A review of the practice and achievements from 50 years of applying OR to agricultural systems in Britain

Eric Audsley Centre for Natural Resources Management Building 42a Cranfield University Bedford MK43 0AL United Kingdom

Tel: 01234 750111 Fax: 01234 752971Email: e.audsley@cranfield.ac.uk

Daniel L SandarsCentre for Natural Resources Management Building 42a Cranfield University Bedford MK43 0AL United Kingdom

Tel: 01234 750111 Fax: 01234 752971Email: Daniel.sandars@cranfield.ac.uk

Eric Audsley is a Principal Research Fellow at Cranfield University. Prior to that, since leaving Hull with an operational research degree, Eric worked for 34 years at Silsoe Research Institute, formerly the Agricultural Research Council’s National Institute of Agricultural Engineering, until its closure in 2005.  He has developed the application of mathematical and operational research techniques to the analysis of decisions concerning a very wide range of agricultural systems. Currently major areas are linear programming modeling of farms to predict future agricultural land use and model-based environmental life cycle assessment.

Daniel Sandars is a Research Fellow at Cranfield University. He received a BSc (Hons) in Agriculture at Seale-Hayne (1990) followed by a masters degree in Applied Environmental Science at Wye College (1994) and a further masters degree in Operation Research at the University of Hertfordshire (2004).  For the last 10 years he has been modelling the financial and environmental aspects of agricultural decisions. Prior to this he managed of a dairy unit in Kent.  He is a board member of the EURO-working group on Operational Research in Agriculture and Forestry Management (EWG-ORAFM),

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ABSTRACT: This paper will survey how things have changed over nearly 50 years of OR

applied to agriculture. The first “OR group” was set up at the National Institute of

Agricultural Engineering by Dan Boyce in 1969 and is now at Cranfield University. It will

examine how, and what, factors have influenced the type of work and the methods used.

What applications have stood the test of time and what are just distant memories in paper

publications? It will show that agricultural OR has moved on from its early beginnings in

agriculture in applying OR techniques with simple analyses, to using and creating complex

computer models. Whilst it might be described as alive, it clearly needs to identify itself

and its specific contribution to analysing decisions, to set it apart from the ‘anyone can

simulate and optimise using a computer’. The skill of holistic systems modelling of

combinations of processes at the decision maker level is as important as the ability to use

techniques.

KEYWORDS: Practice of OR; History of OR; Agriculture; Review

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1. INTRODUCTION

This paper will survey how things have changed over nearly 50 years of OR applied to

agriculture. The first “OR group” was set up in Silsoe (Bedfordshire, United Kingdom) at

the National Institute of Agricultural Engineering (NIAE) by Dan Boyce in 1969 and is

now at Cranfield University. It will examine how, and what, factors have influenced the

type of work and the methods used. What applications have stood the test of time and what

are just distant memories in paper publications?

Modelling provides a logical procedure for predicting process outcomes in

circumstances other than those that have been observed. Operational research or decision

modelling aims to determine the optimum decision that should be taken, define the trade-

offs between different outcomes that are inherent in a range of decisions, or predict the

likely decisions that will be taken by farmers in a range of practical circumstances. Such

models encapsulate knowledge of how a system is constructed of interacting processes and

how each process works. They often combine experimental observations, expert

knowledge, and logic.

In the physical world, models are frequently very precise and allow us, for example,

to send probes to the moons of Jupiter. In the biological world not only are processes less

well understood, often because they are made up of many sub-processes, but also the

systems themselves are designed to be random. Weed plants not only spread their seeds by

various mechanisms - using wind, animals and birds so that their destination could be a

long way from the plant - but seeds are also designed to lie dormant for times ranging from

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months to years so that the species can survive attacks by weather or man. Fungal spores

operate in a similar fashion. Millions are launched into the air, some of them land on a leaf,

some of them germinate, and some of them survive the defences of plant and man to

produce yet more spores. Domesticated seeds have been bred by man to germinate when

planted, but this reliability is confounded by the action of wildlife such as a browsing slug

finding the seed in the soil. Overlaying all is the weather and its variability and

unpredictability - even with the very latest and largest computer.

An operational research model analyses a situation in such as way as to be able to

predict what would happen if things were different. Thus, one can determine a better

decision by looking at all possible alternatives. The simplest procedure is to find the

optimum solution, and then at least you know you could not have found a better one.

