being specific to the feed supply assumptions used. For example, “the user defines inputs which then apply to a unique situation that the linear programming model is analysing” (Anderson & Ridler, 2010).

Other Optimisation Models

McCall et al. (1999) present a comprehensive linear programming model used to compare optimal dairy systems in New Zealand and the Northeast United States. This model was developed to

determine optimum pasture management strategy (rotation lengths), feed input, stocking rate, calving date, lactation length, and associated milk production in order to maximise gross margin. Similar to IDEA, the model comprises a feed supply and a feed requirement component, with feed management activities linking supply and consumption. Components of feed supply were grazed pasture, nitrogen fertilised pasture, pasture conserved as silage, concentrates (grain), and corn and alfalfa silages. Cow production variables included calving date, length of lactation, and stocking rate. In the model, the grazing strategy was optimised by varying the rotation length.

Ludemann (2009) developed a deterministic linear programming model of a sheep livestock system. This bio-economic model was modelled at the whole-farm level and was used to determine the effect of increasing ewe prolificacy (lambs born per ewe lambing) on total farm profitability. As this model was constructed for a specific purpose (to investigate ewe prolificacy), model adaptations are required if this model is to be used to investigate the impact of a wider range of production

parameters. The model is also supply-driven and therefore conclusions on optimal livestock systems are specific to the pastoral environment modelled.

An example of a linear programming model for deer is given by Woodford (1997). This model is also a bio-economic deterministic steady-state model. However, in contrast with Ludemann (2009), the model is demand-driven. In this approach, animal numbers and seasonal feed demands are determined endogenously within the model based on the relative proportions of each animal class and on the energy requirements per animal to reach specified performance levels (Woodford, 1997, p. 162). Therefore, while overall system feed demand is an input, seasonal feed demand is calculated as an output and is a function of performance parameters and animal numbers.

Rendel et al. (2013) describe a linear programming sheep, beef and deer farm model developed at AgResearch. This model is a deterministic steady-state farm resource allocation model and optimises the use of farm resources (land which is used for pasture and crop production; and sheep, cattle, including dairy grazers, and deer) whilst maximising profit (EBITDA). The model is a new generation whole-farm planning model in that, in departure from the use of total farm and average data for decision making, the model allows for the land area to be split into any number of land management units (LMUs) with optimal livestock systems computed in reference to these individual LMUs. The model therefore accounts for real-world complexity and takes into account areas of the farm that have differing characteristics (such as pasture growth rate, slope, and soil characteristics). The model incorporates a feed budget, stock reconciliation and financial budget. The user supplies pasture growth rates, minimum and maximum acceptable pasture covers for each LMU, animal performance, farm costs and market prices (Rendel et al., 2013). Additional constraints can be placed on individual LMUs. The optimisation routine uses this information to identify the mix of production enterprises

and management regimes that maximises profit while balancing feed budget and reconciling livestock numbers. Animal inputs for each species include liveweights, growth rates, reproductive rates (scanning and weaning percentages), mortality rates, parturition date, weaning date, cull dates and replacement rate. Sheep and cattle requirements are estimated using GrazPlan equations (Freer, Moore, & Donnelly, 2012) and the deer feed requirements using Dryden (2011) and NRC (2007). The model’s strength is that it can be used to explore the contribution of each LMU to business

performance. This approach has benefit in that model outputs will more accurately reflect a real farm which may have many different LMUs. However, with accuracy for a given situation comes a lack of generalisable information useful for strategic decision making across a range of contexts. An early linear programming model of a sheep production system is described by McGregor (1979) which was used to determine the optimal stock policy for fat lamb producing farms under dryland and irrigated conditions. The focus of the model was to determine the optimal age ewes should be culled. It was found that ewes should be culled at five and six years of age under irrigated and dry- land conditions respectively. This model was constructed for a specific purpose (to investigate ewe longevity), with the model framework not set up to allow for systems interactions that result from changes to other production parameters. The model is also characterised as a supply-driven model with feed supply constraints set in reference to dryland and irrigated Canterbury farms.

A further optimisation model is the model developed by Herd, Bootle, and Parfett (1993) which was used to examine the overall efficiency of converting feed energy to lean meat in traditional, twinning and sex-controlled beef production system.

Olney and Kirk (1989) present a small linear programming model of a Western Australian dairy farm. Berentsen and Giesen (1994) describe another linear programming model of a dairy farm with this model set up in reference to a dairy system in the Netherlands. In this model, pasture growth is defined is defined on an annual basis and its quality is fixed. However, Berentsen, Giesen, and Renkema (2000) extended the model to incorporate the implications of seasonal pasture growth and spatial diversity in management.

Other optimisation models of dairy systems include the linear programming model described by Stott (2008) and Stott et al. (2005) as well as the INTSCOPT and CamDairy models (Bicknell et al., 2015). The Integrated Suckler Cow Optimisation model (INTSCOPT) is a bio-economic whole-farm

optimisation model developed for pasture-based dairy farms in lowland Switzerland that includes livestock, fodder and nutrient. In contrast, the CamDairy model was first developed in Australia in 1984 and is primarily a dairy nutrition model and is particularly detailed at the individual cow level (Bicknell et al., 2015).