However, finding the optimum has more uses. Firstly, it checks your model for errors –

many times a model has homed in on a silly solution due to a programming error, or vice-

versa, no matter how profitable a crop, it is never chosen because of an error. Secondly, it

checks your model for accuracy – if your solution is totally at odds with current practice,

either the decision maker is an idiot or your model is wrong. Thirdly, you can use the

optimum.

One might define the great OR optimising techniques as critical path analysis, linear

programming, dynamic programming, queuing theory, and inventory theory. From 1945

these made great impacts in industry, but what about agriculture? Then came the growth in

computers and mathematicians became lazy. Thus, we simulate and hope nobody spots

that the answer could have been calculated on an envelope – if not the stamp! Now of

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course we have to add the computer methods – expert systems, decision support systems

and near-optimisation methods. Has (Is?) OR in agriculture made an impact?

2. THE GREAT OR TECHNIQUES

2.1 Network analysis

Following from the work study origins of the OR Group at NIAE, the sequential analysis of

unit times of operations in a network to identify best combinations of procedures to harvest

vegetables in a field and pack house, was natural (Boyce et al, 1971, which followed Fluck

and Splinter, 1966). There now seems to be no work using network analysis as such. It has

been replaced by large computer packages for building simulations of the flow of

(industrial) items from one process to the next.

2.2 Queuing theory

The analysis of cyclic transport systems in agriculture was also an early application of OR.

Cyclic transport refers to tractors and trailers which are served (filled with harvested

material) in the field, travel to the farmstead, where they are served (unloaded) and travel

back to the field. The earliest work (not in the UK) was on sugar cane transport (eg Shulka

et al, 1971). The NIAE group studied silage harvesting (again with work-study of the times

involved) with the aim of identifying the optimum system and number of trailers (Audsley

and Boyce, 1973). Recent references appear rare. Cooper and Parsons, 1999 studied dairy

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cows waiting for automatic milking and Hansen et al, 1998 shows sugar cane transport is

still important – though scheduling sugar cane harvesting to optimise biomass is a more

prevalent problem.

2.3 Dynamic programming (DP)

With the uncertain nature of agriculture, there should certainly be plenty of scope for DP

models. Dynamic programming has many potential uses in agriculture since many

problems are multi-stage and probabilistic. The main constraint has been, and arguably still

is, the computer power to handle the dimensionality curse of the DP. However, few people

outside OR professionals understand DP. The main problems tackled have been weeds

(Fisher et al, 1981) and replacement (Low et al, 1967, Jalvingh et al, 1992, Kennedy, 1993,

Mourits et al, 1999, Yates et al, 1998). In agriculture, replacement tends to mean dairy

cows and sows. It always seems strange to me that irrigation in the UK is never tackled

using a DP. Is this an example of OR failing to make an impact because non-OR people

can always simulate and optimise using a computer that they understand? (Or use an expert

system, Amir, 1992)

An early application was the harvesting of cauliflowers. Cauliflowers in a field

(used to) mature over a number of days. They reach maturity quicker if it is hotter. The

objective of the farmer is to go over the field a number of times, harvest those where the

head is still compact, but as large as possible – maximum yield with minimum wastage and

labour cost. This naturally forms a dynamic programme. (Corrie and Boyce, 1972)

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Nowadays it has been found that cold treatment of the plants synchronises the maturity so

fields are harvested only once.

A weed DP (Sells, 1995) has recently been incorporated in a DSS for farmers

(Benjamin et al, 2008). One of the major criteria in weed control is future losses,

illustrated by the maxim: “one year’s seeding is seven years' weeding”. Control can be

achieved by changing crop, cultivation method, sowing date and by choosing one of a

number of herbicides and doses. However, the level of control achieved becomes more

variable as one tries to reduce costs. The reward function is the loss of yield and cost of

treatments, plus allowance for loss of value or cleaning costs from having weed seeds in the

grain.

For the DP model, the seed bank is divided into discrete states on a logarithmic

scale. It is usually necessary to define the seed bank by two state variables for the surface

and deep levels, ploughing moving the seeds between levels and deep seeds generally

suffering higher mortality. Needing two soil levels and hence n2 states is a classic example

of the dimensionality curse.

The WMSS system allows the user to specify the weeds of concern and their current

levels, examine the impact of alternative options manually, and then optimise. For a

complete system, it is necessary to parameterise the seed and herbicide models for every

arable weed likely to be of concern. This is rather a challenge for experimental data, but by

having a model, the expert can provide parameters by reference to known weeds, their

performance can be simulated and optimised, the results tested against reasonableness, and

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the parameters adjusted if necessary. This is another example of optimisation helping

modelling.

2.4 Linear programming (LP)

There are two very contrasting applications of linear programming to agriculture. Least

cost feed rations (eg Chappell, 1971) enjoys the most use – largely because it is in fact

industrial. Thus, feed mix companies (and large farms with factory size feed processing)

have a large number of possible ingredients they can buy or use and wish to know either at

what price it is worth purchasing, or how to blend the ingredients at minimum cost, to

achieve the required ration – energy, protein, fibre, and as many characteristics as one

desires to consider. However, it is largely not used on farms.

Every university agricultural economics department in the country has one or more

farm linear programmes, to select the cropping that maximises farm profit. They have a

very long history (Barnard, 1959, Stewart, 1961). Each crop requires an amount of labour

in each period of the year, which must be less than that available due to weather and soil

type. Economics versions typically considered cash flow and risk in either the crop gross

margins or the time available for work using stochastic or chance programming. A recent

survey of the economics versions suggested that many are in abeyance now (Garforth et al,

2006).

The NIAE version (Audsley et al, 1978) had significant differences due to its

emphasis on the details of timeliness of operations, machinery use, and crop rotations,

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founded on its origin, which was to compare machinery for direct drilling, minimum

cultivations, and traditional ploughing - faster autumn cultivations in theory mean that less

wheat is planted late. The LP model shows that in fact what happens (the optimum) is that

either more wheat is planted, or fewer men are employed, so that wheat is planted just as

late!

The models are strategic planning tools. Attempts were made to use these models

on farms, but until recently they have been very time consuming to use – a one day visit to

collect the data, followed (weeks) later after the computer has done the runs, by another

visit to report on the results – and thus difficult for a farmer or adviser to justify the expense

(Butterworth, 1985). However, LP models have found widespread use by researchers as a

policy tool in predicting what strategy farmers would adopt in different situations

(‘scenarios’ to use modern parlance). They have been applied to arable (Cevaal et al,

1979), livestock (Conway et al, 1987, Morrison et al, 1986), horticulture (Webster et al,

1969, Audsley, 1985, Gertych et al, 1978, Hamer, 1994). Uncertain prices are a feature of

horticulture LPs (Simpson et al, 1963, Darby-Dowman et al, 2000). Similar LP models can

be used to study whether novel machines are profitable on the farm (Audsley ,1981,

Chamen et al, 1993, Jannot et al, 1994, Kline et al, 1988)

A rather different profit-maximising LP - cutting for high temperature grass drying -

was developed at NIAE (Audsley, 1974a). The problem is that once cut the grass has to be

left for four to seven weeks to re-grow. It should be cut early for highest quality, but when

growth is rapid it is difficult to get round the whole area before the grass becomes over-

mature. Equally, after the initial burst of growth, there are periods when there is

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insufficient grass to make good use of the drier. The LP model determined the optimum

times and areas to cut, and showed that what was thought of as a management problem was

just an unavoidable fact of life, but one could help by cutting the grass very early, when it

seemed hardly worth cutting, in order to delay these fields for a few valuable weeks. The

problem disappeared with the driers when the price of oil increased!

Other such LP models have considered the use of manure (Dodd et al, 1975), space

in a plant nursery (Annevelink, 1992) and scheduling autumn operations.

Multiple criteria

Studying the references to farm LP models over time, one feature that is very clear is the

increasing reference to multi-criteria optimisation, which was not present in the early

studies. These fall into two types. One is purely economic, the other environmental.

Economic criteria (e.g. Patten et al, 1988, Rehman et al, 1993, Schilizzi et al, 1997)

reflect the realisation that simple profit maximisation did not fit the farmers’ choices in all

cases – particularly obvious where prices of crops are very volatile. This has led to

considerations of risk and many other factors (and to the modern trend of Positive

Mathematical Programming (PMP)). However, one could reasonably conclude that no one

has yet found the answer and profit maximisation is as good as any (akin to the football

pools problem - the most successful, but not useful, prediction is that the results of all

football matches are home wins). Most surveys have ended up concluding that for over

90% of farmers, over 90% of their objective is to maximise profit, or the equivalent. Note

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that economic theory itself suggests that if everyone followed the LP model saying that no-

one grows a crop, the price will rise due supply-demand, which would imply that the

farmer should grow the crop which the model said not to!

Environmental and ecological criteria have grown with the trend for concern for the

environment (de Koeijer et al, 1995). While Annetts et al (2002) showed that there are

better solutions for both the farmer and the environment by considering combined criteria

rather than by applying restrictions, by and large the environment does not represent a

monetary value to the farmer. However, the multiple criteria output from an LP model

given different strategies, do provide input to a number of studies concerned with choosing

the best strategy using these and other less numeric criteria, typically for example for the

EU Water Framework Directive (Giupponi, 1999). Current (social science) research is

exploring how much farmers themselves are prepared to forgo profit for a better

environment.

Land Use modelling

Perhaps tied to the growth in computer power and/or the growth of the Geographic

Information Systems (GIS), whole farm models have more recently been used to address

the potential effects of future scenarios such as climate change, by applying the models

over a region or the whole country (Harvey et al, 1990, Donaldson et al, 1995, Oglethorpe

et al, 1995, Veldkamp et al, 2004, Holman et al, 2005a&b). The country is divided into

polygons with common climate and soil type. Other models are used to estimate the effect

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on yields and soil workability. The LP model then predicts what cropping farmers would

adopt under a new climate (global warming), environmental restrictions (nutrient leaching,

pesticides, setaside), or cost and prices (subsidy system, tax, $100 oil, biofuels). In addition

to the effect on land use, the results from the models can be used to estimate changes in

environmental and ecological outcomes. Mostly the models use profit maximisation –

Audsley et al (2006) solve for ten farms with sampled price and yield to accommodate

uncertainty. It is difficult though to say how much impact all these have actually had with

policy makers.

The most recent REGIS decision support system takes land use LP one-step further.

It allows users to study interactively the regional impact of a wide range of economic and

climate variables (Rounsevell et al 2003). However, in order to achieve this, the complex

system models (including the LP models) are replaced by meta-models that, in addition to

being representations of the full models, must exhibit the same robustness-to-data

characteristics. This is a problem. The selected meta-model is just that - selected from an

infinite population of possible meta-models – some with better, some with worse

characteristics to the wide number of possible changes in the input. Thus, a linear

regression or a neural network fitted to the data might have unacceptable properties, so the

modeller will select another form. However, it is not possible to select an optimal meta-

model, only optimise the form of model selected by the modeller. Being able to

systematically examine alternative scenarios in seconds rather than hours, means more

questions can be asked of the models than were previously feasible, which provides a

severe test of the original model.

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2.5 Expert systems

Expert systems are another non-optimisation technique. (Castro-Tendero et al, 1995, Gold

et al, 1990, Plant et al, 1989). One could reasonably argue these are not OR, and there are

serious reservations about the long-term applicability of them in changing circumstances.

However, they would probably benefit from an OR approach to modelling the expert

knowledge – in which case it becomes a model not an expert system. For example, the ear-

disease control module developed for the Wheat Disease Manager (Audsley, 2006), rather

than specifying a fungicide to apply, was a model developed from the expert decisions,

which calculated the value of applying any fungicide and dose.

3. OTHER OPTIMISATION

Not all OR models fit into “techniques”. Many models calculate a cost as a function of

inputs and the objective is to find the optimum inputs. In general, agricultural models are

focused on cost because they are thought under farmer’s control. Incomes are subject to

variations in the uncertain productivity and the variability of the actual economy.

Probably the simplest early model is exemplified by the total cost of combine

harvesting (Boyce and Rutherford, 1972). There are two sorts of losses when combine

harvesting: threshing losses, which increase with speed of working and shedding losses,

which increase as the harvest, takes longer. For a given harvester there is thus an optimum

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speed. Both losses can be reduced by having a larger harvester, but this obviously costs

more. Thus, an optimum can be found – this, in the days before genetic algorithms and

their like, used Nelder & Mead’s still very efficient simplex optimisation (Nelder & Mead,

1965).

This was the first program for which the NIAE in 1973 produced a user version.

The farmer was visited by an Agricultural Development and Advisory Service (ADAS)

adviser who filled in an input form. On his return, this was typed into the computer, which

costed options for the farmer and determined the optimum system. Although now

moribund, the program still exists as a “micro-computer” version!

Computer simulation models using weather data as input are probably the norm.

This led to one of the earliest attempts at a probabilistic weather simulation (Dumont and

Boyce 1974). This is now the province of climate change modellers. In general weather

data was and still is collected daily as total rainfall, maxima or minima or the value at 0900

(GMT), reflecting the daily cycle. Thus, most simulation models also use a daily step,

though some such as Sharp in 1984 used relatively scarce hourly weather data in studying

decisions about how best to dry grain without spoilage. Although technology means you

can have current data every 10 minutes, for decisions it is normal to use 30 years of

historical data, which means daily data. However, due to concern about climate change

over the 30 years and the fact that climate models only provide monthly data, a daily

weather generator is often used. However, there can be flaws in this. For example,

consider the time when the soil becomes unworkable in the autumn. In reality, this occurs

when there is a day in the autumn with heavy rainfall. Climate change (e.g. a 10% increase

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in winter rainfall) is unlikely to change the timing of this day, so that the number of

workable days should be almost unchanged. However, due to the probabilistic simulations,

when this day occurs is very variable (earlier or later) – to the extent that whether the mean

number of days increases or decreases with the same model is random!

As computers have grown, so the growth of process simulations has provided fuel

for our OR models. It is now possible to calculate using these models the likely outcome

from thousands of alternative strategies and combine the results from one process with

those from another to examine decisions about the overall system. This is however, both a

benefit and a curse. Process modellers test their models against experimental data. They

rarely do thousands of systematic runs and analysing these can reveal glaring logical

inconsistencies. The OR modelling approach has led to uncovering errors, faults or

omissions in otherwise well-respected process models.

Initially weather-based simulations (e.g. Parke 1978) simply reported the results for

a number of alternatives. With the development of heuristic optimisation techniques based

on running a simulation thousands of times, it is now possible to find the optimum decision

(or close to it!). The references illustrate this trend. (Parsons, 1998, Kuo, et al 2000, Stacey

et al, 2004, Audsley et al, 2006)

Audsley et al, (2006) uses a genetic algorithm to optimise the choice of chemicals,

doses and timings of fungicide applied to wheat. At present, the UK farmer has a choice of

about 20 active ingredients, formulated in combinations into hundreds of products. These

in turn can be mixed and applied at different doses and timings. Wheat varieties have

different susceptibility to various diseases and weather is very variable. The OR team

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developed models of the relevant processes of leaf growth, disease development and

fungicide action (Audsley et al, 2006; Milne et al, 2007; Parsons and Te Beest, 2004) that

bring together agronomic expertise, biological reasoning and experimental information on

disease growth and fungicide performance into a decision support tool. This process

provides a considerable challenge to the expert knowledge as the modelling process rapidly

highlights inconsistencies and incompleteness, and is thus a major benefit to decision-

making.

The potential future development of the crop, disease, and yield are predicted using

future weather scenarios appropriate to that location. One advantage of genetic algorithms

is that it meets a user demand that the decision model should give a ranked list of near-

optimal spray programmes, not just the best - a classic complaint about LP. The system has

been used by farmers for several years and its recommendations have proved generally

effective (Parsons and Te Beest, 2004). In 2003, it achieved the twin ‘sustainability

successes’ of suggesting lower doses than the experts and achieving the same control

giving higher profits. However, in 2004, it was suggesting high doses “in a tricky Septoria

season” - its target is the most appropriate dose – while farmers were applying lower doses.

Validating the correctness of the decisions is an interesting challenge since the post-harvest

optimum is not the same as the optimum decision at spray time when future weather is

unknown.

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4. NON-OPTIMISATION

Not all OR is however, about determining an optimum. In fact, an analysis of my citations

reveals that simply a formula to calculate an annual equivalent cost of machinery (in the

days of high inflation) (Audsley 1978) is the most cited paper. Applying the OR method

can equally be holistic modelling of complex systems in such a way as to determine values

to allow alternative decisions to be compared. Many of the non-optimisation models

revolve around the impact of weather, most notably on forage production and harvesting.

Most recently, Data Envelopment Analysis (DEA) begins to feature (Fraser, et al 1999) and

given the huge number of farms is perhaps a future fruitful area for OR specialists, whether

from the profit or environmental perspective.

Reflecting concerns for the environment, OR modelling has recently turned to

environmental Life Cycle Assessment (LCA) studies of alternative agricultural commodity

production systems (Audsley et al, 1987, Williams et al, 2006). The objective is to analyse

the system operation to provide accurate measures of performance and calculate

systematically the effect of alternatives, for example using lower inputs of fertiliser, which

comprise over 50% of the input energy.

An important aspect of an LCA is to define the functional unit – what is being

produced; in this case wheat suitable for bread making with a minimum protein content of

12% dry matter weight. It is important to be clear that the functional unit is tonne wheat

not ha land. Lower fertiliser nitrogen (N) inputs are a common suggestion. It reduces both

yield and grain protein content. One option is to choose a very high protein variety but this

also further reduces yield potential.

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Reduced inputs have an effect on the soil. Experimental trials and their associated

simulation models are frequently only one year and reduced inputs of N are not fully

reflected in lower yield or soil N in the soil for the following crop as the soil provides a

buffer. The best method to estimate losses is to derive them from an appropriate process

simulation model such as SUNDIAL (Bradbury et al, 1993), rather than using observations.

Such simulation models are run until a steady-state is obtained, which properly predicts the

(reduced) yield and soil N content.

The outcome is an extensive picture of the ways in which production of the

commodity impacts on the global environment, allowing systems to be compared and

policy perspectives informed. A short form summary is given in Table 1, which shows the

saving of energy per tonne produces is small.

{Table 1}

5. DISCUSSION AND CONCLUSIONS

Operational Research has moved on from its early beginnings in agriculture in applying OR

techniques with simple analyses, to using and creating complex systematic and holistic

computer-based models. More recently, with perhaps the exception of LP, combining

process models has become more relevant than techniques. The skill (art?) of holistic

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systems modelling of combinations of processes at the decision maker level is as important

as the ability to use techniques.

It is somewhat of a challenge to decide how much of decision modelling is OR and

how much is just a process model being optimised, or economics. It would reasonable to

say very little. Certainly, few of the UK authors are qualified OR scientists. One possible

definition is the bringing together of a number of processes to study or determine an

optimum decision. This perhaps suggests that the important skill of the OR person is not

the ability to apply an optimization technique but to systematically and holistically model

complex systems at the decision making level. Optimisation may or may not be necessary.

Alternative explanations are that the limited application of OR techniques to

agricultural problems is because in agriculture there are few OR-qualified scientists, or that

due to rise in computer power, the ability to include a huge number of factors in a model

has destroyed the ability of the classic techniques to solve them. Sandars and Plà (2009)

discuss other issues for the practice of OR in agriculture and related natural resources

industries.

Whilst it might be described as alive, OR clearly needs to identify itself and its

specific contribution to analysing decisions, to set it apart from the ‘anyone can simulate

and optimise using a computer’.

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ACKNOWLEDGEMENTS

The authors would like to thank Dr Lluis Plà (University of LLeida) for his thoughtful

comments.

GENERAL REFERENCES

See also structured review references

Bradbury N J, Whitmore A P, Hart P B S, Jenkinson D S (1993). Modelling the Fate of

Nitrogen in Crop, Soil in the Years Following Application of N-15-Labeled Fertiliser to

Winter-Wheat .J Agr Sci, Cambs 121:363-279.

Garforth C, Rehman T U, McKemey K, Yates C M, Bahadur Rana R, Green K, Wilkinson

M, Beechner S, Hollis K, McIntosh L, (2006). Research to understand, model the

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Department For Environment Food, Rural Affairs.

Nelder J A, Mead R (1965). A simplex method for function minimization. Comput J 7:

308–313.

Sandars D L, Plà L M (2009). A western European perspective on Operational Research

prospects for the biotic natural resource industries. J Opl Res Soc Submitted

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STRUCTURED REVIEW REFERENCES

Network analysis

Boyce D S, Parke D, Corrie, W J (1971). The identification of optimum production systems

by network analysis, dynamic programming. J Agr Engng Res 16(2): 141-145.

Fluck R C, Splinter W E (1966). Optimisation of field harvesting, handling systems by unit-

flow, shortest path techniques. American Society of Agricultural Engineers: Chicago.

Queuing theory

Audsley E, Boyce D S (1973). Exact solutions for cyclic transport systems. J Ag Engng Res

18(3): 217-230.

Cooper K, Parsons D J (1999). An economic analysis of automatic milking using a

simulation model. J Agr Engng Res 73: 311-321.

Hansen A C, Barnes A J, Lyne P W L (1998). An integrated approach to simulating

sugarcane harvest-to-mill delivery systems, ASAE Annual International Meeting, Orlando,

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Shukla L N, Chisholm T S, Phillips A L (1971). Computer program for analysing

harvesting, loading, transportation of sugar cane. ASAE Pap.71-a604 American Society of

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Dynamic programming

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Linear programming

Livestock feed

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On-farm application

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Crop planning

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Livestock planning

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Horticulture planning

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Machinery selection

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Holman I P, Rounsevell M D A, Shackley S, Harrison P A, Nicholls R J, Berry P M,

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Multi-criteria, uncertainty

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Patten L H, Hardaker J B,, Pannell D J (1988). Utility-efficient programming for whole-

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Expert systems

Amir I, Y. Kranz (1992) Expert system for irrigation planning, Water & Irrigation Review

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Castro-Tendero A J (1995). SEMAGI - an expert system for weed control decision making

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Other optimisation

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28

Audsley E, Milne A E, Paveley N (2006). A foliar disease model for use in wheat disease

management decision support systems. Ann Appl Biol 147: 161-172.

Boyce D S, Rutherford I (1972). A deterministic combine harvester cost model. J Agr

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Dumont A G, Boyce D S (1974). Probabilistic simulation of weather variables. J Agr

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Jalvingh A W, Dijkhuizen A A, van Arendonk J A M (1992) Dynamic probabilistic

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Kuo S F, Merkley G P,, Liu C W (2000). Decision support for irrigation project planning

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Parsons D J (1998). Optimising silage harvesting plans in a grass, grazing simulation using

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Parsons D J, Te Beest D (2004). Optimising fungicide applications on winter wheat using

genetic algorithms. Biosyst Eng 88(4): 401-410.

Stacey K F, Parsons D J, Frost A R, Fisher C, Filmer D, Fothergill D (2004). An automatic

growth, nutrition control system for broiler production. Biosyst Eng 89(3): 363-371.

29

Non-optimisation

Audsley E, Wheeler J A (1978). The annual cost of machinery using actual cash flows. J

Agr Engng Res 23: 189-201.

Audsley E, Alber S, Clift R, Cowell S, Crettaz P, Gaillard G, Hausheer J, Jolliett O, Kleijn

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Fraser I, Cordina D (1999). An application of DEA to irrigated dairy farms in Northern

Victoria, Australia, Agr Syst 59: 267-282.

Milne A E, Paveley N, Audsley E, Parsons D J (2007). A model of the effect of fungicides

on disease-induced yield loss, for use in wheat disease management decision support

systems. Ann of Appl Biol 151: 113-125.

Parke D, Dumont A G, Boyce D S (1978). A mathematical model to study forage

conservation methods. Journal of the British Grassland Society 33: 261-272.

Williams A G, Audsley E, Sandars, D L (2006). Final report to Defra on project IS0205:

Determining the environmental burdens, resource use in the production of agricultural,

horticultural commodities. Department for Environment, Food, Rural Affairs (Defra):

London.

30

Impacts (per tonne bread wheat produced)

Conventional 60% fertiliser rate

Organic

Energy used, MJ 2513 2417 2168Global Warming Potential, kg 100 year CO2 equiv

545 454 437

Eutrophication Potential, kg PO43- equiv 2.9 2.2 9.1

Acidification Potential, kg SO2 equiv 2.5 2.1 1.6Pesticides used, dose ha 0.8 1.0 0Abiotic depletion, kg Antimony equiv 1.3 1.3 1.3Land Use, ha Grade 3a 0.14 0.20 0.47

Table 1: A typical outcome of an LCA analysis of a single commodity: bread wheat production

31